Independence of work and entropy for equal energetic finite quantum systems: Passive state energy as an entanglement quantifier

Abstract: Although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic (EE) states in the asymptotic limit, for the finite quantum systems, the relation is not so linear and requires detail investigation. Toward this, we have considered a resource theoretic framework taking the energy preserving operations (EPO) as free, to compare the amount of extractable work from two different quantum states. Under EPO, majorization becomes a necessary criterion for state transformation. It is also shown that the passive state energy is a concave function and for EE states it becomes proportional to the ergotropy in absolute sense. Invariance of the passive state energy under unitary action on the given state makes it an entanglement measure for the pure bipartite states. Further, due to the non additivity of passive state energy for the different system Hamiltonians, one can generate Vidal's monotones which would give the optimal probability for pure entangled state transformation. This measure also quantifies the ergotropic gap which is employed to distinguish some specific classes of three-qubit pure entangled states.