Measure of genuine coherence based of quasi-relative entropy

Abstract

We present a genuine coherence measure based on a quasi-relative entropy as a difference between quasi-entropies of the dephased and the original states. The measure satisfies non-negativity and monotonicity under genuine incoherent operations (GIO). It is strongly monotone under GIO in two- and three-dimensions, or for pure states in any dimension, making it a genuine coherence monotone. We provide a bound on the error term in the monotonicity relation in terms of the trace distance between the original and the dephased states. Moreover, the lower bound on the coherence measure can also be calculated in terms of this trace distance.

References in corpus (27)

• Quantifying Coherence
• Quantum Coherence as a Resource
• Operational Resource Theory of Coherence
• Measuring Quantum Coherence with Entanglement
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Catalytic Coherence
• Converting Coherence to Quantum Correlations
• Frozen Quantum Coherence
• Role of quantum coherence in chromophoric energy transport
• Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences
• Trace-distance measure of coherence
• A Fully Quantum Asymptotic Equipartition Property
• Robustness of asymmetry and coherence of quantum states
• Relating the Resource Theories of Entanglement and Quantum Coherence
• The Fidelity and Trace Norm Distances for Quantifying Coherence
• Distribution of quantum coherence in multipartite systems
• Conditions for coherence transformations under incoherent operations
• Quantum-coherence quantifiers based on the Tsallis relative $\alpha$-entropies
• Alternative framework for quantifying coherence
• Quantum f-divergences and error correction
• A Unified View of Quantum Correlations and Quantum Coherence
• Monotone Riemannian Metrics and Relative Entropy on Non-Commutative Probability Spaces
• Operational one-to-one mapping between coherence and entanglement measures
• Genuine quantum coherence
• Different quantum f-divergences and the reversibility of quantum operations
• Stationary quantum coherence and transport in disordered networks
• Recovery and the Data Processing Inequality for quasi-entropies