We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N=150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical scaling holds for different values of dephasing and monitoring efficiency. We moreover calculate the extra information obtainable via a final strong measurement on the conditional states generated during the dynamics and show that the corresponding ultimate limit is nearly achieved via a projective measurement of the spin-squeezed collective spin operator. We also briefly discuss the difference between our protocol and standard estimation schemes, where the state preparation time is neglected.
Continuously monitored atomic spin-ensembles allow in principle for real-time sensing of external magnetic fields beyond classical limits. Within the linear-Gaussian regime, thanks to the phenomenon of measurement-induced spin-squeezing, they attain a quantum-enhanced scaling of sensitivity both as a function of time, t, and the number of atoms involved, N. In our work, we rigorously study how such conclusions change when inevitable imperfections are taken into account: in the form of collective noise, as well as stochastic fluctuations of the field in time. We prove that even an infinitesimal amount of noise disallows the error to be arbitrarily diminished by simply increasing N, and forces it to eventually follow a classical-like behaviour in t. However, we also demonstrate that, “thanks” to the presence of noise, in some regimes the model based on a homodyne-like continuous measurement actually achieves the ultimate sensitivity allowed by the decoherence, yielding then the optimal quantum-enhancement. We are able to do so by constructing a noise-induced lower bound on the error that stems from a general method of classically simulating a noisy quantum evolution, during which the stochastic parameter to be estimated—here, the magnetic field—is encoded. The method naturally extends to schemes beyond the linear-Gaussian regime, in particular, also to ones involving feedback or active control.
Quantum entanglement plays important roles in many areas of quantum information processing (QIP). Nevertheless, quantum entanglement is not the only form of quantum correlation that is useful for QIP. In fact, some separable states may also speed up certain quantum tasks, relative to their classical counterparts. Example of such quantum correlation is a quantity, called quantum discord (QD), which can effectively capture all quantum correlations present in various kinds of quantum systems. The quantum discord involves a minimization procedure that is difficult to solve in general. To overcome the difficulty encountered with the computability of quantum discord based on von Neumann entropy, we propose a reliable analytical method to evaluate the quantum discord based on linear entropy for an arbitrary qudit- qubit quantum state. The quantum discord based on linear entropy is employed to derive the quantum correlations for a qutrit-qubit system undergoing global (bilocal + collective) classical dephasing environment. Our studies focus mainly on a particular initial qutrit-qubit state in thermal equilibrium at a temperature T. The obtained value of quantum discord (QD) is then compared with the measurement-induced disturbance (MID) and logarithmic negativity (LN). The results for different values of temperature T with in the antiferromagnetic case. The analysis shows that both QD and MID are more robust than entanglement (LN) against the decoherence effect. Besides, the system exhibits interesting behaviors. As for instance, freezing dynamics and entanglement sudden death (ESD). The method developed in this paper to quantify quantum correlations is reliable because it allows us to consider analytically the arbitrary qutrit-qubit quantum states in the classical dephasing environment.
Random access code (RAC), a primitive for many information processing protocols, enables one party to encode a n-bit string into one bit of message such that another party can retrieve partial information of that string. We introduce the multiparty version of RAC in which the n-bit string is distributed among many parties. For this task, we consider two distinct quantum communication scenarios: one allows shared quantum entanglement among the parties with classical communication, and the other allows communication through a quantum channel. We present several multiparty quantum RAC protocols that outclass its classical counterpart in both the aforementioned scenarios.
We study the dynamics of a quantum walker simultaneously subjected to time- independent and -dependent phases. Such dynamics emulates a charged quantum particle in a lattice subjected to a superposition of static and harmonic electric fields. With proper settings, we investigate the possibility to induce Bloch-like superoscillations, resulting from a close tuning of the frequency of the harmonic phase ω and that associated with the regular Bloch-like oscillations ωB . By exploring the frequency spectra of the wave-packet centroid, we are able to distinguish the regimes on which regular and super-Bloch oscillations are predominant. Furthermore, we show that under exact resonant conditions ω = ωB unidirectional motion is established with the wave-packet average velocity being a function of the quantum coin operator parameter, the relative strengths of the static and harmonic terms, as well as the own phase of the harmonic field. We show that the average drift velocity can be well described within a continuous-time analogous model.
