The network configuration may allow for novel forms of nonlocal quantum correlations. This talk will present recent developments in this direction.

The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way around. A fundamental question is whether it is possible, at least in principle, to engineer mechanisms that probe quantum dynamics in the backward direction, or in more general combinations of the forward and the backward direction. To answer this question, we characterize all possible time-reversals that are compatible with four natural requirements, and we show that quantum theory is compatible with the existence of a machine that adds quantum control to the time direction of an unknown dynamics. This machine, which we call the quantum time flip, offers an advantage in a game where a referee challenges a player to identify a hidden relation between two unknown unitary gates. The quantum time flip can be experimentally simulated with photonic systems, shedding light on the information-processing capabilities of exotic scenarios in which the arrow of time between two events is in a quantum superposition of two alternative directions.

Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state for some given marginals. This problem arises in many contexts, ranging from quantum chemistry to entanglement theory and quantum error correcting codes. In this contribution, we prove a correspondence of the marginal problem to the separability problem. Based on this, we describe a sequence of semidefinite programs which can decide whether some given marginals are compatible with some pure global quantum state. As an application, we prove that the existence of multi-particle absolutely maximally entangled states for a given dimension is equivalent to the separability of an explicitly given two-party quantum state. Finally, we show that the existence of quantum codes with given parameters can also be interpreted as a marginal problem, hence, our complete hierarchy can also be used.

We consider a paradigm for discrete quantum heat machines where we allow only for coupling two systems at a time, and there is explicit battery. The evolution in each discrete step is given by energy preserving unitary transformation. We first verify laws of thermodynamics in such a paradigm, emphasizing the role of ergotropy. We then obtain analytically optimal efficiency and work production over all the minimal-coupling heat engines with single qubit working body and minimal number of strokes (i.e. three). One of our main tools is and object which we call control-marginal state. It acts only on the Hilbert space of the working body, but encapsulates all the features of the joint working body and battery system. Thanks to it in our optimization we can take into account possible coherences as well as entanglement between working body and battery.

An important method to test our understanding of quantum theory is the theory-independent approach, where the principles and axioms of quantum theory are formulated in a minimal mathematical structure. This allows a unified view on quantum theory, classical theory, and also a variety of other theories. However, so far it is difficult to address in this framework questions like: How does a system evolve in time? What would be the ground state energy of the harmonic oscillator? In this talk I will approach such questions from a theory-independent perspective, present examples, and discuss the implications for our understanding of quantum theory.

Significant advances in building small scale quantum computers and quantum simulators have been reported with various physical platforms, from atomic and photonic systems to solid state devices. A central aspect in further developments is the verification of proper functioning of these quantum devices. In this talk I will discuss several protocols designed for the characterization, validation and verification of quantum devices.

Harnessing the flow of proper time of arbitrary external systems over which we exert little or no control has been a recurring theme in both science and science-fiction. Unfortunately, all relativistic schemes to achieve this effect beyond mere time dilation are utterly unrealistic. In this talk, I will present non-relativistic scattering experiments which, if successful, freeze out, speed up or even reverse the free dynamics of any ensemble of quantum systems present in the scattering region. This "time warping" effect is universal, i.e., it is independent of the particular interaction between the scattering particles and the target systems, or the (possibly non-Hermitian) Hamiltonian governing the evolution of the latter. The protocols require careful preparation of the probes which are scattered, and success is heralded by projective measurements of these probes at the conclusion of the experiment. We fully characterize the possible time translations which one can effect on n target systems through a scattering protocol of fixed duration; the core result is that time can be freely distributed between the systems, and reversed at a small cost. For high n, our protocols allow one to quickly send a single system to its far future or past.

