Unifying approach to the quantification of bipartite correlations by Bures distance

Abstract

The notion of distance defined on the set of states of a composite quantum system can be used to quantify total, quantum and classical correlations in a unifying way. We provide new closed formulae for classical and total correlations of two-qubit Bell-diagonal states by considering the Bures distance. Complementing the known corresponding expressions for entanglement and more general quantum correlations, we thus complete the quantitative hierarchy of Bures correlations for Bell-diagonal states. We then explicitly calculate Bures correlations for two relevant families of states: Werner states and rank-2 Bell-diagonal states, highlighting the subadditivity which holds for total correlations with respect to the sum of classical and quantum ones when using Bures distance. Finally, we analyse a dynamical model of two independent qubits locally exposed to non-dissipative decoherence channels, where both quantum and classical correlations measured by Bures distance exhibit freezing phenomena, in analogy with other known quantifiers of correlations.

arXiv comment18 pages, 4 figures; published version

References in corpus (46)

• Quantum entanglement
• Introducing Quantum Discord
• Classical, quantum and total correlations
• Quantifying Entanglement
• The classical-quantum boundary for correlations: discord and related measures
• Necessary and sufficient condition for non-zero quantum discord
• Sudden Death of Entanglement
• Unified View of Quantum and Classical Correlations
• Identifying Topological Order by Entanglement Entropy
• Sudden transition between classical and quantum decoherence
• Characterizing Nonclassical Correlations via Local Quantum Uncertainty
• Experimental investigation of classical and quantum correlations under decoherence
• The problem with the geometric discord
• Dynamics of quantum correlations in two-qubit systems within non-Markovian environments
• Entanglement measures and the Hilbert-Schmidt distance
• Bures volume of the set of mixed quantum states
• Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence
• Environment-induced sudden transition in quantum discord dynamics
• Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
• Negativity of quantumness and its interpretations
• One-norm geometric quantum discord under decoherence
• Optical realization of optimal unambiguous discrimination for pure and mixed quantum states
• Geometric quantum discord with Bures distance
• Recovering Entanglement by Local Operations
• Hierarchies of Geometric Entanglement
• Hierarchy and dynamics of trace distance correlations
• Linking a distance measure of entanglement to its convex roof
• Unified view of correlations using the square norm distance
• Interplay between computable measures of entanglement and other quantum correlations
• Measuring bipartite quantum correlations of an unknown state
• Observation of environment-induced double sudden transitions in geometric quantum correlations
• Experimental distribution of entanglement with separable carriers
• Sudden change of quantum discord for a system of two qubits
• The quantumness of correlations revealed in local measurements exceeds entanglement
• Experimental entanglement activation from discord in a programmable quantum measurement
• Geometric quantum discord with Bures distance: the qubit case
• Emergence of the pointer basis through the dynamics of correlations
• Using Separable Bell-Diagonal States to Distribute Entanglement
• Manipulation of p-wave scattering of cold atoms in low dimensions using the magnetic field vector
• Geometric classical and total correlations via trace distance
• Frustration, Entanglement, and Correlations in Quantum Many Body Systems
• Universal aspects in the behavior of the entanglement spectrum in one dimension: scaling transition at the factorization point and ordered entangled structures
• The geometric approach to quantum correlations: Computability versus reliability
• Entanglement quantification by local unitaries
• Discord of response
• Thermal effects on the sudden changes and freezing of correlations between remote atoms in cavity QED network

Cited by in corpus (26)

• Measures and applications of quantum correlations
• Frozen Quantum Coherence
• Observation of time-invariant coherence in a room temperature quantum simulator
• Universal freezing of quantum correlations within the geometric approach
• The dynamics of local quantum uncertainty and trace distance discord for two-qubit X states under decoherence: a comparative study
• Relating the Bures measure to the Cauchy two-matrix model
• Trace-distance correlations for X states and emergence of the pointer basis in Markovian and non-Markovian regimes
• Geometric coherence and quantum state discrimination
• Universal evolution of non-classical correlations due to collective spontaneous emission
• Overcoming ambiguities in classical and quantum correlation measures
• Internal entanglement and external correlations of any form limit each other
• Effect of local filtering on Freezing Phenomena of Quantum Correlation
• Broadcasting of Quantum Correlations: Possibilities & Impossibilities
• Preparing tunable Bell-diagonal states on a quantum computer
• Influence of the external pressure on the quantum correlations of molecular magnets
• Enhancing the geometric quantum discord in the Heisenberg {\it XX} chain by Dzyaloshinsky-Moriya interaction
• Non-Markovianity through Multipartite Correlation Measures
• Scalable quantum computing model in the circuit-QED lattice with circulator function
• Characterizing nonclassical correlation using affinity
• Measurement - induced qudit geometric discord
• Hierarchy of correlation quantifiers comparable to negativity
• Existence of maximally correlated states
• Computing coherence vectors and correlation matrices, with application to quantum discord quantification
• Unified scheme for correlations using linear relative entropy
• Comparison of Perfect and Quasi Werner States
• A variational quantum algorithm for entanglement quantification