Two-party LOCC convertibility of quadpartite states and Kraus-Cirac number of two-qubit unitaries

Abstract

Nonlocal properties (globalness) of a non-separable unitary determine how the unitary affects the entanglement properties of a quantum state. We apply a given two-qubit unitary on a quadpartite system including two reference systems and analyze its "LOCC partial invertibility" under two-party LOCC. A decomposition given by Kraus and Cirac for two-qubit unitaries shows that the globalness is completely characterized by three parameters. Our analysis shows that the number of non-zero parameters (the Kraus-Cirac number) has an operational significance when converting entanglement properties of multipartite states. All two-qubit unitaries have the Kraus-Cirac number at most 3, while those with at most 1 or 2 are equivalent, up to local unitaries, to a controlled-unitary or matchgate, respectively. The presented operational framework distinguishes the untaries with the Kraus-Cirac number 2 and 3, which was not possible by the known measure of the operator Schmidt decomposition. We also analyze how the Kraus-Cirac number changes when two or more two-qubit unitaries are applied sequentially.

arXiv comment13 pages, 2 figures; accepted for publication in a special issue of Journal of Physics A, "50 years of Bell's theorem"; almost published version

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Cited by in corpus (4)

• Network coding for distributed quantum computation over cluster and butterfly networks
• Bipartite discrimination of independently prepared quantum states as a counterexample to a parallel repetition conjecture
• Gaining confidence on the correct realization of arbitrary quantum computations
• Synthesis and upper bound of Schmidt rank of the bipartite controlled-unitary gates