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Understanding the thermodynamic properties of many-body quantum systems and their emergence from microscopic laws is a topic of great significance due to its profound fundamental implications and extensive practical applications. Recent advances in experimental techniques for controlling and preparing these systems have increased interest in this area, as they have the potential to drive the development of quantum technologies. In this study, we present a density-functional theory approach to extract detailed information about the statistics of work and the irreversible entropy associated with quantum quenches at finite temperature. Specifically, we demonstrate that these quantities can be expressed as functionals of thermal and out-of-equilibrium densities, which may serve as fundamental variables for understanding finite-temperature many-body processes. We, then, apply our method to the case of the inhomogeneous Hubbard model, showing that our density functional theory based approach can be usefully employed to unveil the distinctive roles of interaction and external potential on the thermodynamic properties of such a system.

Quantum state transfer protocols are a major toolkit in many quantum information processing tasks, from quantum key distribution to quantum computation. To assess performance of a such a protocol, one often relies on the average fidelity between the input and the output states. Going beyond this scheme, we analyze the entire probability distribution of fidelity, providing a general framework to derive it for the transfer of single- and two-qubit states. Starting from the delta-like shape of the fidelity distribution, characteristic to perfect transfer, we analyze its broadening and deformation due to realistic features of the process, including non-perfect read-out timing. Different models of quantum transfer, sharing the same value of the average fidelity, display different distributions of fidelity, providing thus additional information on the protocol, including the minimum fidelity., Comment: 9 pages, 6 figures

Modern Cloud/Edge architectures need to orchestrate multiple layers of heterogeneous computing nodes, including pervasive sensors/actuators, distributed Edge/Fog nodes, centralized data centers and quantum devices. The optimal assignment and scheduling of computation on the different nodes is a very difficult problem, with NP-hard complexity. In this paper, we explore the possibility of solving this problem with Variational Quantum Algorithms, which can become a viable alternative to classical algorithms in the near future. In particular, we compare the performances, in terms of success probability, of two algorithms, i.e., Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). The simulation experiments, performed for a set of simple problems, %CM230124 that involve a Cloud and two Edge nodes, show that the VQE algorithm ensures better performances when it is equipped with appropriate circuit \textit{ansatzes} that are able to restrict the search space. Moreover, experiments executed on real quantum hardware show that the execution time, when increasing the size of the problem, grows much more slowly than the trend obtained with classical computation, which is known to be exponential., Comment: 14 pages, 13 figures

The efficient management of energy communities relies on the solution of the "prosumer problem", i.e., the problem of scheduling the household loads on the basis of the user needs, the electricity prices, and the availability of local renewable energy, with the aim of reducing costs and energy waste. Quantum computers can offer a significant breakthrough in treating this problem thanks to the intrinsic parallel nature of quantum operations. The most promising approach is to devise variational hybrid algorithms, in which quantum computation is driven by parameters that are optimized classically, in a cycle that aims at finding the best solution with a significant speed-up with respect to classical approaches. This paper provides a reformulation of the prosumer problem, allowing to address it with a hybrid quantum algorithm, namely, Quantum Approximate Optimization Algorithm (QAOA), and with a recent variant, the Recursive QAOA. We report on an extensive set of experiments, on simulators and real quantum hardware, for different problem sizes. Results are encouraging in that Recursive QAOA is able, for problems involving up to 10 qubits, to provide optimal and admissible solutions with good probabilities, while the computation time is nearly independent of the system size, Comment: 14 pages, 13 figures. IEEE Transactions on Smart Grid (2023)

