SLOCC Convertibility between Two-Qubit States

Abstract

In this paper we classify the four-qubit states that commute with $U\otimes U\otimes V\otimes V$, where $U$ and $V$ are arbitrary members of the Pauli group. We characterize the set of separable states for this class, in terms of a finite number of entanglement witnesses. Equivalently, we characterize the two-qubit, Bell-diagonal-preserving, completely positive maps that are separable. These separable completely positive maps correspond to protocols that can be implemented with stochastic local operations assisted by classical communication (SLOCC). This allows us to derive a complete set of SLOCC monotones for Bell-diagonal states, which, in turn, provides the necessary and sufficient conditions for converting one two-qubit state to another by SLOCC.

8 pages, 3 figures; this is Ref.[13] in eprint quant-ph/0703268. Changes made since last version: typos in Eq (5) corrected; Fig 2 and Fig 3 replaced; references updated

References in corpus (20)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Three qubits can be entangled in two inequivalent ways
• Concentrating Partial Entanglement by Local Operations
• Entanglement of a Pair of Quantum Bits
• Entanglement Measures and Purification Procedures
• Quantum Nonlocality without Entanglement
• Conditions for a class of entanglement transformations
• Entanglement monotones
• Entanglement Measures under Symmetry
• Bell's inequalities and density matrices. Revealing hidden nonlocality.
• A complete family of separability criteria
• Entanglement of pure states for a single copy
• Distinguishing separable and entangled states
• Entangling operations and their implementation using a small amount of entanglement
• Local filtering operations on two qubits
• Separability properties of tripartite states with UxUxU-symmetry
• Optimal Entanglement Enhancement for Mixed States
• The Lorentz singular value decomposition and its applications to pure states of 3 qubits
• Local transformation of mixed states of two qubits to Bell diagonal states

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• Matrix Pencils and Entanglement Classification
• Center-of-mass interpretation for bipartite purity analysis of $N$-party entanglement
• Effect of weak measurement on entanglement distribution over noisy channels
• Complete analysis of measurement-induced entanglement localization on a three-photon system
• Correlations, Bell Inequality Violation & Quantum Entanglement
• The entangling power of non-entangling channels