Deterministic transformations of coherent states under incoherent operations

Abstract

It is well known that the majorization condition is the necessary and sufficient condition for the deterministic transformations of both pure bipartite entangled states by local operations and coherent states under incoherent operations. In this paper, we present two explicit protocols for these transformations. We first present a permutation-based protocol which provides a method for the single-step transformation of $d$-dimensional coherent states. We also obtain generalized solutions of this protocol for some special cases of $d$-level systems. Then, we present an alternative protocol where we use $d^{\prime }$-level ($d^{\prime }$ $<$ $d$) subspace solutions of the permutation-based protocol to achieve the complete transformation as a sequence of coherent-state transformations. We show that these two protocols also provide solutions for deterministic transformations of pure bipartite entangled states.

arXiv comment16 pages, 8 figures

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• The block-coherence measures and the coherence measures based on positive-operator-valued measures
• Conversion of Gaussian states under incoherent Gaussian operations
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Coherence, superposition, and Löwdin symmetric orthogonalization
• State convertibility under genuinely incoherent operations