Bhattacharyya Aparajita, Sen Kornikar, Sen Ujjwal
<a href="https://ror.org/0165d9303">Harish-Chandra Research Institute</a>, A CI of <a href="https://ror.org/02bv3zr67">Homi Bhabha National Institute</a>, Chhatnag Road, Jhunsi, Prayagraj 211 019, India.
Phys Rev Lett. 2024 Jun 14;132(24):240401. doi: 10.1103/PhysRevLett.132.240401.
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.
通过完全正定保迹（CPTP）映射从量子电池中提取能量，引出了CPTP局部无源态的概念，该概念用于识别二分态，即对特定子系统应用任何CPTP映射都无法从中挤出能量的态。我们证明，对于任意维度，如果一个态相对于哈密顿量是CPTP局部无源的，那么相同态的任意数量的副本（包括渐近大量的副本）也是CPTP局部无源的。我们进一步表明，利用非完全正定保迹（NCPTP）但仍可物理实现的映射，可以从CPTP局部无源态中高效提取能量，这些映射作用于共享电池中CPTP映射操作无用的同一部分。此外，我们给出了使用局部CPTP操作可提取的最大能量，然后，我们给出了一类明确的态和相应的哈密顿量，对于这类态和哈密顿量，使用物理局部NCPTP映射可以超过最大能量。对于任意二分态，相对于任意但固定的哈密顿量，在一方使用NCPTP操作无法提供任何能量，我们给出了一个充要条件和一个单独的必要条件。我们在量子电池能量提取中CPTP和NCPTP操作的相对地位，与渐近局部纠缠操作中可提纯纠缠与纠缠代价的关联之间建立了类比。对于CPTP无源以及CPTP非无源电池态，NCPTP映射可提取的最大能量的超越，可以作为量子映射非CPTP性的探测器。
