Experimental realization of generalized qubit measurements based on quantum walks

Abstract

We report an experimental implementation of a single-qubit generalized measurement scenario, the positive-operator valued measure (POVM), based on a quantum walk model. The qubit is encoded in a single-photon polarization. The photon performs a quantum walk on an array of optical elements, where the polarization-dependent translation is performed via birefringent beam displacers and a change of the polarization is implemented with the help of wave plates. We implement: (i) trine POVM, i.e., the POVM elements uniformly distributed on an equatorial plane of the Bloch sphere; (ii) symmetric-informationally-complete (SIC) POVM; and (iii) unambiguous discrimination of two nonorthogonal qubit states.

Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

“…This makes them valuable in quantum search algorithms [2] or even for general quantum computing [3]. Experiments on quantum walks range from realizations on trapped ions [4][5][6], to cold atoms in optical lattices [7][8][9], to light on an optical table [10][11][12][13][14][15], but there have been many other experimental proposals [16,17].…”

Pre- and post-selection paradoxes in quantum walks

“…In this subsection we propose an experiment implementing a version of scenario 2 discussed above. We base on a linear optical quantum walk implementation in which a single photon jumps from one optical path to another and the photon's polarization plays the role of the coin (see for example [39,40]). The main component of the setup is a sequence of calcite beam displacers that allow a photon to jump between neighbouring paths.…”

“…Schematic representation of the DTQW evolution on a 7-cycle for the initial state preñ |(40). For example, for t=0 the expresion x=1 denotes that pre 0 ñ | ( ) contains the term 1ñ Ä ñ + ¬ñ | contains the term 7ñ Ä -ñ + ¬ñ | ( | | ), etc.…”

Quantum walk as generalized evolution and measurement device

“…x is the coin flip operator with C(x, t) the qubit operation applied to the coin state at position x in t-th step. The probability distribution of finding the walker in position space cannot be reproduced by its classical counterpart, which makes it widely used in designing quantum algorithms and simulate various quantum dynamics [8,32,33], and the dynamics of QW can be properly engineered by the coin operations which depend on both position and time-step, which makes QW an efficient platform for various quantum information processes including state transfer [34,35], qubit POVM [27][28][29] and our method for arbitrary evolution and POVM.…”

“…POVM can be realized via a number of systems [22][23][24][25][26]. Especially, Kurzyński and Wójcik proposed a universal method of realizing POVM for qubit system based on discrete-time QW [27][28][29]. In this paper, we initialize the QW in multi positions, which plays the role of a high dimensional system, and generalize the method of realizing arbitrary POVM of qubit system to the case of arbitrary dimensional systems.…”