In this work, we explore the space of quantum states composed of N particles. To investigate entanglement resistance to particle loss, we introduce the notion of m-resistant states. A quantum state is m-resistant if it remains entangled after losing an arbitrary subset of m particles, but becomes separable after losing any number of particles larger than m. Celebrated | GHZ and |W states are examples of 0- and 1-resistant states respectively. The notion of m- resistant states shares the spirit of AME states and k-uniform states, where we look at the behavior of the state after certain parts are ignored. Nevertheless, it does not impose the maximal entanglement, which consequently increases the complexity of the problem. This approach share attributes with persistence and robustness of entanglement. It measures how the entanglement of a given state resists ignoring a certain number of non–accessible subsystems, which corresponds to taking the partial trace over them. This process is not as invasive as performing local measurements on selected subsystems or mixing the analyzed state with locally prepared separable states. We establish an analogy to the problem of designing a topological link consisting of N rings such that, after cutting any (m + 1) of them, the remaining rings become disconnected. We present a constructive solution to this problem, which allows us to exhibit several N-particle states with the desired property of entanglement resistance to particle loss. The existence of m- resistant N-parties states is the main problem we addressed. The method based on stellar representation yields m-resistant pure qubit states for values m = 0, 1,..., N−2. This method failed, however, already in search for 1-resistant 5-qubit state. Except for some particular examples, none of the other m-resistant states were yet found. Therefore, we extend our investigation both to mixed qubit states and to pure qudit states with d ≥ 3 level systems. An explicit construction involving the partial trace over a larger system provides examples of m-resistant mixed qubit states. Here, the aforementioned analogy between entangled states and topological links is used. Quantum resistance may be combined into applications that require the simultaneous action of any given number of parties. For instance, consider a digital locker belonging to a certain network of N parties, where each person is in possession of a qubit, being a part of a genuinely entangled N qubit state. One may devise this locker in such a way, that it can be opened through a protocol involving the cooperation of at least m people. In this case, an m-resistant state of N qubits might be used in the protocol. Indeed, any system of m − 1 parties will always be in a separable state, which disallows forming correlations between them.
Contextuality has been reported as a resource for quantum computation, analogous to non-locality as a resource for quantum communication and cryptography. We show that the presence of “event-based” contextuality places new lower bounds on the memory cost for simulating restricted classes of quantum computation. We applied this result to the simulation of the restricted model of quantum computation based on the braiding of Majorana fermions.
Even though very powerful from a theoretical point of view, using the Positive Partial Transpose (PPT) criterion to detect entangled states in an experimental setting is very challenging. Nevertheless, it was recently shown that entanglement can in some cases already be detected from the first three moments of the partial transpose, which can for instance be measured using classical shadows. In this poster, we generalize this approach by showing that each higher order moment can be used to define a new entanglement condition, and that this list of conditions eventually becomes equivalent to the PPT criterion. Inspired by the concept of symmetry- resolution, which uses the symmetry present in certain states as a lens to gain a more detailed characterization of their quantum features, we also propose a Symmetry-Resolved (SR) version of our entanglement detection tools. Interestingly, we show that the SR tools can also be used to detect the entanglement of states without any symmetry.
Quantum information protocols can be realized using the `prepare and measure setups which do not require sharing quantum correlated particles. In this work, we study the equivalence between the quantumness in a prepare and measure scenario involving independent devices, which implements quantum random number generation, and the quantumness in the corresponding scenario which realizes the same task with spatially separated correlated particles. In particular, we demonstrate that quantumness of sequential correlations observed in the prepare and measure scenario gets manifested as superunsteerability, which is a particular kind of spatial quantum correlation in the presence of limited shared randomness. In this scenario consisting of spatially separated quantum correlated particles as resource for implementing the quantum random number generation protocol, we define an experimentally measurable quantity which provides a bound on the amount of genuine randomness generation. Next, we study the equivalence between the quantumness of the prepare and measure scenario in the presence of shared randomness, which has been used for implementing quantum random-access codes, and the quantumness in the corresponding scenario which replaces quantum communication by spatially separated quantum correlated particles. In this case, we demonstrate that certain sequential correlations in the prepare and measure scenario in the presence of shared randomness, which have quantumness but do not provide advantage for random-access codes, can be used to provide advantage when they are realized as spatial correlations in the presence of limited shared randomness. We point out that these spatial correlations are superlocal correlations, which are another kind of spatial quantum correlations in the presence of limited shared randomness, and identify inequalities detecting superlocality.
One of the possible applications of quantum computers in the near future are simulations of physics. An example are quantum gravitational systems associated with the Planck scale physics. Such systems are expected to be of the many-body type, which justifies utility of quantum computations in the analysis of their complex quantum behavior. In this talk, loop quantum gravity - a leading candidate for the theory of quantum gravitational interactions - is considered. In this case, quantum geometry of space is represented by the so-called spin networks, i.e. graphs with nodes associated with the "atoms of space". A construction of quantum circuits which generate states of spin networks will be presented. Furthermore, a quantum algorithm which enables determination of amplitudes of transitions between different states of spin network is proposed. Results of implementation of the approach on 5-qubit (Yorktown) and 15-qubit (Melbourne) IBM superconducting quantum computers will be presented. Obtained results provide building blocks for quantum simulations of complex spin networks, which can give insight into the Planck scale physics in the near future.
We are experimentally investigating possible departures from the standard quantum mechanics predictions at the Gran Sasso underground laboratory in Italy. In particular, we test, with unprecedented sensitivity, collapse models which were proposed to solve the “measurement problem” in quantum physics. We shall present the most recent results we obtained in testing various types of collapse models by searching the spontaneous emission of radiation, predicted by these models. We shall discuss gravity-related wave function collapse and our results in testing them, as well as more generic results on testing CSL (Continuous Spontaneous Localization) collapse models.
