arXiv subjects

Giacomo Guarnieri

Publications and source records attributed to Giacomo Guarnieri.

At least 37 records · Page 2Linked to original sources

arXiv2024

Typical thermalization of low-entanglement states

Proving thermalization from the unitary evolution of a closed quantum system is one of the oldest questions that is still nowadays only partially resolved. Several efforts have led to various formulations of what is called the eigenstate thermalization hypothesis, which leads to thermalization under certain conditions on the initial states. These conditions, however, are sensitive to the precise formulation of the hypothesis. In this work, we focus on the important case of low entanglement initial states, which are operationally accessible in many natural physical settings, including experimental schemes for testing thermalization and for quantum simulation. We prove thermalization of these states under precise conditions that have operational significance. More specifically, motivated by arguments of unavoidable finite resolution, we define a random energy smoothing on local Hamiltonians that leads to local thermalization when the initial state has low entanglement. Finally we show that such a transformation affects neither the Gibbs state locally nor, under generic smoothness conditions on the spectrum, the short-time dynamics.

quant-ph↗

arXiv2024

Artificially intelligent Maxwell's demon for optimal control of open quantum systems

Feedback control of open quantum systems is of fundamental importance for practical applications in various contexts, ranging from quantum computation to quantum error correction and quantum metrology. Its use in the context of thermodynamics further enables the study of the interplay between information and energy. However, deriving optimal feedback control strategies is highly challenging, as it involves the optimal control of open quantum systems, the stochastic nature of quantum measurement, and the inclusion of policies that maximize a long-term time- and trajectory-averaged goal. In this work, we employ a reinforcement learning approach to automate and capture the role of a quantum Maxwell's demon: the agent takes the literal role of discovering optimal feedback control strategies in qubit-based systems that maximize a trade-off between measurement-powered cooling and measurement efficiency. Considering weak or projective quantum measurements, we explore different regimes based on the ordering between the thermalization, the measurement, and the unitary feedback timescales, finding different and highly non-intuitive, yet interpretable, strategies. In the thermalization-dominated regime, we find strategies with elaborate finite-time thermalization protocols conditioned on measurement outcomes. In the measurement-dominated regime, we find that optimal strategies involve adaptively measuring different qubit observables reflecting the acquired information, and repeating multiple weak measurements until the quantum state is "sufficiently pure", leading to random walks in state space. Finally, we study the case when all timescales are comparable, finding new feedback control strategies that considerably outperform more intuitive ones. We discuss a two-qubit example where we explore the role of entanglement and conclude discussing the scaling of our results to quantum many-body systems.

quant-ph↗

arXiv2024

Generalised linear response theory for the full quantum work statistics

We consider a quantum system driven out of equilibrium via a small Hamiltonian perturbation. Building on the paradigmatic framework of linear response theory (LRT), we derive an expression for the full generating function of the dissipated work. Remarkably, we find that all information about the distribution can be encoded in a single quantity, the standard relaxation function in LRT, thus opening up new ways to use phenomenological models to study non-equilibrium fluctuations in complex quantum systems. Our results establish a number of refined quantum thermodynamic constraints on the work statistics that apply to regimes of perturbative but arbitrarily fast protocols, and do not rely on assumptions such as slow driving or weak coupling. Finally, our approach uncovers a distinctly quantum signature in the work statistics that originates from underlying zero-point energy fluctuations. This causes an increased dispersion of the probability distribution at short driving times, a feature that can be probed in efforts to witness non-classical effects in quantum thermodynamics.

quant-ph↗

arXiv2024

Joint statistics of work and entropy production along quantum trajectories

In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the stochastic level by unravelling the system's evolution in terms of quantum jump trajectories. We here derive a general formula for computing the joint statistics of work and entropy production in Markovian driven quantum systems, whose instantaneous steady-states are of Gibbs form. If the driven system remains close to the instantaneous Gibbs state at all times, we show that the corresponding two-variable cumulant generating function implies a joint detailed fluctuation theorem so long as detailed balance is satisfied. As a corollary, we derive a modified fluctuation-dissipation relation (FDR) for the entropy production alone, applicable to transitions between arbitrary steady-states, and for systems that violate detailed balance. This FDR contains a term arising from genuinely quantum fluctuations, and extends an analogous relation from classical thermodynamics to the quantum regime.

