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Open many-body quantum systems can exhibit intriguing nonequilibrium phases of matter, such as time crystals. In these phases, the state of the system spontaneously breaks the time-translation symmetry of the dynamical generator, which typically manifests through persistent oscillations of an order parameter. A paradigmatic model displaying such a symmetry breaking is the boundary time crystal, which has been extensively analyzed experimentally and theoretically. Despite the broad interest in these nonequilibrium phases, their thermodynamics and their fluctuating behavior remain largely unexplored, in particular for the case of coupled time crystals. In this work, we consider two interacting boundary time crystals and derive a consistent interpretation of their thermodynamic behavior. We fully characterize their average dynamics and the behavior of their quantum fluctuations, which allows us to demonstrate the presence of quantum and classical correlations in both the stationary and the time-crystal phases displayed by the system. We furthermore exploit our theoretical derivation to explore possible applications of time crystals as quantum batteries, demonstrating their ability to efficiently store energy., Comment: 15 + 18 pages, 8 figures

In modern society, service robots are increasingly recognized for their wide range of practical applications. In large and crowded social spaces, such as museums and hospitals, these robots are required to safely move in the environment while exhibiting user-friendly behavior. Ensuring the safe and socially acceptable operation of robots in such settings presents several challenges. To enhance the social acceptance in the design process of service robots, we present a systematic analysis of requirements, categorized into functional and non-functional. These requirements are further classified into different categories, with a single requirement potentially belonging to multiple categories. Finally, considering the specific case of a receptionist robotic agent, we discuss the requirements it should possess to ensure social acceptance.

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. 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. We meticulously present derivations of essential concepts alongside straightforward examples, aiming to enhance comprehension and facilitate learning., Comment: Tutorial. Close to the published version. Code available at http://link.aps.org/supplemental/10.1103/PRXQuantum.5.030201

We study the robustness of the evolution of a quantum system against small uncontrolled variations in parameters in the Hamiltonian. We show that the fidelity susceptibility, which quantifies the perturbative error to leading order, can be expressed in superoperator form and use this to derive control pulses which are robust to any class of systematic unknown errors. The proposed optimal control protocol is equivalent to searching for a sequence of unitaries that mimics the first-order moments of the Haar distribution, i.e. it constitutes a 1-design. We highlight the power of our results for error resistant single- and two-qubit gates., Comment: 18 pages, 9 figures

Non-equilibrium effects may have a profound impact on the performance of thermal devices performing thermodynamic tasks such as refrigeration or heat pumping. The possibility of enhancing the performance of thermodynamic operations by means of quantum coherence is of particular interest but requires an adequate characterization of heat and work at the quantum level. In this work, we demonstrate that the presence of even small amounts of coherence in the thermal reservoirs powering a three-terminal machine, enables the appearance of combined and hybrid modes of operation, where either different resources are combined to perform a single thermodynamic task, or more than one task is performed at the same time. We determine the performance of such coherence-enabled modes of operation obtaining their power and efficiency. In the case of hybrid regimes, the presence of coherence in the hot bath allows for an increase in power while maintaining high efficiencies. On the other hand, in combined regimes, a contrasting behavior emerges whereby coherence has a detrimental impact on power output and efficiency.

Quantum collision models normally consist of a system interacting with a set of ancillary units representing the environment. While these ancillary systems are usually assumed to be either two level systems (TLS) or harmonic oscillators, in this work we move further and represent each ancillary system as a structured system, i.e., a system made out of two or more subsystems. We show how this scenario modifies the kind of master equation that one can obtain for the evolution of the open systems. Moreover, we are able to consider a situation where the ancilla state is thermal yet has some coherence. This allows the generation of coherence in the steady state of the open system and, thanks to the simplicity of the collision model, this allows us to better understand the thermodynamic cost of creating coherence in a system. Specifically, we show that letting the system interact with the coherent degrees of freedom requires a work cost, leading to the natural fulfillment of the first and second law of thermodynamics without the necessity of {\it ad hoc} formulations., Comment: 16 pages, 8 figures

