1208.1800 (Pawel Kurzynski et al.)

Quantum walk as a generalized measuring device    [PDF]

Pawel Kurzynski, Antoni Wojcik

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.

View original: http://arxiv.org/abs/1208.1800