Expanding Hermitian operators in a basis of projectors on coherent spin states

S. Weigert

doi:10.1088/1464-4266/6/12/001

Expanding Hermitian operators in a basis of projectors on coherent spin states

S. Weigert

Mathematics

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

Abstract

The expectation values of a Hermitian operator (A) over cap in (2s + 1)(2) specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other set of (2s + 1)(2) coherent state projectors also provide a basis for self-adjoint operators. This is proved by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamiltonian of a fictitious classical spin system. The result guarantees that (almost) any experimentally desirable choice of directions is appropriate for reconstructing the state of a quantum spin by means of a Stem-Gerlach apparatus.

Original language	English
Pages (from-to)	489-490
Number of pages	1
Journal	Journal of Optics B: Quantum and Semiclassical Optics
Volume	6
Issue number	12
DOIs	https://doi.org/10.1088/1464-4266/6/12/001
Publication status	Published - Dec 2004

Bibliographical note

Keywords

state reconstruction
quorum
coherent states
density matrix

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10.1088/1464-4266/6/12/001

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Cite this

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title = "Expanding Hermitian operators in a basis of projectors on coherent spin states",

abstract = "The expectation values of a Hermitian operator (A) over cap in (2s + 1)(2) specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other set of (2s + 1)(2) coherent state projectors also provide a basis for self-adjoint operators. This is proved by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamiltonian of a fictitious classical spin system. The result guarantees that (almost) any experimentally desirable choice of directions is appropriate for reconstructing the state of a quantum spin by means of a Stem-Gerlach apparatus.",

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T1 - Expanding Hermitian operators in a basis of projectors on coherent spin states

AU - Weigert, S.

PY - 2004/12

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N2 - The expectation values of a Hermitian operator (A) over cap in (2s + 1)(2) specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other set of (2s + 1)(2) coherent state projectors also provide a basis for self-adjoint operators. This is proved by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamiltonian of a fictitious classical spin system. The result guarantees that (almost) any experimentally desirable choice of directions is appropriate for reconstructing the state of a quantum spin by means of a Stem-Gerlach apparatus.

AB - The expectation values of a Hermitian operator (A) over cap in (2s + 1)(2) specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other set of (2s + 1)(2) coherent state projectors also provide a basis for self-adjoint operators. This is proved by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamiltonian of a fictitious classical spin system. The result guarantees that (almost) any experimentally desirable choice of directions is appropriate for reconstructing the state of a quantum spin by means of a Stem-Gerlach apparatus.

KW - state reconstruction

KW - quorum

KW - coherent states

KW - density matrix

U2 - 10.1088/1464-4266/6/12/001

DO - 10.1088/1464-4266/6/12/001

M3 - Article

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SP - 489

EP - 490

JO - Journal of Optics B: Quantum and Semiclassical Optics

JF - Journal of Optics B: Quantum and Semiclassical Optics

IS - 12

ER -