A battery is an energy storage device having utilities in a broad spectrum of fields. We consider batteries where quantum effects are inevitable, and compare the amount of energy extractable using local and global operations. We introduce the concept of local passivity for shared quantum batteries with local Hamiltonians, and characterize the set of all locally passive battery states. We find that the relation between energy extractions by local and global operations is closely connected with the entanglement content, for generic battery states.
A battery is an energy storage device having utilities in a broad spectrum of fields. We consider batteries where quantum effects are inevitable, and compare the amount of energy extractable using local and global operations. We introduce the concept of local passivity for shared quantum batteries with local Hamiltonians, and characterize the set of all locally passive battery states. We find that the relation between energy extractions by local and global operations is closely connected with the entanglement content, for generic battery states.
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.
A solvable charger--battery model is introduced in which quantum coherence controls both where a quantum battery's charge is stored and how robustly it survives noise. Charging converts the charger's coherence into charger--battery entanglement and splits the deposited work between a locally extractable part and a correlation-locked part accessible only through joint operations; for a qubit, the split obeys an exact complementarity, and at maximal coherence, the battery is locally passive with the entire charge locked in correlations. Robustness follows local accessibility: the stored energy and locally extractable work are population-based, immune to pure dephasing, and limited only by relaxation, with an energy half-life, whereas the correlation-locked work is fragile to both dephasing and relaxation. Dephasing, global and local depolarization, and amplitude damping are treated through a single gain--loss competition algebra, and the resulting storage lifetimes are made concrete with superconducting-transmon parameters.
ABSTRACT A solvable charger–battery model is introduced in which quantum coherence controls both where a quantum battery's charge is stored and how robustly it survives noise. Charging converts the charger's coherence into charger–battery entanglement and splits the deposited work between a locally extractable part and a correlation‐locked part accessible only through joint operations; for a qubit, the split obeys an exact complementarity, and at maximal coherence, the battery is locally passive with the entire charge locked in correlations. Robustness follows local accessibility: the stored energy and locally extractable work are population‐based, immune to pure dephasing, and limited only by relaxation, with an energy half‐life, whereas the correlation‐locked work is fragile to both dephasing and relaxation. Dephasing, global and local depolarization, and amplitude damping are treated through a single gain–loss competition algebra, and the resulting storage lifetimes are made concrete with superconducting‐transmon parameters.
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.
Abstract The advantage of quantum batteries is that quantum resources can be utilized to enhance charging efficiency. The known available quantum resources are quantum entanglement and quantum coherence. In this study, quantum steering is introduced as a new quantum resource into batteries for the first time. By considering two models, namely the Field‐quantum battery and the Cavity–Heisenberg quantum battery, the relationship is analyzed among quantum steering, quantum entanglement, energy storage, and extractable work. It is found that within the steerable range, the quantum steering of different qubits has a maximum or minimum value, which corresponds to the energy storage of the battery. Moreover, this maximum or minimum value of quantum steering also corresponds to the maximum value of the extractable work. The minimum of quantum entanglement always coincides with the maximum of parameters like energy storage. Ultimately, the reasons for these results are analyzed by analyzing the purity of the system and discover a relatively general conclusion: when the purity is at its maximum, important parameters such as the energy storage of the battery are also at their maximum.
Energy extraction from quantum batteries by means of completely positive trace-preserving (CPTP) maps leads to the concept of CPTP-local passive states, which identify bipartite states from which no energy can be squeezed out by applying any CPTP map to a particular subsystem. We prove, for arbitrary dimension, that if a state is CPTP-local passive with respect to a Hamiltonian, then an arbitrary number of copies of the same state-including an asymptotically large one-is also CPTP-local passive. We show further that energy can be extracted efficiently from CPTP-local passive states employing noncompletely positive trace-preserving (NCPTP) but still physically realizable maps on the same part of the shared battery on which operation of CPTP maps were useless. Moreover, we provide the maximum extractable energy using local-CPTP operations, and then, we present an explicit class of states and corresponding Hamiltonians, for which the maximum can be outperformed using physical local NCPTP maps. We provide a necessary and sufficient condition and a separate necessary condition for an arbitrary bipartite state to be unable to supply any energy using NCPTP operations on one party with respect to an arbitrary but fixed Hamiltonian. We build an analogy between the relative status of CPTP and NCPTP operations for energy extraction in quantum batteries, and the association of distillable entanglement with entanglement cost for asymptotic local manipulations of entanglement. The surpassing of the maximum energy extractable by NCPTP maps for CPTP-passive as well as for CPTP-nonpassive battery states can act as detectors of non-CPTPness of quantum maps.