Positive P-Representations of the Thermal Operator from Quantum Control Theory

Details Positive P-Representations of the Thermal Operator from Quantum Control Theory Positive P-Representations of the Thermal Operator from Quantum Control Theory

2004-01-27

arxiv.org/abs/quant-ph/0401165v1

Physics

Quantum Physics

submitted to Phys. Rev. Lett

Scientific paper

A positive P-representation for the spin-j thermal density matrix is given in closed form. The representation is constructed by regarding the wave function as the internal state of a closed-loop control system. A continuous interferometric measurement process is proved to einselect coherent states, and feedback control is proved to be equivalent to a thermal reservoir. Ito equations are derived, and the P-representation is obtained from a Fokker-Planck equation. Langevin equations are derived, and the force noise is shown to be the Hilbert transform of the measurement noise. The formalism is applied to magnetic resonance force microscopy (MRFM) and gravity wave (GW) interferometry. Some unsolved problems relating to drift and diffusion on Hilbert spaces are noted.

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