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.

arXiv comment13 pages, 2 figures

References in corpus (33)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Three qubits can be entangled in two inequivalent ways
• Concentrating Partial Entanglement by Local Operations
• Distributed Entanglement
• The logarithmic negativity: A full entanglement monotone that is not convex
• Conditions for a class of entanglement transformations
• Fundamental limitations for quantum and nano thermodynamics
• Entanglement monotones
• The second laws of quantum thermodynamics
• Extractable work from ensembles of quantum batteries. Entanglement helps
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• Maximal work extraction from quantum systems
• The Physics and Mathematics of the Second Law of Thermodynamics
• Entanglement of pure states for a single copy
• Work extraction and thermodynamics for individual quantum systems
• Truly work-like work extraction
• Reversible transformations from pure to mixed states, and the unique measure of information
• Faithful Squashed Entanglement
• Entanglement Theory and the Second Law of Thermodynamics
• Should Entanglement Measures be Monogamous or Faithful?
• A short note on passivity, complete passivity and virtual temperatures
• Disentangling Theorem and Monogamy for Entanglement Negativity
• Axiomatic relation between thermodynamic and information-theoretic entropies
• Monogamy of entanglement without inequalities
• Thermodynamics as a Consequence of Information Conservation
• The entropy concept for non-equilibrium states
• Monogamy of the Entanglement of Formation
• Bound on Ergotropic Gap for Bipartite Separable States
• The presence of quantum correlations result in non-vanishing ergotropic gap
• Microcanonical thermodynamics in general physical theories
• Optimal quantum operations at zero energy cost
• Entropy Meters and the Entropy of Non-extensive Systems
• Tsallis entropy, $q$-expectation and constraints on three-party quantum correlations

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• The battery capacity of energy-storing quantum systems
• Thermodynamic advancement in the causally inseparable occurrence of thermal maps
• Thermodynamic Signatures of Genuinely Multipartite Entanglement
• Extraction of ergotropy: free energy bound and application to open cycle engines
• Structure of passive states and its implication in charging quantum batteries
• Extracting work from correlated many-body quantum systems
• Exploring Non-Markovianity in Ergodic Channels: Measuring Memory Retention through Ergotropy
• Multipartite entanglement measures based on the thermodynamic framework
• Complete characterisation of state conversions by work extraction
• General quantum resources providing advantages in work-extraction tasks
• Quantum correlations and ergotropy