Stefan Weigert 2004 J. Opt. B: Quantum Semiclass. Opt. 6 489 doi:10.1088/1464-4266/6/12/001
Expanding Hermitian operators in a basis of projectors on coherent spin states
Stefan Weigert
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Hu|MP
—Hull Mathematical Physics, Department of Mathematics, University of Hull, Hull
HU6 7RX,
UK
The expectation values of a Hermitian operator 
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 Stern–Gerlach apparatus.
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Issue 12 (December 2004)
Received 1 September 2004, accepted for publication 7 October 2004
Published 15 October 2004
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Expanding Hermitian operators in a basis of projectors on coherent spin states
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