quant-ph↗

arXiv2024

Thermodynamic uncertainty relation in slowly driven quantum heat engines

Thermodynamic Uncertainty Relations express a trade-off between precision, defined as the noise-to-signal ratio of a generic current, and the amount of associated entropy production. These results have deep consequences for autonomous heat engines operating at steady-state, imposing an upper bound for their efficiency in terms of the power yield and its fluctuations. In the present manuscript we analyse a different class of heat engines, namely those which are operating in the periodic slow-driving regime. We show that an alternative TUR is satisfied, which is less restrictive than that of steady-state engines: it allows for engines that produce finite power, with small power fluctuations, to operate close to the Carnot efficiency. The bound further incorporates the effect of quantum fluctuations, which reduces engine efficiency relative to the average power and reliability. We finally illustrate our findings in the experimentally relevant model of a single-ion heat engine.

quant-ph↗

arXiv2023

Particle current statistics in driven mesoscale conductors

We propose a highly-scalable method to compute the statistics of charge transfer in driven conductors. The framework can be applied in situations of non-zero temperature, strong coupling to terminals and in the presence of non-periodic light-matter interactions, away from equilibrium. The approach combines the so-called mesoscopic leads formalism with full counting statistics. It results in a generalised quantum master equation that dictates the dynamics of current fluctuations and higher order moments of the probability distribution function of charge exchange. For generic time-dependent quadratic Hamiltonians, we provide closed-form expressions for computing noise in the non-perturbative regime of the parameters of the system, reservoir or system-reservoir interactions. Having access to the full dynamics of the current and its noise, the method allows us to compute the variance of charge transfer over time in non-equilibrium configurations. The dynamics reveal that in driven systems, the average noise should be defined operationally with care over which period of time is covered.

quant-ph↗

arXiv2022

The Thermodynamic Uncertainty Theorem

Thermodynamic uncertainty relations (TURs) express a fundamental tradeoff between the precision (inverse scaled variance) of any thermodynamic current by functionals of the average entropy production. Relying on purely variational arguments, we significantly extend these inequalities by incorporating and analyzing the impact of higher statistical cumulants of entropy production within a general framework of time-symmetrically controlled computation. This allows us to derive an exact expression for the current that achieves the minimum scaled variance, for which the TUR bound tightens to an equality that we name Thermodynamic Uncertainty Theorem (TUT). Importantly, both the minimum scaled variance current and the TUT are functionals of the stochastic entropy production, thus retaining the impact of its higher moments. In particular, our results show that, beyond the average, the entropy production distribution's higher moments have a significant effect on any current's precision. This is made explicit via a thorough numerical analysis of swap and reset computations that quantitatively compares the TUT against previous generalized TURs. Our results demonstrate how to interpolate between previously-established bounds and how to identify the most relevant TUR bounds in different nonequilibrium regimes.

cond-mat.stat-mech↗

arXiv2022

Enhanced steady-state coherence via repeated system-bath interactions

The appearance of steady-state coherence (SSC) from system-bath interaction proves that quantum effects can appear without an external drive. Such SSC could become a resource to demonstrate quantum advantage in the applications. We predict the generation of SSC if the target system repeatedly interacts with independent and non-correlated bath elements. To describe their behavior, we use the collision model approach of system-bath interaction, where the system interacts with one bath element (initially in an incoherent state) at a time, asymptotically (in the fast-collision regime) mimicking a macroscopic Markovian bath coupled to the target system. Therefore, the SSC qualitatively appears to be the same as if the continuous Markovian bath would be used. We confirm that the presence of composite system-bath interactions under the rotating-wave approximation (RWA) is the necessary condition for the generation of SSC using thermal resources in collision models. Remarkably, we show that SSC substantially increases if the target system interacts collectively with more than one bath element at a time. Already few bath elements collectively interacting with the target system are sufficient to increase SSC at non-zero temperatures at the cost of tolerable lowering the final state purity. From the thermodynamic perspective, the SSC generation in our collision models is inevitably linked to a non zero power input (and thus heat dissipated to the bath) necessary to reach the steady-state, although such energetic cost can be lower compared to cases relying on SSC non generating interactions.

