A comparative study of relative entropy of entanglement, concurrence and negativity

Abstract

The problem of ordering of two-qubit states imposed by relative entropy of entanglement (E) in comparison to concurrence (C) and negativity (N) is studied. Analytical examples of states consistently and inconsistently ordered by the entanglement measures are given. In particular, the states for which any of the three measures imposes order opposite to that given by the other two measures are described. Moreover, examples are given of pairs of the states, for which (i) N'=N'' and C'=C'' but E' is different from E'', (ii) N'=N'' and E'=E'' but C' differs from C'', (iii) E'=E'', N'<N'' and C'>C'', or (iv) states having the same E, C, and N but still violating the Bell-Clauser-Horne-Shimony-Holt inequality to different degrees.

8 pages, 7 figures, final version

References in corpus (2)

• Ordering two-qubit states with concurrence and negativity
• Binegativity and geometry of entangled states in two qubits

Cited by in corpus (44)

• Trace-distance measure of coherence
• A classification of entanglement in three-qubit systems
• Quantifying entanglement resources
• Entanglement estimation from Bell inequality violation
• Universal observable detecting all two-qubit entanglement and determinant based separability tests
• Two-qubit mixed states more entangled than pure states: Comparison of the relative entropy of entanglement for a given nonlocality
• Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states
• Multiphoton blockades in pulsed regimes beyond the stationary limits
• Connection among entanglement, mixedness and nonlocality in a dynamical context
• Analysis of Entanglement Measures and LOCC Maximized Quantum Fisher Information of General Two Qubit Systems
• Closed formula for the relative entropy of entanglement
• Generation of Fock states and qubits in periodically pulsed nonlinear oscillator
• Drawbacks of the use of fidelity to assess quantum resources
• An Introduction to Quantum Entanglement: a Geometric Approach
• Increasing relative nonclassicality quantified by standard entanglement potentials by dissipation and unbalanced beam splitting
• Entanglement swapping and swapped entanglement
• Ordering states with coherence measures
• Pearson Correlation Coefficient as a measure for Certifying and Quantifying High Dimensional Entanglement
• Comparison of the relative entropy of entanglement and negativity
• Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix
• Partial transpose as a direct link between concurrence and negativity
• Analytical progress on symmetric geometric discord: Measurement-based upper bounds
• On two-qubit states ordering with quantum discords
• Strongly entangled light from planar microcavities
• Bistability and chaos at low-level of quanta
• Experimental hierarchy of two-qubit quantum correlations without state tomography
• Selective entanglement breaking
• Bell violation versus geometric measure of quantum discord and their dynamical behavior
• Towards an Entanglement Measure for Mixed States in CFTs Based on Relative Entropy
• The intrinsic relations of quantum resources in multiparticle systems
• Tomography, Control and Characterization of Entanglement in Three level Atomic System
• Squeezing in multi-mode nonlinear optical state truncation
• Hierarchy of correlation quantifiers comparable to negativity
• Correlation function and mutual information
• Characteristics and benchmarks of entanglement of mixed states -- the two qubit case
• Upper bounds for relative entropy of entanglement based on active learning
• Experimental relative entanglement potentials of single-photon states
• Quantum discord of 2n-dimensional Bell-diagonal states
• Witnessing random unitary and projective quantum channels: Complementarity between separable and maximally entangled states
• Manipulation of Multipartite Entanglement in an Array of Quantum Dots
• Gain-modified emission dynamics between two quantum emitters in a plasmonic gain cavity system
• Global and short-range entanglement properties in excited, many-body localized spin chains
• Study on Entanglement and its Utility in Information Processing
• Detecting Entanglement by Pure Bosonic Extension