We proposed a new generalized version of the quantum extreme value searching algorithm (QEVSA) [1] named the constrained quantum optimization algorithm (CQOA). We investigated the computational complexity of the CQOA and we showed how it exceeds the QEVSA. The QEVSA finds the extreme (minimum or maximum) value in a database or unconstraint goal function (UGF). it combines the well-known logarithmic binary search algorithm (BSA) with the quantum existence testing (QET) [1,2] method which is a special case of quantum counting. The QET(ref) _ref refers to the updated value which divides the database into two vertical parts _ checks whether the value of the phase equals zero or not, in other words, it tests whether the occurrences of a certain item in the database equals zero or not (i.e., it checks the existence of a given item in the database). If one is interested in finding the extreme value of a constraint goal function (CGF), an evolution of the QET version is needed, we called it constrained quantum relation testing (CQRT). It has three variables, the reference value ref , the index R denotes the type of the used relation (minimization or maximization), and the constraint C. The CQRT answers whether there exist at least one or more database entries with respect to the applied relation R of the reference value ref and the constraint C in a certain region of the database. It is worth mentioning that the power of the QET is derived from the quantum phase estimation (QPE)[2], thus involving the relation R and the constraint C in the QET will not influence the computation of the number of qubits necessary for classical and quantum certainty (it does not affect the estimation of the phase for the CQRT function). Therefore, the mathematical derivation for estimating the computational complexity of the CQRT is similar to one belonging to the QET, it is logarithmic in terms of the size of the search space and the maximum number of steps needed to run the binary search embedded in CQOA. The CQOA combines the BSA and the CQRT. It finds the extreme value of a CGF, while the QEVSA can only perform the search optimization for a UGF. In the future work, we will extend the results in [3], and we will exploit the CQOA for minimizing the constraint energy consumption of the resource distribution management system. We will also prove that the task assignment optimization problem can only be solved by a quantum strategy. [1] S. Imre, ”Quantum Existence Testing and Its Application for Finding Extreme Values in Unsorted Databases” IEEE Transactions on Computers, Vol: 56, Issue: 5, May 2007. [2] Imre, S.; Balázs, F.: Quantum computing and communications: An engineering approach (Wiley, Chichester, UK) 2005 ISBN 0-470-86902-X, DOI: 10.1002/9780470869048. [3] S. El Gaily, S. Imre, "Quantum Optimization of Resource Distribution Management for Multi-Task Multi_Subtasks", Info-communication Journal, Vol. XI, Number 4.
Bell nonlocality is one of the most striking features in quantum mechanics and basically means that the correlations revealed by quantum mechanics cannot be compatible with hidden variable models. Such models can be translated in terms of the known Bell inequalities. In this work we constructed Bell inequalities which are maximally violated by multipartite graph states in every prime dimension, such states form a special class of multipartite entangled states. The Bell operator is constructed with the aid of the stabilizer formalism of the graph states in a such way that we could find a convenient sum-of-squares (SOS) for the Bell inequality associated. For dimension 3, the maximal quantum violation of the proposed Bell inequalities occurs if and only if the state is the graph state, i.e., the self-testing of the graph states.
It is usually believed that coarse-graining of nonlocal quantum correlations leads to classical (local) correlations in the macroscopic limit. Such a principle is known as macroscopic locality [1]. The level of coarse-graining is captured by a simple parameter $\alpha\in[0,1]$, with $N^\alpha$ being the order of the resolution when a collective measurement is performed on a system of size $N$ (number of particles). It is well known that no coarse-graining ($\alpha=0$) exhibits non-local correlations [2], while there are strong indications that fully coarse-grained ($\ alpha=1$) quantum correlations become local in the macroscopic limit [3]. It is natural to ask what is the critical value $\alpha_c$ of the quantum-to-classical transition, such that for $\alpha<\ alpha_c$ nonlocal correlations survive and for $\alpha > \alpha_c$ locality is restored. Currently, it is believed that $\alpha_c \leq 1/2$, as it follows from the result of Navascu\'{e}s and Wunderlich (NW) [1]. This result coincides with the heuristic statement of $\sqrt{N}$ being the error scaling associated with a typical quantum experiment. However, the work of NW is restricted to the study of correlations arising from \emph{independent and identically distributed} (IID) quantum states. In this work [4], we show that relaxing this constraint and employing non-IID states leads to fully quantum correlations. This implies that $\alpha_c \geq 1/2$, and the question of the quantum-to- classical transition still remains open. In fact, we derive a much stronger result by showing that the \emph{quantum superposition principle} remains fully valid in the macroscopic limit for quantum measurements with a resolution of the order of $\sqrt{N}$.\\ [1] M. Navascu\'es and H. Wunderlich, “A glance beyond the quantum model”, \emph{Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, vol. 466, no. 2115, pp. 881–890, 2010.\\ [2] E. Oudot, J.-D. Bancal, P. Sekatski, and N. Sangouard, “Bipartite nonlocality with a many-body system,” \ emph{New Journal of Physics}, vol. 21, no. 10,p. 103043, 2019.\\ [3] R. S. Barbosa, “On monogamy of non-locality and macroscopic averages: examples and preliminary results”, \emph{arXiv preprint arXiv:1412.8541}, 2014.\\ [4] M. Gallego and B. Daki\'c, In preparation, 2021.
