The resource theory of coherence for quantum channels
arXiv:2006.15443 · doi:10.1007/s11128-020-02702-9
Abstract
We define the quantum-incoherent relative entropy of coherence ( REC) of quantum channels in the framework of the resource theory by using the Choi-Jamiolkowsky isomorphism. Coherence-breaking channels are introduced as free operations and their corresponding Choi states as free states. We also show the relationship between the coherence of channel and the quantum discord and find that basis-dependent quantum asymmetric discord can never be more than the REC for any quantum channels. {Also}, we prove the REC is decreasing for any divisible quantum incoherent channel and we also claim it can be considered as the quantumness of quantum channels. Moreover, we demonstrate that for qubit channels, the relative entropy of coherence (REC) can be equivalent to the REC of their corresponding Choi states and the basis-dependent quantum symmetric discord can never exceed the coherence.
arXiv comment13 pages, 2 figures
References in corpus (41)
- Quantum entanglement
- Mixed State Entanglement and Quantum Error Correction
- Advances in Quantum Metrology
- Introducing Quantum Discord
- Quantifying Coherence
- Bell nonlocality
- Quantum Coherence as a Resource
- Entanglement Measures and Purification Procedures
- Quantum Resource Theories
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Operational Resource Theory of Coherence
- Measuring Quantum Coherence with Entanglement
- Quantum Computers and Dissipation
- Reference frames, superselection rules, and quantum information
- Unified View of Quantum and Classical Correlations
- The Resource Theory of Quantum States Out of Thermal Equilibrium
- General Entanglement Breaking Channels
- The resource theory of quantum reference frames: manipulations and monotones
- Converting Coherence to Quantum Correlations
- Intrinsic randomness as a measure of quantum coherence
- The resource theory of informational nonequilibrium in thermodynamics
- The general structure of quantum resource theories
- Global Quantum Discord in Multipartite Systems
- Relating the Resource Theories of Entanglement and Quantum Coherence
- The Fidelity and Trace Norm Distances for Quantifying Coherence
- (Quantumness in the context of) Resource Theories
- Assisted distillation of quantum coherence
- Decoherence of quantum registers
- The ultimate precision limits for noisy frequency estimation
- Numerical approach for unstructured quantum key distribution
- Cohering and de-cohering power of quantum channels
- Resource Destroying Maps
- Coherence susceptibility as a probe of quantum phase transitions
- Quantum resource theories in the single-shot regime
- Coherence number as a discrete quantum resource
- Coherence breaking channels and coherence sudden death
- Complete positivity, finite temperature effects, and additivity of noise for time-local qubit dynamics
- Coherence of quantum channels
- Quantumness of quantum channels
- Coherence makes quantum systems 'magical'
- Time-invariant Discord: High Temperature Limit and Initial Environmental Correlations