Noncompletely Positive Quantum Maps Enable Efficient Local Energy Extraction in Batteries

TL;DR

This paper explores how non-completely positive trace-preserving (NCPTP) maps can extract energy from quantum batteries more efficiently than traditional CPTP maps, revealing new operational capabilities and conditions for energy extraction.

Contribution

It introduces the concept that NCPTP maps can outperform CPTP maps in energy extraction from quantum states, providing conditions and explicit examples for this advantage.

Findings

NCPTP maps can surpass CPTP maps in energy extraction.

CPTP-local passive states remain passive under multiple copies.

Explicit states and Hamiltonians demonstrate the advantage of NCPTP maps.

Abstract

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 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 non-completely positive trace-preserving (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 non-passive battery states can act as detectors of non-CPTPness of quantum maps.