The optomechanical interactions take place by the radiation pressure force of the cavity field on the mechanical system [1,2]. Our model considers a trapped ion in the optomechanical system to study the interaction between the ion and mechanical mode [3]. The coupling between the ion and mechanical mode is mediated by cavity mode. We adiabatically eliminate the electronic states of ion in large cavity detuning limit [4]. We show that the state can be transferred between an ion's vibrational mode and mechanical mode mediated by cavity mode. We also study the steady-state entanglement between the mechanical mode and motional mode of ion [5]. We further investigate the effect of temperature on entanglement. We also analyse the effect of sympathetic cooling of the mechanical system with the help of ion vibrational mode. The systems can be used to facilitate quantum information transfer between mechanical systems and the ion. [1] M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod.Phys. 86, 1391 (2014). [2] F. Marquardt, J. P. Chen, A. A. Clerk, and S.M. Girvin, Phys. Rev. Lett. 99, 093902 (2007). [3] Devender Garg and Asoka Biswas, Phys. Rev. A 100, 053822 (2019) [4] C. Maschler and H. Ritsch, Opt. Commun. 243, 145 (2004). [5] R. Simon, Phys. Rev.Lett 84, 2726(1999).
The Heisenberg limit is the fundamental bound for the precision of estimation in terms of the amount of resources N used in an experiment (where resources may be understood, depending on the context, as number of photons, number of quantum gates, total energy, total time of interrogation etc.). It provides better scaling with N comparing to situations where resources are used separately. However, as achieving this limit requires the use of all available resources in single realization of the experiment, a tool which is typically used to derived bounds for the precision of estimation – quantum Fisher information – is not operationally meaningful here. In our work, by applying the methods based on Bayesian estimation theorem, we show that conventional Heisenberg limit should be rescaled by constant factor π.
We study how an arbitrary Gaussian state of two localized wave packets, prepa red in an inertial frame of reference, is described by a pair of uniformly accelerated observers that can move either collinearly or noncollinearly [1,2]. Even if the initial, inertial resource is the vacuum state, the spatial entanglement becomes present in the accelerated frame of reference. Moreover, such a framework allows us to study how relativistic acceleration of the observers can affect the performance of the quantum teleportation and dense coding for continuous variable states [3]. [1] Ahmadi et al., Phys. Rev. D 93, 124031 (2016). [2] Grochowski et al., Phys. Rev. D 100, 025007 (2019). [3] Grochowski et al., Phys. Rev. D 95, 105005 (2017).
Quantum networks are currently at the heart of much research due to their many applications, e.g., in long-distance quantum communication. It has been shown that the forms of entanglement arising in quantum networks are more subtle than the multipartite entanglement usually considered. We aim at characterizing the set of states that can be generated in network structures, via necessary and/or sufficient criteria. In order to do that, we analyze the structure of the covariance matrices (CMs) of those states. CMs are powerful tools that have been previously used to characterize quantum entanglement. We focus here on triangle networks, i.e. networks consisting of three nodes connected by three edges, along which bipartite entangled states distributed. For that we give a detailed characterization of the potential CMs, which has allowed us to derive strong criteria that exclude several states from the triangle scenario.
We study the entanglement of formation and the quantum discord contained in even and odd multipartite j-spin coherent states. The key element of this investigation is the fact that a single j-spin coherent state is viewed as comprising 2j qubit states. We compute the quantum correlations present in the n even and odd j-spin coherent states by considering all possible bipartite splits of the multipartite system. We discuss the different bi-partition schemes of quantum systems and we examine in detail the conservation rules governing the distribution of quantum correlations between the dierent qubits of the multipartite system. Finally, we derive the explicit expressions of quantum correlations present in even and odd spin coherent states decomposed in four spin sub-systems. We also analyze the properties of monogamy and we show in particular that the entanglement of the formation and the quantum discord obey the relation of monogamy only for even multipartite j-spin coherent states.
I numerically simulate and compare the entanglement of two quanta using the conventional formulation of quantum mechanics and a time-symmetric formulation that has no collapse postulate. The experimental predictions of the two formulations are identical, but the entanglement predictions are significantly different. The time-symmetric formulation reveals an experimentally testable discrepancy in the original quantum analysis of the Hanbury Brown–Twiss experiment, suggests solutions to some parts of the nonlocality and measurement problems, fixes known time asymmetries in the conventional formulation, and answers Bell’s question “How do you convert an ’and’ into an ’or’?”
I will present two new approaches to resource theories: one arising as category- theoretic generalisation of the approach by del Rio--Kraemer--Renner in terms of adjoint functors, another arising from consideration of constrained maximisation of Brègman class of relative entropies as the nonlinear morphisms between quantum and postquantum state spaces, replacing the role of CPTP maps. The former approach allows to analyse the separation of the knowledge and actions available to the agent in terms of his comonads and monads, respectively. The latter provides a functional analytic implementation of Mielnik's notion of nonlinear transmitters, by means of (post)quantum Bregman nonexpansive operations, with explicit examples specified in terms of Lp and Orlicz spaces over W*- and JBW-algebras. I will show also in what sense the latter approach provides a nontrival example of the former.
