Coherence and complementarity based on modified generalized skew information

Abstract

We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalized Wigner-Yanase-Dyson (MWGWYD) skew information. By revisiting state-channel interaction based on MGWYD skew information, a family of coherence measures with respect to quantum channels is proposed. Furthermore, explicit analytical expressions of these coherence measures of qubit states are derived with respect to different quantum channels. Moreover, complementarity relations based on MGWYD skew information and MWGWYD skew information are also presented. Specifically, the conservation relations are investigated, while two interpretations of them including symmetry-asymmetry complementarity and wave-particle duality have been proposed.

20pages

References in corpus (6)

• Measuring Quantum Coherence with Entanglement
• Max- relative entropy of coherence: an operational coherence measure
• Equivalence of wave-particle duality to entropic uncertainty
• Quantifying quantum coherence based on the generalized $\alpha -z-$relative R$\acute{e}$nyi entropy
• Average coherence and its typicality for random mixed quantum states
• Uncertainty Relation Based on Skew Information with Quantum Memory

Cited by in corpus (7)

• Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information
• Skew information-based coherence generating power of quantum channels
• Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm
• Uncertainty and complementarity relations based on generalized skew information
• Sum uncertainty relations based on $(\alpha ,\beta ,\gamma )$ weighted Wigner-Yanase-Dyson skew information
• Quantifying coherence of quantum channels based on the generalized $\alpha$-$z$-relative Rényi entropy
• Coherence monotones of quantum channels based on two generalized quantum relative entropies