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Spin flip of multiqubit states in discrete phase space. (English) Zbl 1360.81104

Summary: Time reversal and spin flip are discrete symmetry operations of substantial importance to quantum information and quantum computation. Spin flip arises in the context of separability, quantification of entanglement and the construction of universal NOT gates. The present work investigates the relationship between the quantum state of a multiqubit system represented by the discrete Wigner function (DWFs) and its spin-flipped counterpart. The two are shown to be related through a Hadamard matrix that is independent of the choice of the quantum net used for the tomographic reconstruction of the DWF. These results are of interest to cases involving the direct tomographic reconstruction of the DWF from experimental data, and in the analysis of entanglement related properties purely in terms of the DWF.

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81P40 Quantum coherence, entanglement, quantum correlations
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81P68 Quantum computation
15B34 Boolean and Hadamard matrices
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