We study the problem of Bayesian phase estimation in optical interferometry in order to rigorously demonstrate that, given some partial knowledge about the true value of phase, simple quantum states, e.g. twin-Fock states, of finite photon number can significantly outperform all the relevant classical strategies. In particular, our observation questions the need of considering complex superpositions of two-mode Fock states that, despite being provably optimal, are virtually impossible to prepare in real life. We support our claims by computing the minimal average error attained when most general quantum measurements are allowed, but also by considering adaptive measurements that may be realised with help of photon counting. We conclude that, as long as the prior knowledge about the estimated phase is good enough, significant quantum-enhancement of precision can always be achieved.
Everett’s relative-state construction in quantum theory has never been satisfactorily expressed in the Heisenberg picture. What one might have expected to be a straightforward process was impeded by conceptual and technical problems that we solve here. The result is a construction which, unlike Everett’s one in the Schrödinger picture, makes manifest the locality of Everettian multiplicity, and its inherently approximative nature, and its origin in certain kinds of entanglement and locally inaccessible information. (By Everettian, we are referring not only to Everett’s own work, but also to versions of quantum theory that elaborate and refine his.) Our construction also allows us to give a more precise definition of an Everett ‘universe’, under which it is fully quantum, not quasi-classical.
Quantum catalysis is a fascinating concept which demonstrates that certain transformations can only become possible when given access to a specific resource that has to be returned unaffected. It was first discovered in the context of entanglement theory and since then applied in a number of resource-theoretic frameworks, including quantum thermodynamics. Although in that case the necessary (and sometimes also sufficient) conditions on the existence of a catalyst are known, almost nothing is known about the precise form of the catalyst state required by the transformation. In particular, it is not clear whether it has to have some special properties or be finely tuned to the desired transformation. In this work we describe a surprising property of multi-copy states: we show that in resource theories governed by majorization all resourceful states are catalysts for all allowed transformations. In quantum thermodynamics this means that the so-called "second laws of thermodynamics" do not require a fine-tuned catalyst but rather any state, given sufficiently many copies, can serve as a useful catalyst.
We calculate numerically the capacity of a lossy photon channel assuming photon number resolving detection at the output. We consider scenarios of input Fock and coherent states ensembles and show that the latter always exhibits worse performance than the former. We obtain capacity of a discrete-time Poisson channel as a limiting behavior of the Fock states ensemble capacity. We show also that in the regime of a moderate number of photons and low losses the Fock states ensemble with direct detection is beneficial with respect to capacity limits achievable with quadrature detection.
Measurement noise is one of the main sources of errors in currently available quantum devices based on superconducting qubits. At the same time, the complexity of its characterization and mitigation often exhibits exponential scaling with the system size. In this work, we introduce a correlated measurement noise model that can be efficiently described and characterized, and which admits effective noise-mitigation on the level of marginal probability distributions. Noise mitigation can be performed up to some error for which we derive upper bounds. Characterization of the model is done efficiently using a generalization of the recently introduced Quantum Overlapping Tomography. We perform experiments on 15 (23) qubits using IBM's (Rigetti's) devices to test both the noise model and the error-mitigation scheme, and obtain an average reduction of errors by a factor >22 (>5.5) compared to no mitigation. Interestingly, we find that correlations in the measurement noise do not correspond to the physical layout of the device. Furthermore, we study numerically the effects of readout noise on the performance of the Quantum Approximate Optimization Algorithm (QAOA). We observe in simulations that for numerous objective Hamiltonians, including random MAX-2-SAT instances and the Sherrington-Kirkpatrick model, the noise-mitigation improves the quality of the optimization. Finally, we provide arguments why in the course of QAOA optimization the estimates of the local energy (or cost) terms often behave like uncorrelated variables, which greatly reduces sampling complexity of the energy estimation compared to the pessimistic error analysis. We also show that similar effects are expected for Haar-random quantum states and states generated by shallow-depth random circuits. The poster is based on a recent preprint arXiv:2101.02331 (2021) by Filip B. Maciejewski, Flavio Baccari, Zoltán Zimborás, and Michał Oszmaniec.
Self-testing is a device-independent method for certification of entangled quantum states and measurements. The aim of our work is to extend the applicability of self-testing from entangled states to subspaces. To this end, we introduce a general framework for constructing self-testing strategies for multipartite entangled subspaces, which is based on the stabilizer formalism mostly known for its usefulness in quantum error correction.
We study the Hamiltonian of a circuit containing multiple superconducting qubits coupled via shared resonators. The qubits we take into account contain higher excited levels and we use perturbative block diagonalizing formalism to accurately simplify and obtain all-qubit interactions. We consider some example pattern of qubit connectivities with qubits being fully or partly coupled. We derived effective qubit-qubit Hamiltonian from the complete circuit Hamiltonian. We do an in-depth analysis on a superconducting circuit containing multi-level transmons coupled to resonator couplers and readout devices. We have successfully derived the effective qubit-qubit coupling for up to 3 qubits and accurately reproduced and obtained new analytical results for IBM-style circuits from a Hamiltonian model.