quant-ph↗

arXiv2022

Experimental Observation of Curved Light-Cones in a Quantum Field Simulator

We investigate signal propagation in a quantum field simulator of the Klein-Gordon model realized by two strongly coupled parallel one-dimensional quasi-condensates. By measuring local phononic fields after a quench, we observe the propagation of correlations along sharp light-cone fronts. If the local atomic density is inhomogeneous, these propagation fronts are curved. For sharp edges, the propagation fronts are reflected at the system's boundaries. By extracting the space-dependent variation of the front velocity from the data, we find agreement with theoretical predictions based on curved geodesics of an inhomogeneous metric. This work extends the range of quantum simulations of non-equilibrium field dynamics in general spacetime metrics.

cond-mat.quant-gas↗

arXiv2022

Periodically refreshed quantum thermal machines

We introduce unique class of cyclic quantum thermal machines (QTMs) which can maximize their performance at the finite value of cycle duration $τ$ where they are most irreversible. These QTMs are based on single-stroke thermodynamic cycles realized by the non-equilibrium steady state (NESS) of the so-called Periodically Refreshed Baths (PReB) process. We find that such QTMs can interpolate between standard collisional QTMs, which consider repeated interactions with single-site environments, and autonomous QTMs operated by simultaneous coupling to multiple macroscopic baths. We discuss the physical realization of such processes and show that their implementation requires a finite number of copies of the baths. Interestingly, maximizing performance by operating in the most irreversible point as a function of $τ$ comes at the cost of increasing the complexity of realizing such a regime, the latter quantified by the increase in the number of copies of baths required. We demonstrate this physics considering a simple example. We also introduce an elegant description of the PReB process for Gaussian systems in terms of a discrete-time Lyapunov equation. Further, our analysis also reveals interesting connections with Zeno and anti-Zeno effects.

quant-ph↗

arXiv2022

Work extraction from coherently activated maps via quantum switch

We characterize the impact that the application of two maps in a quantum-controlled order has on the process of work extraction via unitary cycles and its optimization. The control is based on the quantum switch model that applies maps in an order not necessarily compatible with the underlying causal structure and, in principle, can be implemented experimentally. First, we show that the activation of quantum maps through the quantum switch model always entails a non-negative gain in ergotropy compared to their consecutive application. We also establish a condition that the maps should fulfill in order to achieve a non-zero ergotropic gain. We then perform a thorough analysis of maps applied to a two-level system and provide general conditions for achieving a positive gain on the incoherent part of ergotropy. Our results are illustrated with several examples and applied to qubit and $d$-dimensional quantum systems. In particular, we demonstrate that a non-zero work can be extracted from a system thermalized by two coherently controlled reservoirs.

quant-ph↗

arXiv2021

Hyperaccurate thermoelectric currents

Thermodynamic currents can fluctuate significantly at the nanoscale. But some currents fluctuate less than others. Hyperaccurate currents are those which fluctuate the least, in the sense that they maximize the signal-to-noise ratio (precision). In this letter we analytically determine the hyperaccurate current in the case of a quantum thermoelectric, modeled by the Landauer-Büttiker formalism.

