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arXiv:0906.2101 · Journal of Physics A Mathematical and Theoretical

Quantum tomography, phase-space observables and generalized Markov kernels

Juha-Pekka Pellonpää

Published Oct 22, 2009• 7 citations
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Abstract

We construct a generalized Markov kernel which transforms the observable associated with the homodyne tomography into a covariant phase-space observable with a regular kernel state. Illustrative examples are given in the cases of a 'Schrödinger cat' kernel state and the Cahill–Glauber s -parametrized distributions. Also we consider an example of a kernel state when the generalized Markov kernel cannot be constructed.

DOI
10.1088/1751-8113/42/46/465303

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We construct a generalized Markov kernel which transforms the observable associated with the homodyne tomography into a covariant phase-space observable with a regular kernel state. Illustrative examples are given in the cases of a 'Schrödinger cat' kernel state and the Cahill–Glauber s -parametrized distributions. Also we consider an example of a kernel state when the generalized Markov kernel cannot be constructed.
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By means of a mod(N)\mathrm{mod}(N)mod(N)-invariant operator basis, sss-parametrized phase-space functions associated with bounded operators in a finite-dimensional Hilbert space are introduced in the context of the extended Cahill-Glauber formalism, and their properties are discussed in details. The discrete Glauber-Sudarshan, Wigner, and Husimi functions emerge from this formalism as specific cases of sss-parametrized phase-space functions where, in particular, a hierarchical process among them is promptly established. In addition, a phase-space description of quantum tomography and quantum teleportation is presented and new results are obtained.
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