Coherence monotones of quantum channels based on two generalized quantum relative entropies

Abstract

By using the Choi-Jamiołkowski isomorphism, we propose two classes of coherence monotones of quantum channels based on the unified $(r,s)$-relative entropy and the sandwiched Rényi relative entropy. Elegant properties of the coherence monotones for quantum channels are explored. Moreover, we present the upper bounds of the coherence monotones and derive the explicit formulas of the coherence monotones for qubit unitary channels.

13 pages

References in corpus (31)

• Quantifying Coherence
• 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
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Quantum Coherence via Skew Information and Its Polygamy
• A quantitative theory of coherent delocalization
• Operational Resource Theory of Quantum Channels
• Asymmetry and coherence weight of quantum states
• Cohering power of quantum operations
• A new coherence measure based on fidelity
• Measures of coherence generating power for quantum unital operations
• Coherifying quantum channels
• Coherence non-generating channels
• Coherence of quantum channels
• Witnessing quantum coherence in the presence of noise
• 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
• Average skew information-based coherence and its typicality for random quantum states
• 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