Time-translation symmetry breaking is a mechanism for the emergence of non-stationary many-body phases, so-called time-crystals, in Markovian open quantum systems. Dynamical aspects of time-crystals have been extensively explored over the recent years. However, much less is known about their thermodynamic properties, also due to the intrinsic nonequilibrium nature of these phases. Here, we consider the paradigmatic boundary time-crystal system, in a finite-temperature environment, and demonstrate the persistence of the time-crystalline phase at any temperature. Furthermore, we analyze thermodynamic aspects of the model investigating, in particular, heat currents, power exchange and irreversible entropy production. Our work sheds light on the thermodynamic cost of sustaining nonequilibrium time-crystalline phases and provides a framework for characterizing time-crystals as possible resources for, e.g., quantum sensing. Our results may be verified in experiments, for example with trapped ions or superconducting circuits, since we connect thermodynamic quantities with mean value and covariance of collective (magnetization) operators., Comment: 21 pages, 4 figures

Production of quantum states exhibiting a high degree of entanglement out of noisy conditions is one of the main goals of quantum information science. Here, we provide a conditional yet efficient entanglement distillation method which functions within the framework of spatially localized operations and classical communication. This method exploits indistinguishability effects due to the spatial overlap between two identical qubits in distinct sites and encompasses particle statistics imprint. We derive the general conditions for the maximum entanglement distillation out of mixed states. As applications, we give a thorough description of distilled entanglement and associated success probability starting from typical noisy states, such as thermal Gibbs states and Werner states. The influence of local temperatures and of noise parameter is discussed, respectively, in these two cases. The proposed scheme paves the way towards quantum repeaters in composite networks made of controllable identical quantum particles., Comment: 9 pages, 6 figures

We consider the problem of finding the energy minimum of a complex quantum Hamiltonian by employing a non-Markovian bath prepared in a low energy state. The energy minimization problem is thus turned into a thermodynamic cooling protocol in which we repeatedly put the system of interest in contact with a colder auxiliary system. By tuning the internal parameters of the bath, we show that the optimal cooling is obtained in a regime where the bath exhibits a quantum phase transition in the thermodynamic limit. This result highlights the importance of collective effects in thermodynamic devices. We furthermore introduce a two-step protocol that combines the interaction with the bath with a measure of its energy. While this protocol does not destroy coherence in the system of interest, we show that it can further enhance the cooling effect.

We investigate the thermodynamics of a hybrid quantum device consisting of two qubits collectively interacting with a quantum rotor and coupled dissipatively to two equilibrium reservoirs at different temperatures. By modelling the dynamics and the resulting steady state of the system using a collision model, we identify the functioning of the device as a thermal engine, a refrigerator or an accelerator. In addition, we also look into the device's capacity to operate as a heat rectifier, and optimise both the rectification coefficient and the heat flow simultaneously. Drawing an analogy to heat rectification and since we are interested in the conversion of energy into the rotor's kinetic energy, we introduce the concept of angular momentum rectification which may be employed to control work extraction through an external load., Comment: Close to the published version. Microscopic models updated

The introduction of the quantum analogue of a Carnot engine based on a bath comprising of particles with a small amount of coherence initiated an active line of research on the harnessing of different quantum resources for the enhancement of thermal machines beyond the standard reversible limit, with an emphasis on non-thermal baths containing quantum coherence. In our work, we investigate the impact of coherence on the thermodynamic tasks of a collision model which is composed of a system interacting, in the continuous time limit, with a series of coherent ancillas of two baths at different temperatures. Our results show the advantages of utilising coherence as a resource in the operation of the machine, and allows it: (i) to exhibit unconventional behaviour such as the appearance of a hybrid refrigerator, capable of simultaneous refrigeration and generation of work, and (ii) to function as an engine or a refrigerator with efficiencies larger than the Carnot bound. Moreover, we find an effective upper bound to the efficiency of the thermal machine operating as an engine in the presence of a coherent reservoir., Comment: Accepted version

We investigate several control strategies for the transport of an excitation along a spin chain. We demonstrate that fast, high fidelity transport can be achieved using protocols designed with differentiable programming. Building on this, we then show how this approach can be effectively adapted to control a disordered quantum system. We consider two settings: optimal control for a known unwanted disorder pattern, i.e. a specific disorder realisation, and optimal control where only the statistical properties of disorder are known, i.e. optimizing for high average fidelities. In the former, disorder effects can be effectively mitigated for an appropriately chosen control protocol. However, in the latter setting the average fidelity can only be marginally improved, suggesting the presence of a fundamental lower bound., Comment: 10 pages, 7 figures, 1 table. Close to published version

