SLOCC Convertibility between Two-Qubit States

Details SLOCC Convertibility between Two-Qubit States SLOCC Convertibility between Two-Qubit States

2007-10-29

arxiv.org/abs/0710.5350v2

Physical Review A, vol. 77, art. 012332 (2008)

Physics

Quantum Physics

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

Scientific paper

10.1103/PhysRevA.77.012332

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.

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