Partial coherence and quantum correlation with fidelity and affinity distances

Abstract

A fundamental task in any physical theory is to quantify certain physical quantity in a meaningful way. In this paper we show that both fidelity distance and affinity distance satisfy the strong contractibility, and the corresponding resource quantifiers can be used to characterize a large class of resource theories. Under two assumptions, namely, convexity of "free states" and closure of free states under "selective free operations", our general framework of resource theory includes quantum resource theories of entanglement, coherence, partial coherence and superposition. In partial coherence theory, we show that fidelity partial coherence of a bipartite state is equal to the minimal error probability of a mixed quantum state discrimination (QSD) task and vice versa, which complements the main result in [Xiong and Wu, J. Phys. A: Math. Theor. 51, 414005 (2018)]. We also compute the analytic expression of fidelity partial coherence for $(2,n)$ bipartite X-states. At last, we study the correlated coherence in the framework of partial coherence theory. We show that partial coherence of a bipartite state, with respect to the eigenbasis of a subsystem, is actually a measure of quantum correlation.

arXiv comment12 pages, major revision, references updated

References in corpus (44)

• Quantum entanglement
• Mixed State Entanglement and Quantum Error Correction
• Quantifying Coherence
• Entanglement detection
• Quantifying Entanglement
• Quantum Coherence as a Resource
• The classical-quantum boundary for correlations: discord and related measures
• Entanglement Measures and Purification Procedures
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Necessary and sufficient condition for non-zero quantum discord
• The Role of Relative Entropy in Quantum Information Theory
• Conditions for a class of entanglement transformations
• Operational Resource Theory of Coherence
• Measuring Quantum Coherence with Entanglement
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Quantum discord for two-qubit X-states
• Unknown Quantum States and Operations, a Bayesian View
• Unified View of Quantum and Classical Correlations
• Fundamental limitations for quantum and nano thermodynamics
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• The second laws of quantum thermodynamics
• Frozen Quantum Coherence
• Quantum coherence in multipartite systems
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• An improved bound on distillable entanglement
• Quantum Coherence via Skew Information and Its Polygamy
• Quantum discord and its allies: a review
• A rigorous treatment of distillable entanglement
• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• A Unified View of Quantum Correlations and Quantum Coherence
• A resource theory of superposition
• Channel Capacities versus Entanglement Measures in Multiparty Quantum States
• Geometric quantum discord with Bures distance
• Algebraic characterization of X-states in quantum information
• Linking a distance measure of entanglement to its convex roof
• Convex geometry of quantum resource quantification
• Minimum-error discrimination between symmetric mixed quantum states
• Quantum correlations and distinguishability of quantum states
• Family of coherence measures and duality between quantum coherence and path distinguishability
• Genuine Multipartite Entanglement Trends in Gapless-gapped Transitions of Quantum Spin Systems
• Entanglement as the symmetric portion of correlated coherence
• Von Neumann Measurement is Optimal for Detecting Linearly Independent Mixed Quantum States
• Interrelation between Partial Coherence and Quantum Correlations
• Geometric coherence and quantum state discrimination

Cited by in corpus (13)

• Quantum Discord for multiqubit Systems
• Affinity-based measurement-induced nonlocality and its robustness against noise
• Average skew information-based coherence and its typicality for random quantum states
• Wave-particle duality employing quantum coherence in superposition with non-orthogonal pointers
• Geometry of skew information-based quantum coherence
• Partial coherence versus entanglement
• Noncommutative coherence and quantum phase estimation algorithm
• Unambiguous state discrimination with intrinsic coherence
• Discrimination of Coherent States via Atom-Field Interaction without Rotation Wave Approximation
• Analytic Formulas for Quantum Discord of Special Families of N-Qubit States
• Imaginarity measures induced by real part states and the complementarity relations
• The uncertainty of quantum states with respect to the projective measurement
• Quantum partial coherence measures constructed from Fisher information