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15 p, 532.3 KB Implementing unitary 2-designs using random diagonal-unitary matrices / Nakata, Yoshifumi (Leibniz Universität Hannover) ; Hirche, Christoph (Leibniz Universität Hannover) ; Morgan, Ciara (Leibniz Universität Hannover) ; Winter, Andreas (Universitat Autònoma de Barcelona. Departament de Física)
Unitary 2-designs are random unitary matrices which, in contrast to their Haar-distributed counterparts, have been shown to be efficiently realized by quantum circuits. Most notably, unitary 2-designs are known to achieve decoupling, a fundamental primitive of paramount importance in quantum Shannon theory. [...]
Dagstuhl : Leibniz-Zentrum fuer Informatik, 2015 (Leibniz International Proceedings in Informatics (LIPIcs) ; 44) - 10.4230/LIPIcs.TQC.2015.191
10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015), 2015, p. 191-205  
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16 p, 581.4 KB Decoupling with random diagonal unitaries / Nakata, Yoshifumi (Universitat Autònoma de Barcelona. Departament de Física) ; Hirche, Christoph (Universitat Autònoma de Barcelona. Departament de Física) ; Morgan, Ciara (Universität Leipzig (1991- ). Institut für Theoretische Physik) ; Winter, Andreas (Universitat Autònoma de Barcelona. Departament de Física)
We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with repeated applications of random unitaries diagonal in the Pauli-Z and -X bases. [...]
2017 - 10.22331/q-2017-07-21-18
Quantum, Vol. 1 (2017) , p. 18  

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