The preparation of an equilibrium thermal state of a quantum many-body system on noisy intermediate-scale quantum (NISQ) devices is an important task in order to extend the range of applications of quantum computation. Faithful Gibbs state preparation would pave the way to investigate protocols such as thermalization and out-of-equilibrium thermodynamics, as well as providing useful resources for quantum algorithms, where sampling from Gibbs states constitutes a key subroutine. We propose a variational quantum algorithm (VQA) to prepare Gibbs states of a quantum many-body system. The novelty of our VQA consists in implementing a parameterized quantum circuit acting on two distinct, yet connected (via CNOT gates), quantum registers. The VQA evaluates the Helmholtz free energy, where the von Neumann entropy is obtained via post-processing of computational basis measurements on one register, while the Gibbs state is prepared on the other register, via a unitary rotation in the energy basis. Finally, we benchmark our VQA by preparing Gibbs states of the transverse field Ising and Heisenberg XXZ models and achieve remarkably high fidelities across a broad range of temperatures in statevector simulations. We also assess the performance of the VQA on IBM quantum computers, showcasing its feasibility on current NISQ devices., Comment: 15 pages, 13 figures

The distribution of entangled states is a key task of utmost importance for many quantum information processing protocols. A commonly adopted setup for distributing quantum states envisages the creation of the state in one location, which is then sent to (possibly different) distant receivers through some quantum channels. While it is undoubted and, perhaps, intuitively expected that the distribution of entangled quantum states is less efficient than that of product states, a thorough quantification of this inefficiency (namely, of the difference between the quantum-state transfer fidelity for entangled and factorized states) has not been performed. To this end, in this work, we consider $n$-independent amplitude-damping channels, acting in parallel, i.e., each, locally, on one part of an $n$-qubit state. We derive exact analytical results for the fidelity decrease, with respect to the case of product states, in the presence of entanglement in the initial state, for up to four qubits. Interestingly, we find that genuine multipartite entanglement has a more detrimental effect on the fidelity than two-qubit entanglement. Our results hint at the fact that, for larger $n$-qubit states, the difference in the average fidelity between product and entangled states increases with increasing single-qubit fidelity, thus making the latter a less trustworthy figure of merit., Comment: Contribution to the Entropy Special Issue of IQIS22 (Italian Quantum Information Science) conference, Palermo (Italy) 12-16 September 2022

The transfer of quantum information between different locations is key to many quantum information processing tasks. Whereas, the transfer of a single qubit state has been extensively investigated, the transfer of a many-body system configuration has insofar remained elusive. We address the problem of transferring the state of n interacting qubits. Both the exponentially increasing Hilbert space dimension, and the presence of interactions significantly scale-up the complexity of achieving high-fidelity transfer. By employing tools from random matrix theory and using the formalism of quantum dynamical maps, we derive a general expression for the average and the variance of the fidelity of an arbitrary quantum state transfer protocol for n interacting qubits. Finally, by adopting a weak-coupling scheme in a spin chain, we obtain the explicit conditions for high-fidelity transfer of 3 and 4 interacting qubits., Comment: 24 pages, comments welcome

Constraints on work extraction are fundamental to our operational understanding of the thermodynamics of both classical and quantum systems. In the quantum setting, finite-time control operations typically generate coherence in the instantaneous energy eigenbasis of the dynamical system. Thermodynamic cycles can, in principle, be designed to extract work from this non-equilibrium resource. Here, we isolate and study the quantum coherent component to the work yield in such protocols. Specifically, we identify a coherent contribution to the ergotropy (the maximum amount of unitarily extractable work via cyclical variation of Hamiltonian parameters). We show this by dividing the optimal transformation into an incoherent operation and a coherence extraction cycle. We obtain bounds for both the coherent and incoherent parts of the extractable work and discuss their saturation in specific settings. Our results are illustrated with several examples, including finite-dimensional systems and bosonic Gaussian states that describe recent experiments on quantum heat engines with a quantized load., Comment: v1: 5+3 pages, 3 figures. Comments welcome. v2: Accepted version

