Generalized entropic measures of quantum correlations

Abstract

We propose a general measure of non-classical correlations for bipartite systems based on generalized entropic functions and majorization properties. Defined as the minimum information loss due to a local measurement, in the case of pure states it reduces to the generalized entanglement entropy, i.e., the generalized entropy of the reduced state. However, in the case of mixed states it can be non-zero in separable states, vanishing just for states diagonal in a general product basis, like the Quantum Discord. Simple quadratic measures of quantum correlations arise as a particular case of the present formalism. The minimum information loss due to a joint local measurement is also discussed. The evaluation of these measures in a few simple relevant cases is as well provided, together with comparison with the corresponding entanglement monotones.

9 pages, 2 figures

References in corpus (34)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• A computable measure of entanglement
• Introducing Quantum Discord
• Concentrating Partial Entanglement by Local Operations
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Efficient classical simulation of slightly entangled quantum computations
• Classical, quantum and total correlations
• Quantum discord and the power of one qubit
• The Role of Relative Entropy in Quantum Information Theory
• Conditions for a class of entanglement transformations
• On the Power of One Bit of Quantum Information
• Experimental quantum computing without entanglement
• Universal state inversion and concurrence in arbitrary dimensions
• Unified View of Quantum and Classical Correlations
• Entanglement monotones
• On the role of entanglement in quantum computational speed-up
• Information-theoretic aspects of quantum inseparability of mixed states
• Classical Correlation and Quantum Discord in Critical Systems
• Almost all quantum states have non-classical correlations
• Entanglement and the Power of One Qubit
• Vanishing quantum discord is necessary and sufficient for completely positive maps
• Separable states are more disordered globally than locally
• Classical Correlations and Entanglement in Quantum Measurements
• Largest separable balls around the maximally mixed bipartite quantum state
• I-concurrence and tangle for isotropic states
• Signatures of non-classicality in mixed-state quantum computation
• Tsallis entropy and entanglement constraints in multi-qubit systems
• Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality
• Separable balls around the maximally mixed multipartite quantum states
• Entanglement for rank-2 mixed states
• Generalized non-additive entropies and quantum entanglement
• Generalized entropic criterion for separability
• Violation of majorization relations in entangled states and its detection by means of generalized entropic forms

Cited by in corpus (35)

• The classical-quantum boundary for correlations: discord and related measures
• Layer aggregation and reducibility of multilayer interconnected networks
• Measures and applications of quantum correlations
• Quantum discord for general two--qubit states: Analytical progress
• Are general quantum correlations monogamous?
• Observable measure of bipartite quantum correlations
• Interplay between computable measures of entanglement and other quantum correlations
• Factorization and Criticality in the Anisotropic XY Chain via Correlations
• Quantifying non-classicality with local unitary operations
• Nonclassical correlations in continuous-variable non-Gaussian Werner states
• System-time entanglement in a discrete time model
• Characterizing quantumness via entanglement creation
• Decoherence dynamics of geometric measure of quantum discord and measurement-induced nonlocality for noninertial observers at finite temperature
• Bayes' rule, generalized discord, and nonextensive thermodynamics
• Measurements, quantum discord and parity in spin 1 systems
• Quantum correlations and least disturbing local measurements
• Entanglement of two harmonic modes coupled by angular momentum
• Weak quantum discord
• Bipartite separability of one parameter families of states using conditional quantum relative Tsallis entropy
• One-body information loss in fermion systems
• Unified entropic measures of quantum correlations induced by local measurements
• Generalized conditional entropy optimization for qudit-qubit states
• Generalized conditional entropy in bipartite quantum systems
• Quantum discord and information deficit in spin chains
• Generalised monogamy relation of convex-roof extended negativity in multi-level systems
• Entanglement and coherence in a spin-s XXZ system under non-uniform fields
• Theoretical insights on measuring quantum correlations
• Quantum correlations from classically correlated states
• Natural information measures in Cox' approach for contextual probabilistic theories
• Complexity of the XY antiferromagnet at fixed magnetization
• Approximation, Proof Systems, and Correlations in a Quantum World
• Behavior of quantum correlations under nondissipative decoherence by means of the correlation matrix
• Conditional states and entropy in qudit-qubit systems
• Conditional purity and quantum correlation measures in two qubit mixed states
• Shareability of Quantum Correlations in a Many-Body Spin System with Two- and Three-Body Interactions