Periodic and discrete Zak bases

Weyl's displacement operators for position and momentum commute if the product of the elementary displacements equals Planck's constant. Then, their common eigenstates constitute the Zak basis, each state specified by two phase parameters. Upon enforcing a periodic dependence on the phases, one gets a one-to-one mapping of the Hilbert space on the line onto the Hilbert space on the torus. The Fourier coefficients of the periodic Zak bases make up the discrete Zak bases. The two bases are mutually unbiased. We study these bases in detail, including a brief discussion of their relation to Aharonov's modular operators, and mention how they can be used to associate with the single degree of freedom of the line a pair of genuine qubits.Comment: 15 pages, 3 figures; displayed abstract is shortened, see the paper for the complete abstrac

Introduction

This special issue of IJQI marks a year since the passing away of Asher Peres. It is a sad honor to be its editors. Eighteen papers from his friends and colleagues represent different (but by no means all) areas of quantum physics that Asher was interested in and left his mark.3 page(s

Inadequacy of a classical interpretation of quantum projective measurements via Wigner functions

10.1103/PhysRevA.79.014104Physical Review A - Atomic, Molecular, and Optical Physics791-PLRA

Choice of Measurement as the Signal

10.1103/PhysRevLett.110.260502Physical Review Letters11026-PRLT