We investigate the steady state properties arising from the open system dynamics described by a memoryless (Markovian) quantum collision model, corresponding to a master equation in the ultra-strong coupling regime. By carefully assessing the work cost of switching on and off the system-environment interaction, we show that only a coupling Hamiltonian in the energy-preserving form drives the system to thermal equilibrium, while any other interaction leads to non-equilibrium steady states that are supported by steady-state currents. These currents provide a neat exemplification of the housekeeping work and heat. Furthermore, we characterize the specific form of system-environment interaction that drives the system to a steady-state exhibiting coherence in the energy eigenbasis, thus, giving rise to families of states that are non-passive., Comment: 11 pages, 3 figures. Substantially revised and expanded in v2; v3 close to published version

We present a general and non-invasive probing scheme to perform full momentum-resolved spectroscopy of a cold atomic gas loaded into an optical lattice using a single quantum impurity. The protocol relies on weak collisional interactions and subsequent population measurements of the impurity. By tuning a few controllable external parameters the impurity-lattice interaction can be engineered, and using two sets of measurements, performed with the impurity in two different positions, the full dispersion relation of the superfluid phonons can be reliably extracted., Comment: arXiv admin note: substantial text overlap with arXiv:1511.00833

We analyze the role of indirect quantum measurements in work extraction from quantum systems in nonequilibrium states. In particular, we focus on the work that can be obtained by exploiting the correlations shared between the system of interest and an additional ancilla, where measurement backaction introduces a nontrivial thermodynamic tradeoff. We present optimal state-dependent protocols for extracting work from both classical and quantum correlations, the latter being measured by discord. We show that, while the work content of classical correlations can be fully extracted by performing local operations on the system of interest, the amount of work related to quantum discord requires a specific driving protocol that includes interaction between system and ancilla., Comment: 5 + 5 pages, 2 figures; comments are welcomed. v2: minor corrections and few improvements; accepted in Phys. Rev. Lett

In this contribution, we aim to illustrate how quantum work statistics can be used as a tool in order to gain insight on the universal features of non-equilibrium many-body systems. Focusing on the two point measurement approach to work, we first outline the formalism and show how the related irreversible entropy production may be defined for a unitary process. We then explore the physics of sudden quenches from the point of view of work statistics and show how the characteristic function of work can be expressed as the partition function of a corresponding classical statistical physics problem in a film geometry. Connections to the concept of fidelity susceptibility are explored along with the corresponding universal critical scaling. We also review how large deviation theory applied to quantum work statistics gives further insight to universal properties. The quantum-to- classical mapping turns out to have close connections with the historical problem of orthogonality catastrophe: we therefore discuss how this relationship may be exploited in order to experimentally extract quantum work statistics in many-body systems., Comment: As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (eds.), "Thermodynamics in the quantum regime - Recent Progress and Outlook", (Springer International Publishing)

We study finite size scaling for the magnetic observables of an impurity residing at the endpoint of an open quantum Ising chain in a transverse magnetic field, realized by locally rescaling the magnetic field by a factor $\mu \neq 1$. In the homogeneous chain limit at $\mu = 1$, we find the expected finite size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit, $\mu = 0$, we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. For this case, we provide both analytic approximate expressions for the magnetization and the susceptibility as well as numerical evidences for the scaling behavior. At intermediate values of $\mu$, finite size scaling is violated, and we provide a possible explanation of this result in terms of the appearance of a second, impurity related length scale. Finally, on going along the standard quantum-to-classical mapping between statistical models, we derive the classical counterpart of the quantum Ising chain with an impurity at its endpoint as a classical Ising model on a square lattice wrapped on a half-infinite cylinder, with the links along the first circle modified as a function of $\mu$., Comment: Update closer to published version

We investigate the open dynamics of an atomic impurity embedded in a one-dimensional Bose-Hubbard lattice. We derive the reduced evolution equation for the impurity and show that the Bose-Hubbard lattice behaves as a tunable engineered environment allowing to simulate both Markovian and non-Markovian dynamics in a controlled and experimentally realisable way. We demonstrate that the presence or absence of memory effects is a signature of the nature of the excitations induced by the impurity, being delocalized or localized in the two limiting cases of superfluid and Mott insulator, respectively. Furthermore, our findings show how the excitations supported in the two phases can be characterized as information carriers.

Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model's microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time $\tau_{bd}$, proportional to the size of the system. This behaviour is explained by noticing that the low-energy modes, responsible for the scaling properties, are resilient to the absorption of energy. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving., Comment: 11 pages, 7 figures

We investigate how the presence of quantum correlations can influence work extraction in closed quantum systems, establishing a new link between the field of quantum non-equilibrium thermodynamics and the one of quantum information theory. We consider a bipartite quantum system and we show that it is possible to optimise the process of work extraction, thanks to the correlations between the two parts of the system, by using an appropriate feedback protocol based on the concept of ergotropy. We prove that the maximum gain in the extracted work is related to the existence of quantum correlations between the two parts, quantified by either quantum discord or, for pure states, entanglement. We then illustrate our general findings on a simple physical situation consisting of a qubit system., Comment: 7 pages, 3 figures; RevTeX4

We study the coexistence of the quantum Zeno effect and non-Markovianity for a system decaying in a structured bosonic environment and subject to a control field. The interaction with the environment induces decay from the excited to the ground level, which, in turn, is coherently coupled to another meta-stable state. The control of the strength of the coherent coupling between the stable levels allows the engineering of both the dissipation and of the memory effects, without modifying neither the system-reservoir interaction, nor environmental properties. We use this framework in two different parameter regimes corresponding to fast (bad cavity limit) and slow dissipation (good cavity limit) in the original, un-controlled qubit system. Our results show a non-monotonic behavior of memory effects when increasing the effectiveness of the Zeno-like freezing. Moreover, we identify a new source of memory effects which allows the persistence of non-Markovianity for long times while the excited state has already been depleted.

We address some key conditions under which many-body lattice models, intended mainly as simulated condensed matter systems, can be investigated via immersed, fully controllable quantum objects, namely quantum probes. First, we present a protocol that, for a certain class of many-body systems, allows for full momentum resolved spectroscopy using one single probe. Furthermore, we demonstrate how one can extract the two-point correlations using two entangled probes. We apply our theoretical proposal to two well-known exactly solvable lattice models, a 1D Kitaev chain and 2D superfluid Bose-Hubbard model, and show its accuracy as well as its robustness against external noise.

We study the competing effects of simultaneous Markovian and non-Markovian decoherence mechanisms acting on a single spin. We show the existence of a threshold in the relative strength of such mechanisms above which the spin dynamics becomes fully Markovian, as revealed by the use of several non-Markovianity measures. We identify a measure-dependent nested structure of such thresholds, hinting at a causality relationship amongst the various non-Markovianity witnesses used in our analysis. Our considerations are then used to argue the unavoidably non-Markovian evolution of a single-electron quantum dot exposed to both intrinsic and Markovian technical noise, the latter of arbitrary strength.

Two different models for performing efficiently routing of a quantum state are presented. Both cases involve an XX spin chain working as data bus and additional spins that play the role of sender and receivers, one of which is selected to be the target of the quantum state transmission protocol via a coherent quantum coupling mechanism making use of local/global magnetic fields. Quantum routing is achieved, in the first of the models considered, by weakly coupling the sender and the receiver to the data bus. In the second model, strong magnetic fields acting on additional spins located between the sender/receiver and the data bus allow us to perform high fidelity routing., Comment: added references in v2

Some of the recent developments concerning the propagation of quantum correlations across spin channels are reviewed. In particular, we focus on the improvement of the transport efficiency obtained by the manipulation of few energy parameters (either end-bond strengths or local magnetic fields) near the sending and receiving sites. We give a physically insightful description of various such schemes and discuss the transfer of both entanglement and of quantum discord., Comment: Review submitted to Int. J. Mod. Phys. B, special issue "Classical Vs Quantum correlations in composite systems", edited by L. Amico, S. Bose, V. Korepin and V. Vedral

