Discrete Q- and P-symbols for spin s

Amiet, Jean-Pierre and Weigert, S. (2000) Discrete Q- and P-symbols for spin s. Journal of Optics B: Quantum and Semiclassical Optics. pp. 118-121. ISSN 1464-4266

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Abstract

Non-orthogonal bases of projectors on coherent states are introduced to expand Hermitean operators acting on the Hilbert space of a spin s. It is shown that the expectation values of a Hermitean operator (A) over cap in a family of (2s + 1)(2) spin-coherent states determine the operator unambiguously. In other words, knowing the Q-symbol of (A) over cap at (2s + 1)(2) points on the unit sphere is already sufficient in order to recover the operator. This provides a straightforward method to reconstruct the mixed state of a spin since its density matrix is explicitly parametrized in terms of expectation values. Furthermore, a discrete P-symbol emerges naturally which is related to a basis dual to the original one.

Item Type:	Article
Copyright, Publisher and Additional Information:	© 2000 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Optics B: Quantum and Semiclassical Optics.
Keywords:	discrete phase-space representation
Academic Units:	The University of York > Mathematics (York)
Depositing User:	Repository Officer
Date Deposited:	22 Jun 2006
Last Modified:	19 Feb 2013 12:07
Published Version:	http://dx.doi.org/10.1088/1464-4266/2/2/309
Status:	Published
Refereed:	Yes
Related URLs:	http://www-users.york.ac.uk/~slow500/Pub... http://dx.doi.org/10.1088/1464-4266/2/2/...
URI:	http://eprints.whiterose.ac.uk/id/eprint/1357

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