Binegativity and geometry of entangled states in two qubits

Abstract

We prove that the binegativity is always positive for any two-qubit state. As a result, as suggested by the previous works, the asymptotic relative entropy of entanglement in two qubits does not exceed the Rains bound, and the PPT-entanglement cost for any two-qubit state is determined to be the logarithmic negativity of the state. Further, the proof reveals some geometrical characteristics of the entangled states, and shows that the partial transposition can give another separable approximation of the entangled state in two qubits.

5 pages, 3 figures. I made the proof more transparent

References in corpus (18)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Quantifying Entanglement
• Bell Inequalities and the Separability Criterion
• Optimization of entanglement witnesses
• Information-theoretic aspects of quantum inseparability of mixed states
• The entanglement cost under operations preserving the positivity of partial transpose
• Detection of entanglement with few local measurements
• Quantum inseparability as local pseudomixture
• Separability and entanglement of composite quantum systems
• Local filtering operations on two qubits
• A comparison of the entanglement measures negativity and concurrence
• Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant States
• On the geometry of entangled states
• Separable approximation for mixed states of composite quantum systems
• Local transformation of mixed states of two qubits to Bell diagonal states

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• Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states
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• Negativity as a counter of entangled dimensions
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• Multi-particle entanglement manipulation under positive partial transpose preserving operations
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• $\alpha$-Logarithmic negativity
• Experimental measurement of the collectibility of two-qubit states
• Decoherence of two maximally entangled qubits in a lossy nonlinear cavity
• Entanglement detection in arbitrary dimensional bipartite quantum systems through partial realigned moments
• Direct method for measuring and witnessing quantum entanglement of arbitrary two-qubit states through Hong-Ou-Mandel interference
• Progress towards a unified approach to entanglement distribution
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
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• Entanglement and quantum state geometry of spin system with all-range Ising-type interaction
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• Exact entanglement cost of quantum states and channels under PPT-preserving operations
• Geometry and speed of evolution for a spin-s system with long-range zz-type Ising interaction
• Generalized Two-Qubit Whole and Half Hilbert-Schmidt Separability Probabilities
• Hierarchy of correlation quantifiers comparable to negativity
• Computable entanglement cost under positive partial transpose operations
• Geometrically induced singular behavior of entanglement
• Binegativity of two qubits under noise
• Strong monotonicity in mixed-state entanglement manipulation
• Resource-efficient quantum correlation measurements via multicopy neural network methods
• The binegativity of two qubits