Partial coherence versus entanglement
arXiv:2302.01760 · doi:10.1103/PhysRevA.108.012416
Abstract
We study partial coherence and its connections with entanglement. First, we provide a sufficient and necessary condition for bipartite pure state transformation under partial incoherent operations: A bipartite pure state can be transformed to another one if and only if a majorization relationship holds between their partial coherence vectors. As a consequence, we introduce the concept of maximal partial coherent states in the sense that they can be used to construct any bipartite state of the same system via partial incoherent operations. Second, we provide a strategy to construct measures of partial coherence by the use of symmetric concave functions. Third, we establish some relationships between partial coherence and entanglement. We show that the minimal partial coherence under local unitary operations is a measure of entanglement for bipartite pure states, which can be extended to all mixed states by convex-roof. We also show that partial coherence measures are induced through maximal entanglement under partial incoherent operations for bipartite pure states. There is a one-to-one correspondence between entanglement and partial coherence measures.
arXiv comment12 pages, 2 figures, 1 table
References in corpus (47)
- Quantum entanglement
- Introducing Quantum Discord
- Quantifying Coherence
- Bell nonlocality
- Classical, quantum and total correlations
- Quantum Coherence as a Resource
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Operational Resource Theory of Coherence
- Measuring Quantum Coherence with Entanglement
- Entanglement monotones
- Quantum Steering
- Robustness of coherence: An operational and observable measure of quantum coherence
- Observable measure of quantum coherence in finite dimensional systems
- Converting Coherence to Quantum Correlations
- Intrinsic randomness as a measure of quantum coherence
- Entanglement-assisted local manipulation of pure quantum states
- Trace-distance measure of coherence
- Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
- The Fidelity and Trace Norm Distances for Quantifying Coherence
- Duality of Quantum Coherence and Path Distinguishability
- Relations between coherence and path information
- Max- relative entropy of coherence: an operational coherence measure
- Conditions for coherence transformations under incoherent operations
- Quantum-coherence quantifiers based on the Tsallis relative -entropies
- Converting Nonclassicality into Entanglement
- Alternative framework for quantifying coherence
- Measuring Coherence with Entanglement Concurrence
- Operational one-to-one mapping between coherence and entanglement measures
- Entanglement and coherence in quantum state merging
- Geometric lower bound for a quantum coherence measure
- Structure of the resource theory of quantum coherence
- Maximally coherent states and coherence-preserving operations
- On the Role of Coherence in Shor's Algorithm
- Catalytic coherence transformations
- Extracting quantum coherence via steering
- Family of coherence measures and duality between quantum coherence and path distinguishability
- Coherence, Quantum Fisher Information, Superradiance and Entanglement are Interconvertible Resources
- Entanglement and superposition are equivalent concepts in any physical theory
- Partial coherence and quantum correlation with fidelity and affinity distances
- Interrelation between Partial Coherence and Quantum Correlations
- Quantum Coherence: Reciprocity and Distribution
- Protocol for unambiguous quantum state discrimination using quantum coherence
- Quantifying dynamical coherence with coherence measures
- Converting coherence based on positive-operator-valued measures into entanglement
- Anomalies of weight-based coherence measure and mixed maximally coherent states
- Characterizing entanglement using quantum discord over state extensions
- Coherence of assistance and assisted maximally coherent states