Isocoherent Work Extraction from Quantum Batteries: Basis-Dependent Response

TL;DR

This paper explores how quantum coherence affects the maximum work extractable from quantum batteries, revealing basis-dependent effects and deriving analytical relations for qubits and higher-dimensional systems.

Contribution

It introduces the coherence-constrained maximal work (CCMW) concept and provides analytical and numerical results linking CCMW to quantum coherence in various bases.

Findings

Maximal extractable work decreases with coherence in the energy basis.

CCMW increases with coherence when basis basis has off-diagonal Hamiltonian elements.

Analytical relations between CCMW and coherence are derived for qubits and higher dimensions.

Abstract

We identify a connection between quantum coherence and the maximum extractable work from a quantum battery, and to this end, we define the coherence-constrained maximal work (CCMW) as the highest amount of work extractable via coherence-preserving unitaries, optimized over all quantum states with fixed coherence in a given dimension. For qubit systems, we derive an analytical relation between the CCMW and the input coherence, defined with respect to an arbitrary fixed basis. Strikingly, we find that for fixed quantum coherence in the energy eigenbasis, the maximal extractable work decreases with increase of coherence. In contrast, when quantum coherence is with respect to a basis for which the Hamiltonian possesses off-diagonal elements, and has equal diagonal elements, the CCMW increases with the level of quantum coherence. We numerically observe that the basis-dependent response of the CCMW also persists in higher-dimensional quantum systems. Moreover, we show that even in higher dimensions one can derive closed-form relations between the CCMW and the input quantum coherence within certain numerically-assessed conclusions. We also comment on the structure of passive states in an isocoherent scenario, that is, states from which no energy can be extracted under coherence-preserving unitaries.