Quantifying coherence of quantum channels based on the generalized $\alpha$-$z$-relative Rényi entropy

Abstract

By using the Choi-Jamiołkowski isomorphism, we propose a well-defined coherence measure of quantum channels based on the generalized $\alpha$-$z$-relative Rényi entropy. In addition, we present an alternative coherence measure of quantum channels by quantifying the commutativity between the channels and the completely dephasing channels with the generalized $\alpha$-$z$-relative Rényi entropy. Some elegant properties of the measures are illustrated in detail. Explicit formulas of these coherence measures are derived for some detailed typical quantum channels.

arXiv comment23 pages, 4 figues, 1 table

References in corpus (39)

• Decoherence, einselection, and the quantum origins of the classical
• Introducing Quantum Discord
• Quantifying Coherence
• Classical, quantum and total correlations
• The classical-quantum boundary for correlations: discord and related measures
• The Role of Relative Entropy in Quantum Information Theory
• Measuring Quantum Coherence with Entanglement
• Dephasing assisted transport: Quantum networks and biomolecules
• Robustness of coherence: An operational and observable measure of quantum coherence
• Catalytic Coherence
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• All non-classical correlations can be activated into distillable entanglement
• Quantum Coherence via Skew Information and Its Polygamy
• A quantitative theory of coherent delocalization
• Alternative framework for quantifying coherence
• Operational Resource Theory of Quantum Channels
• Quantifying Operations with an Application to Coherence
• Resource Theory of Coherence - Beyond States
• Asymmetry and coherence weight of quantum states
• Cohering power of quantum operations
• Dynamical Resource Theory of Quantum Coherence
• A new coherence measure based on fidelity
• Measures of coherence generating power for quantum unital operations
• Coherifying quantum channels
• Coherence and entanglement measures based on Rényi relative entropies
• Coherence non-generating channels
• Quantifying the Nonclassicality of Operations
• Witnessing quantum coherence in the presence of noise
• A universal set of qubit quantum channels
• Coherence of quantum channels
• Quantifying quantum coherence based on the generalized $\alpha -z-$relative R$\acute{e}$nyi entropy
• Maximum Relative Entropy of Coherence for Quantum Channels
• Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information
• Coherence and complementarity based on modified generalized skew information
• Skew information-based coherence generating power of quantum channels
• Sum uncertainty relations based on $(\alpha ,\beta ,\gamma )$ weighted Wigner-Yanase-Dyson skew information
• An alternative framework for quantifying coherence of quantum channels
• Tighter uncertainty relations based on $(\alpha ,\beta ,\gamma )$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels
• On coherence of quantum operations by using Choi-Jamiołkowski isomorphism

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