TY - JOUR
T1 - Convertibility between two-qubit states using stochastic local quantum operations assisted by classical communication
AU - Liang, Yeong Cherng
AU - Masanes, Lluís
AU - Doherty, Andrew C.
PY - 2008/1/25
Y1 - 2008/1/25
N2 - In this paper we classify the four-qubit states that commute with U U V 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.
AB - In this paper we classify the four-qubit states that commute with U U V 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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U2 - 10.1103/PhysRevA.77.012332
DO - 10.1103/PhysRevA.77.012332
M3 - Article
AN - SCOPUS:38549132379
SN - 1050-2947
VL - 77
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 1
M1 - 012332
ER -