quant-ph↗

arXiv2021

Periodically refreshed baths to simulate open quantum many-body dynamics

Obtaining dynamics of an interacting quantum many-body system connected to multiple baths initially at different, finite, temperatures and chemical potentials is a challenging problem. This is due to a combination of the prevalence of strong correlations in the system, the infinite nature of the baths and the long time to reach steady state. In this work we develop a general formalism that allows access to the full non-Markovian dynamics of such open quantum many-body systems up to the non-equilibrium steady state (NESS), provided its uniqueness. Specifically, we show how finite-time evolution in presence of finite-sized baths, whose opportune size is determined by their original spectral density, can be recursively used to faithfully reconstruct the exact dynamics without requiring any small parameter. Such a reconstruction is possible even in parameter regimes which would otherwise be inaccessible by current state-of-the-art techniques. We specifically demonstrate this by obtaining the full numerically exact non-Markovian dynamics of interacting fermionic chains in two terminal set-ups with finite temperature and voltage biases, a problem which previously remained outstanding despite its relevance in a wide range of contexts, for example, quantum heat engines and refrigerators.

quant-ph↗

arXiv2021

Time periodicity from randomness in quantum systems

Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the vibration of a cello string. While self-oscillation is well understood in classical non-linear systems and their quantized counterparts, the spontaneous emergence of periodicity in quantum systems without a semi-classical limit is more elusive. Here, we show that this behavior can emerge within the repeated-interaction description of open quantum systems. Specifically, we consider a many-body quantum system that undergoes dissipation due to sequential coupling with auxiliary systems at random times. We develop dynamical symmetry conditions that guarantee an oscillatory long-time state in this setting. Our rigorous results are illustrated with specific spin models, which could be implemented in trapped-ion quantum simulators.

quant-ph↗

arXiv2021

Action quantum speed limits

We introduce action quantum speed limits (QSLs) as a family of bounds on the minimal time to connect two states that, unlike the usual geometric approach, crucially depend on how the path is traversed, i.e. on the instantaneous speed. The two approaches provide consistent bounds when the instantaneous speed is optimized along a fixed path and we demonstrate this explicitly for the case of a thermalizing qubit employing techniques from optimal control theory. In addition, we critically analyze the interpretation of QSLs based on different choices of metric establishing that, in general, these open system QSL times provide an indication of optimality with respect to the geodesic path, rather than necessarily being indicative of an achievable minimal time.

quant-ph↗

arXiv2020

Thermodynamics of precision in quantum nano-machines

Fluctuations strongly affect the dynamics and functionality of nanoscale thermal machines. Recent developments in stochastic thermodynamics have shown that fluctuations in many far-from-equilibrium systems are constrained by the rate of entropy production via so-called thermodynamic uncertainty relations. These relations imply that increasing the reliability or precision of an engine's power output comes at a greater thermodynamic cost. Here we study the thermodynamics of precision for small thermal machines in the quantum regime. In particular, we derive exact relations between the power, power fluctuations, and entropy production rate for several models of few-qubit engines (both autonomous and cyclic) that perform work on a quantised load. Depending on the context, we find that quantum coherence can either help or hinder where power fluctuations are concerned. We discuss design principles for reducing such fluctuations in quantum nano-machines, and propose an autonomous three-qubit engine whose power output for a given entropy production is more reliable than would be allowed by any classical Markovian model.

quant-ph↗

arXiv2020

Quantum Coherence and Ergotropy

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.

quant-ph↗

arXiv2020

Quantum fluctuations hinder finite-time information erasure near the Landauer limit

Information is physical but information is also processed in finite time. Where computing protocols are concerned, finite-time processing in the quantum regime can dynamically generate coherence. Here we show that this can have significant thermodynamic implications. We demonstrate that quantum coherence generated in the energy eigenbasis of a system undergoing a finite-time information erasure protocol yields rare events with extreme dissipation. These fluctuations are of purely quantum origin. By studying the full statistics of the dissipated heat in the slow driving limit, we prove that coherence provides a non-negative contribution to all statistical cumulants. Using the simple and paradigmatic example of single bit erasure, we show that these extreme dissipation events yield distinct, experimentally distinguishable signatures.

quant-ph↗