Skew information-based coherence generating power of quantum channels

Abstract

We study the ability of a quantum channel to generate quantum coherence when it applies to incoherent states. We define the measure of coherence generating power (CGP) for a generic quantum channel to be the average coherence generated by the quantum channel acting on a uniform ensemble of incoherent states based on the skew information-based coherence measure. We present explicitly the analytical formulae of the CGP for any arbitrary finite dimensional unitary channels. We derive the mean value of the CGP over the unitary groups and investigate the typicality of the normalized CGP. Furthermore, we give an upper bound of the CGP for the convex combinations of unitary channels. Detailed examples are provided to calculate exactly the values of the CGP for the unitary channels related to specific quantum gates and for some qubit channels.

arXiv comment21pages. arXiv admin note: text overlap with arXiv:2101.07427

References in corpus (56)

• Quantifying Coherence
• Operational Resource Theory of Coherence
• Measuring Quantum Coherence with Entanglement
• Robustness of coherence: An operational and observable measure of quantum coherence
• Induced measures in the space of mixed quantum states
• Converting Coherence to Quantum Correlations
• Intrinsic randomness as a measure of quantum coherence
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences
• Relating the Resource Theories of Entanglement and Quantum Coherence
• Assisted distillation of quantum coherence
• Quantum Coherence via Skew Information and Its Polygamy
• Max- relative entropy of coherence: an operational coherence measure
• Complementarity relations for quantum coherence
• Cohering and de-cohering power of quantum channels
• Operational one-to-one mapping between coherence and entanglement measures
• One-shot coherence distillation
• Quantifying Operations with an Application to Coherence
• Random matrix techniques in quantum information theory
• Resource Theory of Coherence - Beyond States
• Energy Cost of Creating Quantum Coherence
• Probabilistic distillation of quantum coherence
• One-Shot Coherence Dilution
• Experimental cyclic inter-conversion between Coherence and Quantum Correlations
• Deterministic Coherence Distillation
• Coherence generating power of quantum unitary maps and beyond
• Coherence and asymmetry cannot be broadcast
• Average coherence and its typicality for random pure states
• A no-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting
• Family of coherence measures and duality between quantum coherence and path distinguishability
• Measures of coherence generating power for quantum unital operations
• Coherifying quantum channels
• Generic bound coherence under strictly incoherent operations
• One-Shot Coherence Distillation: Towards Completing the Picture
• Coherence non-generating channels
• Coherence of quantum channels
• Interrelation between Partial Coherence and Quantum Correlations
• Entropy power inequalities for qudits
• Detecting and estimating coherence based on coherence witnesses
• Coherence of quantum channels
• Coherence measure: Logarithmic coherence number
• Average subentropy, coherence and entanglement of random mixed quantum states
• Quantifying quantum coherence based on the generalized $\alpha -z-$relative R$\acute{e}$nyi entropy
• Quantifying coherence in terms of the pure-state coherence
• Maximum Relative Entropy of Coherence for Quantum Channels
• Average coherence and its typicality for random mixed quantum states
• Coherence generating power of unitary transformations via probabilistic average
• Inequivalent Multipartite Coherence Classes and New Coherence Monotones
• Coherence and complementarity based on modified generalized skew information
• Examining the validity of Schatten-$p$-norm-based functionals as coherence measures
• Average skew information-based coherence and its typicality for random quantum states
• Generalized coherence vector applied to coherence transformations and quantifiers
• Geometry of skew information-based quantum coherence
• The Average Quantum Coherence of Pure State Decomposition
• Relating relative Rényi entropies and Wigner-Yanase-Dyson skew information to generalized multiple quantum coherences
• Average of uncertainty-product for bounded observables

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