Once we model any physical phenomenons within a mathematical framework, we have to face classical computation cost, either as memory, time or approximations used. Here, we propose a protocol that can realize a given quantum system's unitary evolution in a quantum computer, provided the system is in a finite-dimensional Hilbert space. We decompose the Hamiltonian into the appropriate basis and construct the unitary operators. If the interaction term commutes with the free Hamiltonian, we directly compute the time evolution and realize the system in a quantum circuit simulator. To illustrate, we use the simplest Hamiltonian that resembles the Jaynes Cummings model, except we consider only two two-level systems in the rotating wave approximation. If the terms do not commute, we approximate the unitary evolution to an N product as in detuned qubits. We study the time evolution of two qubits with different initial states and founds that the N product approximation works irrespective of the initial state for a given detuning. The whole experiment was constructed and performed using IBM's Qiskit Aer simulator.
The term "Layers of classicality" in the context of quantum measurements, was introduced in [T. Heinosaari, Phys. Rev. A 93, 042118 (2016)]. The strongest layer among these consists of the sets of observables that can be broadcast and the weakest layer consists of the sets of compatible observables. There are several other layers in between those two layers. In this work, we show the differences and similarities in their physical and geometric properties. We also show the existence of POVMs that are not individually broadcastable. We call this theorem as "no broadcasting theorem for a single POVM". Then we also show that unlike compatibility, other layers of classicality are not convex, in general. Finally, we discuss the connections among these layers. Arxiv preprint number- arXiv:2101.05752
The VIP-2 experiment currently in data taking at the Gran Sasso underground laboratories (LNGS) targets several scenarios beyond the standard quantum theory. It is sensitive in particular to violations of the Pauli Exclusion Principle (PEPV) and models describing the collapse of the wave function. In this poster, I will focus on preliminary PEPV results of the final VIP-2 configuration. I shall present searches of PEPV violating processes detected with Silicon Drift Detectors, SDDs, via anomalous x-ray in copper atoms, as a consequence of electron transitions in Pauli-forbidden ground states (1-s level), already occupied by two electrons. The experimental procedure will be explained and the new limits obtained will be discussed with respect to the VIP-2 goal.
The dynamical behavior of quantum correlations between two atoms coupled with thermal reservoirs is captured by different forms of Measurement-Induced Nonlocality (MIN). It is shown that the MIN quantities are more robust against noise, while noise causes sudden death in entanglement. Further, the impact of mean photon number and weak measurement on quantum correlation are also observed. Reference 1. R. Muthuganesan and R. Sankaranarayanan, Quantum. Inf. Process. 17, 305 (2018).
Two bipartite entangled states S and T are said to exhibit entanglement transitivity if for all tripartite states with two marginal states equal to S and T, the remaining bipartite marginal is also entangled. Using the Peres-Horodecki criterion, the transitivity of any pair of entangled qubit states can be tested via a semidefinite program. From the quantum channel-state duality, we have an equivalent definition of entanglement transitivity in terms of the degradability properties of quantum operations associated with the Stinespring representation. When S and T are identical, the existence of a joint state reduces to the problem of symmetric extendibility. Based on several examples derived from symmetric extensions, we prove that a two-qubit state has a pure unique symmetric extension if and only if it is the Choi state of a non-entanglement-breaking, self- complementary quantum operation. In this special case, entanglement transitivity follows when all the bipartite marginal states are entangled.
In this work we study the problem of discrimination of von Neumann measurements and measurements with rank-one effects, which we associate with measure-and-prepare channels. There are two possible approaches to this problem. The first one is simple and does not utilize entanglement. We focus only on the discrimination of classical probability distributions, which are outputs of the channels. We find necessary and sufficient criterion for perfect discrimination in this case. A more advanced approach requires the usage of entanglement. We quantify the distance between two measurements in terms of the diamond norm. We provide an exact expression for the optimal probability of correct distinction and relate it to the discrimination of unitary channels. Next, we consider unambiguous discrimination schemes. Finally, while studying the case of measurements with rank-one effects, we provide an explicit construction for an adaptive discrimination scheme.
Given two quantum channels, we examine the task of determining whether they are compatible - meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired, while forfeiting the output of the other channel. For POVMs, the Jordan product gives a simple guess for the joint measurement. We extend the notion of the Jordan product of POVMs to quantum channels and present sufficient conditions for channel compatibility. We also generalize the construction for channels, yielding also the generalization of Jordan product of measurements. We use the formulations of the different notions of compatibility as semidefinite programs to numerically compare compatibility and positivity of Jordan product for families of partially dephasing-depolarizing channels.
Quantification of quantum coherence is a fundamental and key issue in the field of resource theory and quantum information processing. Exploiting an affinity-based metric, in this article, we define a faithful measure of quantum coherence. It is shown that the affinity-based coherence is bounded by that based on fidelity and trace distance. The measure of quantumness in terms of the difference between bipartite coherence and corresponding product state coherence is also identified. We interpret the operational meaning of the affinity-based coherence as a lower bound of interferometric power of the quantum state.
