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Physical Review Letters

Quantum-State Tomography and Discrete Wigner Function

Ulf Leonhardt

Published May 22, 1995• 276 citations
Publisher

Abstract

A tomographical scheme is proposed to infer the quantum states of finite–dimensional systems from experiments. For this a new discrete Wigner formalism is developed.Received 3 January 1995DOI:https://doi.org/10.1103/PhysRevLett.74.4101©1995 American Physical Society

DOI
10.1103/physrevlett.74.4101

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A tomographical scheme is proposed to infer the quantum states of finite–dimensional systems from experiments. For this a new discrete Wigner formalism is developed.Received 3 January 1995DOI:https://doi.org/10.1103/PhysRevLett.74.4101©1995 American Physical Society
The theory of discrete Wigner functions and of discrete quantum-state tomography [U. Leonhardt, Phys. Rev. Lett. 74, 4101 (1995)] is studied in more detail guided by the picture of precession tomography. Odd- and even-dimensional systems (angular momenta and spins, bosons, and fermions) are considered separately. Relations between simple number theory and the quantum mechanics of finite-dimensional systems are pointed out. In particular, the multicomplementarity of the precession states distinguishes prime dimensions from composite ones. \textcopyright{} 1996 The American Physical Society.