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arXiv:2304.01270 · Physical Review Letters

Work Extraction Processes from Noisy Quantum Batteries: The Role of Nonlocal Resources

Salvatore Tirone, Raffaele Salvia, Stefano Chessa, Vittorio Giovannetti

Published Aug 8, 2023• 50 citations
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Abstract

We demonstrate an asymmetry between the beneficial effects one can obtain using nonlocal operations and nonlocal states to mitigate the detrimental effects of environmental noise in the work extraction process from quantum battery models. Specifically, we show that using nonlocal recovery operations after the noise action can, in general, increase the amount of work one can recover from the battery even with separable (i.e., nonentangled) input states. On the contrary, employing entangled input states with local recovery operations will generally not improve the battery performance.

DOI
10.1103/physrevlett.131.060402

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•Mar 19, 2013•5 citations
We demonstrate an asymmetry between the beneficial effects one can obtain using nonlocal operations and nonlocal states to mitigate the detrimental effects of environmental noise in the work extraction process from quantum battery models. Specifically, we show that using nonlocal recovery operations after the noise action can, in general, increase the amount of work one can recover from the battery even with separable (i.e., nonentangled) input states. On the contrary, employing entangled input states with local recovery operations will generally not improve the battery performance.
Quantum work capacitances and maximal asymptotic work/energy ratios are figures of merit characterizing the robustness against noise of work extraction processes in quantum batteries formed by collections of quantum systems. In this paper we establish a direct connection between these functionals and, exploiting this result, we analyze different types of noise models mimicking self-discharging (amplitude damping channels), thermalization (generalized amplitude damping channels), and dephasing effects (simultaneous phase-amplitude damping channels). In this context we show that input quantum coherence can significantly improve the storage performance of noisy quantum batteries and that the maximum output ergotropy is not always achieved by the maximum available input energy.
Going beyond isolated system dynamics, we examine how local and spatially correlated reservoirs influence the work extraction in quantum batteries. By employing a one-dimensional spin-1/2 model coupled to baths via dephasing and amplitude-damping noise, we demonstrate that correlations in reservoirs can significantly enhance battery's performance compared to local noise. In the dephasing scenario, we prove that correlated reservoirs produce a finite amount of extractable work, or ergotropy, during the transient regime when a two-cell battery is initialized in a product state while local noise yields vanishing ergotropy at all times, despite nonvanishing stored energy in both cases. Numerical simulations confirm that this advantage persists across larger system sizes and for both entangled and product initial states. We also find that the dynamics of quantum coherence closely mirror those of ergotropy, highlighting coherence as a key resource underlying the enhanced performance of quantum batteries. Further, we observe that the fraction of stored energy extracted from quantum batteries displays a sharper contrast between the correlated and local reservoirs. Moreover, for dephasing noise, this fraction remains independent of system size, whereas in the amplitude damping case, it exhibits a clear system-size dependence within the transient regime, highlighting distinct operational behaviors under different noise models. In addition, we reveal that when the battery dynamics is governed by an effective Hamiltonian with long-range interactions, it yields higher ergotropy compared to short-range interactions, emphasizing the advantages of reservoir engineering for efficient device design.
We present a theoretical analysis of the energy recovery efficiency for quantum batteries composed of many identical quantum cells undergoing noise. While the possibility of using quantum effects to speed up the charging processes of batteries have been vastly investigated, In order to traslate these ideas into working devices it is crucial to assess the stability of the storage phase in the quantum battery elements when they are in contact with environmental noise. In this work we formalize this problem introducing a series of operationally well defined figures of merit (the work capacitances and the Maximal Asymptotic Work/Energy Ratios) which gauge the highest efficiency one can attain in recovering useful energy from quantum battery models that are formed by large collections of identical and independent elements (quantum cells or q-cells). Explicit evaluations of such quantities are presented for the case where the energy storing system undergoes through dephasing and depolarizing noise.
In realistic situations, physical systems can not be completely isolated from its environment. Its inevitable interaction with the environment can influence the working process of the device. In this paper, we consider two-qubit quantum batteries where one qubit of the battery is successively interacting with the spins present in the surrounding environment. We examine the effect of the interaction on the maximum amount of energy that can be extracted from the battery using unitaries. In this context, we use the notion of locally passive states. In particular, we examine the behavior of the amount of extractable work from the noisy battery, initially prepared in a locally passive or ordinary pure state, having a fixed initial entanglement, with the number of interactions the qubit has gone through. We also examine the amount of locally extractable work from the noisy battery. We realize though the amount of extractable energy, be it global or local, as a whole will decrease with the number of spins of environment it interacted with, but if we increase the time interval of the interaction with each spin, after a cut off value of the interval, the small time behavior shows a peculiarity, i.e., the extractable energy within a single interaction starts to increase with time. The cut-off time indicates the Markovian-to-non-Markovian transition of the interaction. We also observe a non-Markovian increase in extractable energy from the Markovian scenario.
One of the main challenges in developing high-performance quantum batteries is the self-discharging process, where energy is dissipated from a quantum battery into the environment. In this work, we investigate the influence of non-Markovian noises on the performance of a quantum battery. Our results demonstrate that adding auxiliary qubits to a quantum battery system can effectively suppress the self-discharging process, leading to an improvement in both the steady-state energy and extractable work. We reveal that the physical mechanism inhibiting the self-discharging process is the formation of system-environment bound states, rather than an increase in non-Markovianity. Our results could be of both theoretical and experimental interest in exploring the ability of quantum batteries to maintain long stored energy in the environment.
We consider reversible work extraction from identical quantum batteries. From an ensemble of individually passive states, work can be produced only via global unitary (and thus entangling) operations. However, we show here that there always exists a method to extract all possible work without creating any entanglement, at the price of generically requiring more operations (i.e. additional time). We then study faster methods to extract work and provide a quantitative relation between the amount of generated multipartite entanglement and extractable work. Our results suggest a general relation between entanglement generation and the power of work extraction.