Bound on ergotropic gap for bipartite separable states

Abstract

Presence of correlations among the constituent quantum systems has a great relevance in thermodynamics. Significant efforts have been devoted to investigate the role of correlations in work extraction, among others. Here, we derive a bound on the difference between global and local extractable work by unitary operations (ergotropic gap), for bipartite separable states. Violation of this bound necessarily certifies the presence of entanglement. This gap is shown to be a monotone under LOCC assisted state transformations for pure bipartite quantum states. Our criterion has an implication in witnessing the dimension of a bipartite quantum state, with same local dimensions. On the other hand, our result gives an operational meaning to the Nielsen-Kempe disorder criterion. We also propose a schematic model to realize the separability bound experimentally and to detect entanglement for a restricted class of quantum states.

No-go results in quantum thermodynamics

“…In quantum thermodynamics the difference between local and global extractable work termed as ergotropic gap plays a significant role in identifying the structure of a quantum state shared between its constituents. In particular, it is shown that separability of a bipartite quantum state invokes an upper bound on this quantity [28]. The importance of those bipartite states for which local marginals are passive has also been studied.…”

“…Another important question in this regime is regarding the gap between locally and globally extractable amount of work. This quantity namely the ergotropy gap plays a significant role in certifying quantum entanglement present in a bipartite system [27,28]. In the extreme case of non-zero ergotropy gap the locally extractable work is zero whereas the global work is non-zero.…”

Energy upper bound for structurally stableN-passive states

“…zero maximum mean energy decrement when forcing the system to undergo an unitary evolution induced by cyclic external modulations of H. In the Kelvin-Planck formulation of the second law of thermodynamics, ergotropy can be interpreted as the maximum work that can be extracted from a system [2,8], suggesting the identification of passive states as a primitive form of thermal equilibrium. In view of this property, ergotropy and passive states play a key role in quantum thermodynamics [1,9], where they help in clarifying several aspects of the theory, spanning from foundational issues at the interplay between physics and information [10,11,12,13,14,15,16,17,18,19], to more practical issues, such as the characterisation of optimal thermodynamical cycles [1,20,21,22,23,24,25] and the charging efficiency of quantum batteries models [8,26,27,28,29,30]. Passive states have been also identified as optimisers for several entropic functionals which are relevant in the theory of quantum communication [31,32,33], and as suitable generalizations of the vacuum state for quantum field theory in curved space-time models [34].…”

Thermodynamic advancement in the causally inseparable occurrence of thermal maps

“…Alternatively, the superiority of non-classical features, viz. entanglement and discord of quantum correlations have been studied from the perspective of work extraction in [4][5][6]. The key feature in all these is the quantum superposition, presence of which at the single particle level can cause locking of work extraction in a different scenario [7].…”