Quantum non Markovianity and quantum Darwinism are two phenomena linked by a common theme: the flux of quantum information between a quantum system and the quantum environment it interacts with. In this work, making use of a quantum collision model, a formalism initiated by Sudarshan and his school, I will analyse the efficiency with which the information about a single qubit gained by a quantum harmonic oscillator, acting as a meter, is transferred to a bosonic environment. I will show how, in some regimes, such quantum information flux is inefficient, leading to the simultaneous emergence of non Markovian and non Darwinistic behaviours. I will then combine the collisional picture for open system dynamics and the control of the rate of decoherence provided by the quantum (anti-)Zeno effect to illustrate the temporal unfolding of the redundant encoding of information into a multipartite environment that is at the basis of Quantum Darwinism, and to control it. The rate at which such encoding occurs can be enhanced or suppressed by tuning the dynamical conditions of system-environment interaction in a suitable and remarkably simple manner. This would help the design of a new generation of quantum experiments addressing the phenomenology of Quantum Darwinism and thus its characterization.

We investigate the correlations that can arise in prepare-and-measure communication scenarios where the source (Alice) and the measurement device (Bob) can share prior entanglement. The paradigmatic example of such a scenario is the quantum dense coding protocol, where the communication capacity of a qubit can be amplified if a two-qubit entangled state is shared between Alice and Bob. We show that the most general correlations that can be established between Alice and Bob actually require higher-dimensional entanglement. This motivates us to investigate the set of correlations that can be obtained from communicating either a classical or a quantum d-dimensional system in the presence of an unlimited amount of entanglement. We show how such correlations can be bounded through a series of semidefinite programming relaxations. For classical communication, this follows from a reduction to standard Bell nonlocality. For general communication, in particular quantum communication, this follows from a relaxation to the set of informationally-restricted quantum correlations. As an application, we introduce device-independent tests of the dimension of classical and quantum systems that, in contrast to previous results, do not make the implicit assumption that Alice and Bob share no entanglement.

In the past, quasiclassical branches in the wavefunction were described through carefully choreographed and enthusiastic handwaving. Within the many-body lattice context, we now have two mathematically precise guiding principles: *redundantly recorded observables*, a generalization of quantum Darwinism concepts that avoids a-priori preferred subsystems, and *N-point non-interference*, a formalization of effective wavefunction collapse relevant to numerical simulations. These conditions are respectively too strong and too weak in a particular sense, but they clearly illuminate and roughly bound the goal of identifying a mathematically precise definition of wavefunction branches. I argue that achieving this goal (1) would allow us to ask deep questions about quantum foundations that cannot otherwise be clearly formulated, (2) would have (maybe modest) real-world applications, and (3) is the single most promising approach to making progress on the measurement problem. The question of how to define branches is simultaneously neglected, tractable, and profound.

It is important to be able to quantify in a meaningful way quantum phenomena which can be thought of as resources, such as entanglement, coherence, or measurement informativeness. In this talk I will discuss recent work which has shown that resources quantifiers based upon their robustness to noise, which are geometrical in nature, completely characterise the biggest advantage provided by that resource in discrimination tasks. I will also present a second parallel work which found an analogous relationship between resource quantifiers based upon 'resource weight', which completely characterise the biggest advantage provided by that resource in exclusion tasks.

Quantum non-locality and entanglement are inextricably linked. However, while entanglement is necessary to achieve non-locality, it is not sufficient in the standard Bell scenario. Notwithstanding, this does not preclude the equivalence of entanglement and non-locality if the set of possible states is restricted or if more general scenarios are considered. On the one hand, it has been proven that all pure entangled states are nonlocal. On the other hand, it is known that local entangled states distributed in networks can lead to non-local correlations. In this talk I will address these questions in the genuine multipartite scenario. I will show that any star network in which each external node shares an arbitrary pure entangled state with the central node can give rise to genuine multipartite non-local (GMNL) behaviours. Interestingly, I will use this result to prove that all pure genuine multipartite entangled (GME) states are GMNL in the sense that measurements on a finite number of copies of any GME state lead to GMNL behaviours. This is joint work with P. Contreras-Tejada and C. Palazuelos.