At low-temperatures a gas of bosons will undergo a phase transition into a quantum state of matter known as a Bose-Einstein condensate (BEC), in which a large fraction of the particles will occupy the ground state simultaneously. Here we explore the performance of an endoreversible Otto cycle operating with a harmonically confined Bose gas as the working medium. We analyze the engine operation in three regimes, with the working medium in the BEC phase, in the gas phase, and driven across the BEC transition during each cycle. We find that the unique properties of the BEC phase allow for enhanced engine performance, including increased power output and higher efficiency at maximum power., Comment: 23 pages, 6 figures

The study of quantum thermodynamics is key to the development of quantum thermal machines. In contrast to most of the previous proposals based on discrete strokes, here we consider a working substance that is permanently coupled to two or more baths at different temperatures and continuously driven. To this end, we investigate parametrically driven quantum harmonic oscillators coupled to heat baths via a collision model. Using a thermodynamically consistent local master equation, we derive the heat flows and power of the working device which can operate as an engine, refrigerator or accelerator and analyze the instantaneous and average efficiencies and coefficients of performance. Studying the regimes of both slow and fast driving of the system, we find that an increased driving frequency can lead to a change of functioning to a dissipator. Finally, we investigate the effect of squeezing one of the thermal baths: it leads to an apparent higher efficiency compared to the corresponding Carnot value of an equilibrium bath with the same temperature and to sustained entanglement between the working substance oscillators in the limit cycle., Comment: Accepted version. See associated Scilight summary: https://doi.org/10.1063/10.0009575

We present a general quantum fluctuation theorem for the entropy production of an open quantum system coupled to multiple environments, not necessarily at equilibrium. Such a general theorem, when restricted to the weak-coupling and Markovian regime, holds for both local and global master equations, corroborating the thermodynamic consistency of local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of a Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is also valid when the system is described by a time-dependent Hamiltonian. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to nonthermal baths, as long as microreversibility is preserved. We present some numerical examples to showcase the exact results previously obtained. We finally generalize the fluctuation theorem to the case where the interaction between the system and the bath is explicitly taken into account. We show that the fluctuation theorem amounts to a relation between time-reversed dynamics of the global density matrix and a two-time correlation function along the forward dynamics involving the baths' entropy alone., Comment: Accepted version

Recently, nanomaterials are arousing increasing interest and a wide variety of opto-electronic devices have been developed, such as light-emitting diodes, solar cells, and photodetectors. However, the study of the light emission properties of quantum dots under pressure is still limited. By using a joint theoretical and experimental approach, we developed a polymer waveguide doped with CdSe quantum dots for pressure sensing. Absorption and re-emission effects of the quantum dots are affected by the pressure applied on the waveguide. Specifically, since both amplitude and wavelength are modulated, not only the pressure can be detected, but also its location along the waveguide. The calibration results demonstrate the feasibility of the proposed force sensor design. Theoretical model and simulations further validate the presented sensing principle. The proposed prototype benefits from the main advantages of optical sensors, such as their predisposition to miniaturization, small cable sizes and weights, immunity to electromagnetic interference, and safe operation in hazard environments. In addition, bio-compatibility, non-toxicity and flexibility make the presented sensor potentially appealing to various application fields such as nanobiotechnology and robotic sensing.

Crossing a quantum critical point in finite time challenges the adiabatic condition due to the closing of the energy gap, which ultimately results in the formation of excitations. Such non-adiabatic excitations are typically deemed detrimental in many scenarios, and consequently several strategies have been put forward to circumvent their formation. Here, however, we show how these non-adiabatic excitations -- originated from the failure to meet the adiabatic condition due to the presence of a quantum critical point -- can be controlled and thus harnessed to perform certain tasks advantageously. We focus on closed cycles reaching the quantum critical point of fully-connected models analyzing two examples. First, a quantum battery that is loaded by approaching a quantum critical point, whose stored and extractable work increases exponentially via repeating cycles. Second, a scheme for the fast preparation of spin squeezed states containing multipartite entanglement that offer a metrological advantage. The corresponding figure of merit in both cases crucially depends on universal critical exponents and the scaling of the protocol driving the system in the vicinity of the transition. Our results highlight the rich interplay between quantum thermodynamics and metrology with critical nonequilibrium dynamics., Comment: Comments welcome! 6+6 pages