Generalized Coherence Concurrence and Path distinguishability

Abstract

We propose a new family of coherence monotones, named the \emph{generalized coherence concurrence} (or coherence $k$-concurrence), which is an analogous concept to the generalized entanglement concurrence. The coherence $k$-concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than $k$, and a state can be converted to a state with nonzero entanglement $k$-concurrence via incoherent operations if and only if the state has nonzero coherence $k$-concurrence. We apply the coherence concurrence family to the problem of wave-particle duality in multi-path interference phenomena. We obtain a sharper equation for path distinguishability (which witness the duality) than the known value and show that the amount of each concurrence for the quanton state determines the number of slits which are identified unambiguously.

9 pages, Revtex 4.1; (v3) new analysis on the application of generalized coherence concurrence to multi-path interference problems, former title "Generalized Coherence Concurrence and Coherence Number", (v4) minor error corrections

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• Coherence measure: Logarithmic coherence number
• Some notes on the robustness of k-coherence and k-entanglement
• Unification of quantum resources in distributed scenarios
• Majorization and the time complexity of linear optical networks
• Polynomial measure of coherence
• Partial Distinguishability as a Coherence Resource in Boson Sampling