We present a detailed perturbative study of the dynamics of several types of atom-atom correlations in the famous Fermi problem. This is an archetypal model to study micro-causality in the quantum domain where two atoms, the first initially excited and the second prepared in its ground state, interact with the vacuum electromagnetic field. The excitation can be transferred to the second atom via a flying photon and various kinds of quantum correlations between the two are generated during this process. Among these, prominent examples are given by entanglement, quantum discord and nonlocal correlations. It is the aim of this paper to analyze the role of the light cone in the emergence of such correlations., Comment: 14 pages, 7 figures

We study the interplay between forgetful and memory-keeping evolution enforced on a two-level system by a multi-spin environment whose elements are coupled to local bosonic baths. Contrarily to the expectation that any non-Markovian effect would be buried by the forgetful mechanism induced by the spin-bath coupling, one can actually induce a full Markovian-to-non-Markovian transition of the two-level system's dynamics, controllable by parameters such as the mismatch between the energy of the two-level system and of the spin environment. For a symmetric coupling, the amount of non-Markovianity surprisingly grows with the number of decoherence channels., Comment: 7 pages, 6 figures, PRA version

A simple relationship between recently proposed measures of non-Markovianity and the Loschmidt echo is established, holding for a two-level system (qubit) undergoing pure dephasing due to a coupling with a many-body environment. We show that the Loschmidt echo is intimately related to the information flowing out from and occasionally back into the system. This, in turn, determines the non-Markovianity of the reduced dynamics. In particular, we consider a central qubit coupled to a quantum Ising ring in the transverse field. In this context, the information flux between system and environment is strongly affected by the environmental criticality; the qubit dynamics is shown to be Markovian exactly and only at the critical point. Therefore non-Markovianity is an indicator of criticality in the model considered here.

Using an exact approach, we study the dynamics of entanglement between two qubits coupled to independent reservoirs and between the two, initially disentangled, reservoirs. We also describe the transfer of bipartite entanglement from the two-qubits to their respective reservoirs focussing on the case of two atoms inside two different leaky cavities with a specific attention to the role of the detuning. We present a scheme to prepare the cavity fields in a maximally entangled state, without direct interaction between the cavities, by exploiting the initial qubits entanglement. We discuss a deterministic protocol, working in the presence of cavity losses, for the generation of a W-state of one qubit and two cavity fields and we describe a probabilistic scheme to entangle one of the atoms with the reservoir (cavity field) of the other atom.

We put forward a framework to study the dynamics of a chain of interacting quantum particles affected by individual or collective multi-mode environment, focussing on the role played by the environmental quantum correlations over the evolution of the chain. The presence of entanglement in the state of the environmental system magnifies the non-Markovian nature of the chain's dynamics, giving rise to structures in figures of merit such as entanglement and purity that are not observed under a separable multi-mode environment. Our analysis can be relevant to problems tackling the open-system dynamics of biological complexes of strong current interest., Comment: 9 pages, 12 figures

We discuss the finite size behavior of the adiabatic Dicke model, describing the collective coupling of a set of N-two level atoms (qubits) to a faster (electromagnetic) oscillator mode. The energy eigen-states of this system are shown to be directly related to those of another widely studied collective spin model, the uniaxial one. By employing an approximate continuum approach, we obtain a complete characterization of the properties of the latter, which we then use to evaluate the scaling properties of various observables for the original Dicke model near its quantum phase transition., Comment: 8 pages, 4 figures

We investigate the build-up of quasi-long-range order in the XX chain with transverse magnetic field at finite size. As the field is varied, the ground state of the system displays multiple level crossings producing a sequence of entanglement jumps. Using the partial fidelity and susceptibility, we study the transition to the thermodynamic limit and argue that the topological order can be described in terms of kink-antikink pairs and marked by edge spin entanglement., Comment: 5pages and 6 figures

