Dynamics of cohering and decohering power under Markovian channels

Abstract

In this paper, we investigate the cohering and decohering power for the one-qubit Markovian channels with respect to coherence in terms of the $l_1$-norm, the R$\acute{e}$nyi $\alpha$-relative entropy and the Tsallis $\alpha$-relative entropy. In the case of $\alpha =2$, the cohering and decohering power of the amplitude damping channel, the phase damping channel, the depolarizing channel, and the flip channels under the three measures of coherence are calculated analytically. The decohering power on the $x,y,z$ basis referring to the amplitude damping channel, the phase damping channel, the flip channel for every measure we investigated is equal. This property also happens in the cohering power of the phase damping channel, the depolarizing channel, and the flip channels. However, the decohering power of the depolarizing channel is independent to the reference basis, and the cohering power of the amplitude damping channel on the $x,y$ basis is different to that on the $z$ basis.

arXiv comment11 pages, 4 figures.Because the picture is too big, this paper makes some delation. Formally submitted version is slightly different to this paper

References in corpus (26)

• Quantifying Coherence
• Operational Resource Theory of Coherence
• Measuring Quantum Coherence with Entanglement
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• The second laws of quantum thermodynamics
• Robustness of coherence: An operational and observable measure of quantum coherence
• Observable measure of quantum coherence in finite dimensional systems
• Frozen Quantum Coherence
• Quantum coherence in multipartite systems
• Low-temperature thermodynamics with quantum coherence
• Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences
• Trace-distance measure of coherence
• The Fidelity and Trace Norm Distances for Quantifying Coherence
• Duality of Quantum Coherence and Path Distinguishability
• Conditions for coherence transformations under incoherent operations
• Quantum-coherence quantifiers based on the Tsallis relative $\alpha$-entropies
• Complementarity relations for quantum coherence
• Cohering and de-cohering power of quantum channels
• Measure-Independent Freezing of Quantum Coherence
• Thermodynamic resource theories, non-commutativity and maximum entropy principles
• Energy Cost of Creating Quantum Coherence
• Measures of coherence generating power for quantum unital operations
• Coherence non-generating channels
• Ordering states with coherence measures
• Coherence breaking channels and coherence sudden death
• Quantifying the coherence of pure quantum states