We present two classical algorithms for the simulation of universal quantum circuits on n qubits constructed from c instances of Clifford gates and t arbitrary-angle Z-rotation gates such as T gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (which scales like ≈1.17t for T gates). Our algorithm is state-of-the-art for this task: as an example, in approximately 25 hours (on a standard desktop computer), we estimated the Born rule probability to within an additive error of 0.03, for a 50 qubit, 60 non-Clifford gate quantum circuit with more than 2000 Clifford gates. The Compute algorithm calculates the probability of a chosen measurement outcome to machine precision with run-time O(2t−r(t−r)t) where r is an efficiently computable, circuit-specific quantity. With high probability, r is very close to min{t,n−w} for random circuits with many Clifford gates, where w is the number of measured qubits. Compute can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+T circuits with n=55, w=5, c=105 and t=80 T-gates, and then compute the Born rule probability with a run-time consistently less than 104 seconds using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms.
A generalized measurement can be considered as an ideal or a projective measurement accompanies some noises. A question then arises that to what extent a generalized measurement deviates from projective ones. We address this question by exploiting the central role of positive operator-valued measures (POVMs) in the task of quantum state discrimination. Instead of searching for the best possible POVM to discriminate the quantum states of a given set, we consider a dual problem; Having a POVM, which set of quantum states is our POVM the best for discrimination? In this paper, we specify the minimum error, associated with the dual problem, as the extent to which the given POVM is far from being porojective. Finding an analytical solution for a measurement in qubit systems, we show that the best possible quantum state is the eigenbasis of the POVM's elements.
Motivation. To realize genuine quantum technologies such as cryptographic systems, quantum simulators or quantum computing devices, the user should be ensured that the quantum devices work as specified by the provider. Methods to certify that a quantum device really operates in a nonclassical way are therefore needed. The most compelling one, developed in the cryptographic context, is self-testing [1]. It exploits non-locality, i.e., the existence of quantum correlations that can not be reproduced by the local-realist models, and provides the complete form of device-independent characterization of quantum devices only from the statistical data the devices generate. However, since self-testing, as defined in Ref. [1], it is restricted to preparations of composite quantum systems and local measurements on them. Therefore, it poses a fundamental question of how to characterize (i) quantum systems of prime dimension that are not capable of exhibiting nonlocal correlations, and (ii) quantum systems without entanglement or spatial separation between subsystems, presuming the minimum features of the devices. One possible way to address such instances is to employ quantum contextuality (Kochen-Specker contextuality), a generalization of nonlocal correlations obtained from the statistics of commuting measurements that are performed on a single quantum system [2]. Since quantum contextual correlations have been shown to be essential in many aspects of quantum computation and communication, self-testing statements are crucial for certifying quantum technology. Apart from that, it is, nonetheless, fundamentally interesting to seek the maximum information one can infer about the quantum devices only from the observed statistics in a contextuality experiment. Results. In this work, for the first time, we provide the sum-of-squares decompositions for a family of non-contextuality inequalities in the simplest (odd-cycle) scenario capable to demonstrate Kochen-Specker contextuality. These inequalities are modified versions of celebrated KCBS inequality [2]. The sum-of-squares decompositions allow us to obtain the optimal quantum values of the respective non-contextuality inequalities, and a set of algebraic relations necessarily satisfied by any state and measurements that yield the optimal values. By solving those relations we show that the algebra generated by those measurement operators can be projected into three-dimensional vector-space. Subsequently, we prove the uniqueness of those three- dimensional measurements and state up to unitary equivalence, that is, self-testing properties of the quantum devices. Our self-testing approach assumes neither the dimension of the preparations nor the projectivity of measurements. References. [1] D. Mayers et al., Quantum Info. Comput. 4, 273 (2004). [2] A. A. Klyachko et al., Phys. Rev. Lett. 101, 020403 (2008).
Ensembles of composite quantum states can exhibit nonlocal behaviour in the sense that their optimal discrimination may require global operations. Such an ensemble containing N pairwise orthogonal pure states, however, can always be perfectly distinguished under adaptive local scheme if (N-1) copies of the state are available. Here we show that under such adaptive schemes perfect local discrimination of some ensembles require no less than (N-1) copies. Our explicit examples form orthonormal bases for two-qubit system. For this composite system we analyze multi-copy adaptive local distinguishability of orthogonal ensembles in full generality which in turn assigns varying nonlocal strength to different such ensembles. We also come up with ensembles whose discrimination under adaptive separable scheme require less number of copies than adaptive local schemes. Our construction finds important application in multipartite secret sharing tasks and indicates towards an intriguing super-additivity phenomenon for locally accessible information.
It remains a highly nontrivial problem to propose a certification scheme of d-dimensional quantum states based on violation of a single d-outcome Bell inequality. We propose the first self- testing protocol for the maximally entangled state of any local dimension using minimum of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion from quantum correlations which is log_2d of perfect randomness, while it requires one random bit to encode the measurement choice. We further extend the approach to arbitrary number of measurements per subsystem. We also certify GHZ states of arbitrary local dimension and any number of parties with only two measurements per subsystem.
In the presence of indefinite causal order, two identical copies of a completely depolarizing channel can transmit non-zero information. This effect emerges due to the quantum superposition of two alternative orders of these channels. Here, we study how well we can transmit classical information with the superposition of N depolarizing channels in a number of causal orders and find that there is always an additional classical communication advantage. We also show that the gain in classical communication rate decreases exponentially with the dimension of the message qubit (target state), and increases rapidly with the increase in the number of causal orders. However, for qubit systems, it saturates at 0.31 bits per transmission, and can never reach the noise- less transmission scenario. Finally, we derive analytical expressions for the Holevo quantity for N completely depolarizing channels with the superposition of the arbitrary number of cyclic and non-cyclic causal orders.