We analytically and numerically study the effects of pulsed control on the decoherence of a qubit coupled to a quantum spin bath. When the environment is critical, decoherence is faster and we show that the control is relatively more effective. Two coupling models are investigated, namely a qubit coupled to a bath via a single link and a spin star model, yielding results that are similar and consistent., Comment: 10 pages, 4 figures, replaced with published version

We study the effects of a magnetic impurity on the behavior of a $S=1/2$ spin chain. At T=0, both with and without an applied uniform magnetic field, an oscillating magnetization appears, whose decay with the distance from the impurity is ruled by a power law. As a consequence, pairwise entanglement is either enhanced or quenched, depending on the distance of the spin pair with respect to the impurity and on the values of the magnetic field and the intensity of the impurity itself. This leads us to suggest that acting on such control parameters, an adiabatic manipulation of the entanglement distribution can be performed. The robustness of our results against temperature is checked, and suggestions about possible experimental applications are put forward., Comment: 4 pages, 8 figures

We study the exact entanglement dynamics of two atoms in a lossy resonator. Besides discussing the steady-state entanglement, we show that in the strong coupling regime the system-reservoir correlations induce entanglement revivals and oscillations and propose a strategy to fight against the deterioration of the entanglement using the quantum Zeno effect., Comment: 4 pages, 3 figures

We discuss the effect of a single diagonal defect on both the static and dynamical properties of entanglement in a spin chain. We show that entanglement localizes at the defect and discuss its localization length, arguing that this can be used as a mean to store entanglement. We also show that the impurity site can behave as an entanglement mirror and characterize the bouncing process in terms of reflection and transmission coefficients.

We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an $N$ qubit register coupled to a slow oscillator mode. We show that, in the thermodynamic limit, a non zero Berry phase is obtained only if a path in parameter space is followed that encircles the critical point. Furthermore, we investigate the precursors of this critical behavior for a system with finite size and obtain the leading order in the 1/N expansion of the Berry phase and its critical exponent.

We develop a theory of coherent quantum oscillations in two, in general interacting, qubits measured continuously by a mesoscopic detector with arbitrary non-linearity and discuss an example of SQUID magnetometer that can operate as such a detector. Calculated spectra of the detector output show that the detector non-linearity should lead to mixing of the oscillations of the two qubits. For non-interacting qubits oscillating with frequencies $\Omega_1$ and $\Omega_2$, the mixing manifests itself as spectral peaks at the combination frequencies $\Omega_1\pm \Omega_2$. Additional nonlinearity introduced by the qubit-qubit interaction shifts all the frequencies. In particular, for identical qubits, the interaction splits coherent superposition of the single-qubit peaks at $\Omega_1=\Omega_2$. Quantum mechanics of the measurement imposes limitations on the height of the spectral peaks., Comment: 14 pages, 6 figures

We examine decoherence effects in the Josephson current of a Cooper pair shuttle. Dephasing due to gate voltage fluctuations can either suppress or enhance the critical current and also change its sign. The current noise spectrum displays a peak at the Josephson coupling energy and shows a phase dependence., Comment: 11 pages, 5 figures; v3 (published version): major changes, added refernces

We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even--odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasi-particle tunneling rates are comparable to the coherent Cooper-pair oscillation frequency. Furthermore the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling., Comment: 10 pages, 11 figures

We propose a scheme to generate and detect entanglement between charge states in superconducting nanocircuits. We discuss different procedures to discriminate such entanglement from classical correlations. The case of maximally entangled states of two and three coupled Josephson junctions is discussed as example., Comment: 9 pages, 3 figures

We study intrinsic noise of current in a superconducting single-electron transistor, taking into account both coherence effects and Coulomb interaction near a Cooper-pair resonance. Due to this interplay, the statistics of tunneling events deviates from the Poisson distribution and, more important, it shows even-odd asymmetry in the transmitted charge. The zero-frequency noise is suppressed significantly when the quasiparticle tunneling rates are comparable to the coherent oscillation frequency of Cooper pairs., Comment: A few minor changes; To appear in Phys. Rev. Lett