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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.
We define quantum phase in terms of inverses of annihilation and creation operators. We show that like Susskind - Glogower phase operators, the measured phase operators and the unitary phase operators can be defined in terms of the inverse operators.
This paper explains some fundamental ideas of {em feedback} control of quantum systems through the study of a relatively simple two-level system coupled to optical field channels. The model for this system includes both continuous and impulsive dynam
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting eigenvalue di
We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In particular
This paper is concerned with the concept of {em information state} and its use in optimal feedback control of classical and quantum systems. The use of information states for measurement feedback problems is summarized. Generalization to fully quantu