Catalytic Transformations in Coherence Theory

Abstract

In 2016, A. Winter et al.(Physical Review Letters 116 (12) (2016) 120404) provided an operational meaning to relative entropy of coherence and coherence of formation by introducing coherence distillation and dilation protocol in asymptotic setup. Though relative entropy of coherence introduced in 2014 by T. Baumgratz ( Physical Review Letters 113 (14) (2014) 140401) as a coherence measure but it's operational meaning in single copy setup was unknown so far. Here we have provided relative entropy of coherence (via IO (Incoherent Operations)) and coherence of formation (via IO) and quantum incoherent relative entropy (via LQICC(Local Quantum Incoherent Operations with Classical Communications)) a clear operational significance in single copy setup using the concept of catalyst. We have proved an existential correspondence between asymptotic and catalytic state transformation using IO, LICC(Local Incoherent Operations with Classical Communications) and LQICC. We have also discussed two very important protocols, assisted distillation and quantum incoherent state merging, in single copy setup using catalyst. Monotone property of relative entropy of coherence, coherence of formation and quantum incoherent relative entropy under the catalytic transformation are also discussed here.

arXiv comment8 pages, revtex, comments welcome

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Cited by in corpus (10)

• Catalysis of entanglement and other quantum resources
• Fundamental limits on anomalous energy flows in correlated quantum systems
• Entanglement catalysis for quantum states and noisy channels
• Quantum catalysis in cavity quantum electrodynamics
• Catalytic transformations for thermal operations
• Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound
• Teleportation with Embezzling Catalysts
• Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
• Communication with Quantum Catalysts
• Finite-size catalysis in quantum resource theories