Comparison of the relative entropy of entanglement and negativity

Abstract

It is well known that for two qubits the upper bounds of the relative entropy of entanglement (REE) for a given concurrence as well as the negativity for a given concurrence are reached by pure states. We show that, by contrast, there are two-qubit mixed states for which the REE for some range of a fixed negativity is higher than that for pure states. Moreover, we demonstrate that a mixture of a pure entangled state and pure separable state orthogonal to it is likely to give the maximal REE. By noting that the negativity is a measure of entanglement cost under operations preserving positivity of partial transpose, our results provide an explicit example of operations such that, even though the entanglement cost for an exact preparation is the same, the entanglement of distillation of a mixed state can exceed that of pure states. This means that the entanglement manipulation via a pure state can result in a larger entanglement loss than that via a mixed state.

arXiv comment8 pages, 3 figures

References in corpus (22)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Separability of Mixed States: Necessary and Sufficient Conditions
• Quantifying Entanglement
• Entanglement Measures and Purification Procedures
• On the volume of the set of mixed entangled states
• Entanglement Measures under Symmetry
• Distinguishing separable and entangled states
• A comparison of entanglement measures
• The entanglement cost under operations preserving the positivity of partial transpose
• Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
• A comparison of the entanglement measures negativity and concurrence
• The asymptotic relative entropy of entanglement
• Ordering two-qubit states with concurrence and negativity
• A comparative study of relative entropy of entanglement, concurrence and negativity
• Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant States
• Closed formula for the relative entropy of entanglement
• Binegativity and geometry of entangled states in two qubits
• Analytical formula connecting entangled state and the closest disentangled state
• Quantification of entanglement by means of convergent iterations

Cited by in corpus (13)

• Trace-distance measure of coherence
• Entanglement estimation from Bell inequality violation
• Quantum steering ellipsoids, extremal physical states and monogamy
• 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
• Connection among entanglement, mixedness and nonlocality in a dynamical context
• Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
• Increasing relative nonclassicality quantified by standard entanglement potentials by dissipation and unbalanced beam splitting
• Quantum correlations of two-qubit states with one maximally mixed marginal
• Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix
• The intrinsic relations of quantum resources in multiparticle systems
• Monogamous property of generalized W states in three-qubit systems in terms of relative entropy of entanglement
• Relative Entropy of Entanglement for Two-Qubit State with $z$-directional Bloch Vectors