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 in a family of (2s+1)(2s+1) spin-coherent states determine the operator unambiguously. In other words, knowing the Q-symbol of A at (2s+1)(2s+1) 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.

6 pages, Latex2e

References in corpus (2)

• Quantum Time Evolution in Terms of Nonredundant Expectation Values
• Reconstructing the density matrix of a spin s through Stern-Gerlach measurements (II)

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