Asymptotic Convertibility of Entanglement: A General Approach to Entanglement Concentration and Dilution

Abstract

We consider asymptotic convertibility of an arbitrary sequence of bipartite pure states into another by local operations and classical communication (LOCC). We adopt an information-spectrum approach to address cases where each element of the sequences is not necessarily in tensor power of a bipartite pure state. We derive necessary and sufficient conditions for the LOCC convertibility of one sequence to another in terms of spectral entropy rates of entanglement of the sequences. Based on these results, we also provide simple proofs for previously known results on the optimal rates of entanglement concentration and dilution of general sequences of pure states.

References in corpus (9)

• The role of quantum information in thermodynamics --- a topical review
• Smooth Renyi Entropies and the Quantum Information Spectrum
• Error exponents in hypothesis testing for correlated states on a spin chain
• Large deviations and Chernoff bound for certain correlated states on a spin chain
• Hypothesis testing for Gaussian states on bosonic lattices
• Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems
• Quantum statistical mechanical derivation of the second law of thermodynamics: a hybrid setting approach
• Large Deviation implies First and Second Laws of Thermodynamics
• Regularized Boltzmann entropy determines macroscopic adiabatic accessibility

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