The Quantum Internet, a network interconnecting remote quantum devices through quantum links in synergy with classical ones, is envisioned as the final stage of the quantum revolution, opening fundamentally new communications and computing capabilities. But the Quantum Internet is governed by the laws of quantum mechanics. Phenomena with no counterpart in classical networks, such as no-cloning, quantum measurement, entanglement and quantum teleportation, impose new challenging constraints for network design. Specifically, classical network functionalities are based on the assumption that classical information can be safely read and copied. However, this assumption does not hold in the Quantum Internet. As a consequence, its design requires a major network-paradigm shift to harness the quantum mechanics specificities. The goal of this work is to shed light on the challenges and open problems of Quantum Internet design. We first introduce some basic knowledge of quantum mechanics, needed to understand the differences between a classical and a quantum network. Then, we introduce quantum teleportation as the key strategy for transmitting quantum information without physically transferring the particle that stores the quantum information or violating the principles of quantum mechanics. Finally, the key research challenges to design quantum communication networks are discussed.

Recent years have witnessed an explosion of interest in quantum devices for the production, storage, and transfer of energy. This Colloquium concentrates on the field of quantum energy storage by reviewing recent theoretical and experimental progress in quantum batteries. Provided first is a theoretical background discussing the advantages that quantum batteries offer with respect to their classical analogs. The existing quantum many-body battery models are then reviewed and a thorough discussion of important issues related to their “open nature” is presented. The Colloquium concludes with a discussion of promising experimental implementations, preliminary results available in the literature, and perspectives.

A quantum battery is a work reservoir that stores energy in quantum degrees of freedom. When immersed in an environment, an open quantum battery needs to be stabilized against free-energy leakage due to decoherence, unavoidably entailing entropy production. For this purpose we here propose a stabilization protocol given by a nonunitary open-loop control action able to compensate for the entropy increase and to maintain the open quantum battery in its highest ergotropy state. The protocol relies on nonselective, frequent, projective measurements that are interspersed by optimized time intervals. In accordance with a second-law-like inequality derived for the entropy production rate of the controlled battery, the proposed procedure results in minimized control power. The effectiveness of the method is finally tested on a qubit subject to decoherence, achieving an average fidelity value around $95\%$.

Elucidating the energy transfer between a quantum system and a reservoir is a central issue in quantum nonequilibrium thermodynamics, which could provide novel tools to engineer quantum-enhanced heat engines. The lack of information on the reservoir inherently limits the practical insight that can be gained on the exchange process of open quantum systems. Here we investigate the energy transfer for an open quantum system in the framework of quantum fluctuation relations. As a novel toolbox, we employ a nitrogen-vacancy center spin qubit in diamond, subject to repeated quantum projective measurements and a tunable dissipation channel. In the presence of energy fluctuations originated by dissipation and quantum projective measurements, the experimental results, supplemented by numerical simulations, show the validity of the energy exchange fluctuation relation, where the energy scale factor encodes missing reservoir information in the system out-of-equilibrium steady-state properties. This result is complemented by a theoretical argument showing that, also for an open three-level quantum system, the existence of an out-of-equilibrium steady state dictates a unique time-independent value of the energy scale factor for which the fluctuation relation is verified. Our findings pave the way to the investigation of energy exchange mechanisms in arbitrary open quantum systems.

In this tutorial, we present the definition, interpretation, and properties of some of the main quasiprobabilities that can describe the statistics of measurement outcomes evaluated at two or more times. Such statistics incorporate the incompatibility of the measurement observables and the state of the measured quantum system. We particularly focus on Kirkwood-Dirac quasiprobabilities and related distributions. We also discuss techniques to experimentally access a quasiprobability distribution, ranging from the weak two-point measurement scheme, to a Ramsey-like interferometric scheme and procedures assisted by an external detector. Once defined the fundamental concepts following the standpoint of joint measurability in quantum mechanics, we illustrate the use of quasiprobabilities in quantum thermodynamics to describe the quantum statistics of work and heat, and to explain anomalies in the energy exchanges entailed by a given thermodynamic transformation. On the one hand, in work protocols, we show how absorbed energy can be converted to extractable work and vice versa due to Hamiltonian incompatibility at distinct times. On the other hand, in exchange processes between two quantum systems initially at different temperatures, we explain how quantum correlations in their initial state may induce cold-to-hot energy exchanges, which are unnatural between any pair of equilibrium nondriven systems. We conclude the tutorial by giving simple examples where quasiprobabilities are applied to many-body systems: scrambling of quantum information, sensitivity to local perturbations, and quantum work statistics in the quenched dynamics of models that can be mapped onto systems of free fermions, for instance, the Ising model with a transverse field. Throughout the tutorial, we meticulously present derivations of essential concepts alongside straightforward examples, aiming to enhance comprehension and facilitate learning. Published by the American Physical Society 2024

Quantum correlation functions are a natural way to encode multitime information, as they are ubiquitous in analysis from fluctuation theorems to information scrambling. Correlation functions can be identified with quasiprobabilities associated to quantum processes. In this work we show how these can be measured via error-cancellation techniques, using projective measurements only and no ancillae. The scheme is implemented in a nitrogen-vacancy center in diamond undergoing a unitary quantum work protocol. We reconstruct quantum-mechanical time correlations encoded in the Margenau-Hills quasiprobabilities by observing work extraction peaks five times those of sequential projective energy measurement schemes and in violation of newly derived stochastic bounds. We interpret the phenomenon via anomalous energy exchanges due to the underlying negativity of the quasiprobability distribution. Published by the American Physical Society 2024