Discrete Q- and P-symbols for spin s

Jean-Pierre Amiet; S. Weigert

doi:10.1088/1464-4266/2/2/309

Discrete Q- and P-symbols for spin s

Jean-Pierre Amiet, S. Weigert

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	118-121
Number of pages	3
Journal	Journal of Optics B: Quantum and Semiclassical Optics
Volume	2
Issue number	2
DOIs	https://doi.org/10.1088/1464-4266/2/2/309
Publication status	Published - Apr 2000

Bibliographical note

Keywords

discrete phase-space representation

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10.1088/1464-4266/2/2/309

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Cite this

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title = "Discrete Q- and P-symbols for spin s",

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.",

keywords = "discrete phase-space representation",

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T1 - Discrete Q- and P-symbols for spin s

AU - Amiet, Jean-Pierre

AU - Weigert, S.

PY - 2000/4

Y1 - 2000/4

N2 - 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.

AB - 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.

KW - discrete phase-space representation

U2 - 10.1088/1464-4266/2/2/309

DO - 10.1088/1464-4266/2/2/309

M3 - Article

SN - 1464-4266

VL - 2

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EP - 121

JO - Journal of Optics B: Quantum and Semiclassical Optics

JF - Journal of Optics B: Quantum and Semiclassical Optics

IS - 2

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