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arXiv · 1208.1800

Quantum walk as a generalized measuring device

Pawel Kurzynski·Antoni Wojcik
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Abstract

We show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of rank 1 and rank 2 POVM elements can be generated by a properly engineered quantum walk. In such a scenario the measurement of particle at position x=i corresponds to a measurement of a POVM element E_i on a qubit. We explicitly construct quantum walks implementing unambiguous state discrimination and SIC-POVM.

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Pawel Kurzynski, Antoni Wojcik. 2012-08-09. Quantum walk as a generalized measuring device. https://doi.org/10.1103/physrevlett.110.200404

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