Quantifying quantum coherence based on the generalized $\alpha -z-$relative R$\acute{e}$nyi entropy

Abstract

We present a family of coherence quantifiers based on the generalized $\alpha -z-$relative R$\acute{e}$nyi entropy. These quantifiers satisfy all the standard criteria for well-defined measures of coherence, and include some existing coherence measures as special cases.

9 pages, 1 figures

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• Coherence measures with respect to general quantum measurements
• Coherence and complementarity based on modified generalized skew information
• Skew information-based coherence generating power of quantum channels
• Average skew information-based coherence and its typicality for random quantum states
• Geometry of skew information-based quantum coherence
• Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm
• Uncertainty and complementarity relations based on generalized skew information
• Quantumness of pure-state ensembles via coherence of Gram matrix based on generalized $\alpha$-$z$-relative Rényi entropy
• Estimating coherence with respect to general quantum measurements
• Quantifying coherence of quantum channels based on the generalized $\alpha$-$z$-relative Rényi entropy
• Imaginarity measures induced by relative entropy
• Coherence and entanglement dynamics in Shor's algorithm
• Coherence monotones of quantum channels based on two generalized quantum relative entropies