In the Bloch sphere based representation of qudits with dimensions greater than two, the Heisenberg-Weyl operator basis is not preferred because of presence of complex Bloch vector components. We try to address this issue and parametrize a qutrit using the Heisenberg-Weyl operators by identifying eight real parameters and separate them as four weight and four angular parameters each. The four weight parameters correspond to the weights in front of the four mutually unbiased bases sets formed by the eigenbases of Heisenberg-Weyl observables and they form a four-dimensional unit radius Bloch hypersphere. Inside the four-dimensional hypersphere all points do not correspond to a physical qutrit state but still it has several other features which indicate that it is a natural extension of the qubit Bloch sphere. We study the purity, rank of three level systems, orthogonality and mutual unbiasedness conditions and the distance between two qutrit states inside the hypersphere. We also analyze the two and three-dimensional sections centered at the origin which gives a close structure for physical qutrit states inside the hypersphere. Significantly, we have applied our representation to find mutually unbiased bases(MUBs) and to characterize the unital maps in three dimensions. It should also be possible to extend this idea in higher dimensions.
We introduce a new generalization of the Pauli channels using the mutually unbiased measurement operators. The resulting channels are bistochastic but their eigenvectors are not unitary. We analyze the channel properties, such as complete positivity, entanglement breaking, and multiplicativity of maximal output purity. We illustrate our results with the maps constructed from the Gell-Mann matrices and the Heisenberg-Weyl observables.
One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with arbitrarily large local unitary symmetry. We explain that such states can be realised in a quantum system of distinguishable traps with bosons or fermions occupying a finite number of modes. Then, local symmetries of the designed quantum state are equal to the unitary group of local mode operations acting diagonally on all traps. Therefore, such a group of symmetries is naturally protected against errors that occur in a physical realisation of mode operators. We also link our results with the existence of so-called strictly semistable states with particular asymptotic diagonal symmetries. Our main technical result states that the Nth tensor power of any irreducible representation of SU(N) contains a copy of the trivial representation. This is established via direct combinatorial analysis of Littlewood- Richardson rules utilising certain combinatorial objects which we call telescopes.
The difference between the energy of a ground state of a given Hamiltonian and the energy of the first excited state, called spectral gap, yields a key parameter of the system, useful for applications in adiabatic quantum computing and studies of quantum phase transitions in the model. We present a novel way to determine the upper bound for the energy gap based on properties of the set of expectation values of auxiliary observables. This formalism can be applied to obtain a new criterion of gaplessness, which we illustrate by a study of the XY model - an exemplary physical system with vanishing energy gap.
This work presents a robust semi device-independent quantum random number generator (QRNG) that offers an excellent trade-off between security, ease-of-implementation, and generation-rate. The system works in a prepare-and-measure scenario where measurement is completely untrusted, while a bound on the prepared states’ energy is assumed. We compare the results of two well-known measurement schemes, homodyne and heterodyne detection. Moreover, taking into account the experimental imperfections, we discuss the experimental feasibility of the d-outcome design. Lastly, we experimentally realized this semi-DI QRNG based on heterodyne detection with a simple setup featuring only commercial-off-the-shelf components.
We present an iterative algorithm to find a multipartite density matrix compatible with a prescribed set of compatible marginals and spectra (or rank), if it exists. Based on dynamical systems theory, our algorithm proceeds via successive compositions of a family of operators we introduce, being the compatible global state (when existing) an attractive fixed point of the composition. Numerical simulations show that our algorithm performs well in a wide range of multipartite scenarios. We illustrate this for the case of three and four parties with two to six internal levels each.
We argue that the quantum-theoretical structures studied in several recent lines of research cannot be adequately described within the standard framework of quantum circuits. This is in particular the case whenever the combination of subsystems is described by a nontrivial blend of direct sums and tensor products of Hilbert spaces. We therefore propose an extension to the framework of quantum circuits, given by routed linear maps and routed quantum circuits. We prove that this new framework allows for a consistent and intuitive diagrammatic representation in terms of circuit diagrams, applicable to both pure and mixed quantum theory, and exemplify its use in several situations, including the superposition of quantum channels and the causal decompositions of unitaries. We show that our framework encompasses the `extended circuit diagrams' of Lorenz and Barrett [arXiv:2001.07774 (2020)], which we derive as a special case, endowing them with a sound semantics. arxiv pre-print: https://arxiv.org/abs/2011.08120.
In a tripartite Bell experiment, the observed correlation between measurement outcomes is said to exhibit transitivity in Bell-nonlocality if the observation of Bell-nonlocality among two out of the three marginal distributions necessarily implies the Bell-nonlocality of the remaining marginal correlation. Examples of tripartite, no-signaling correlation that feature transitivity of Bell-nonlocality are known but quantum examples of this kind have so far remained elusive. Here, we report our progress on the search for such quantum examples in the tripartite scenario.