On quantum tomography on locally compact groups

• URL: http://arxiv.org/abs/2201.06049v1
• Date: Sun, 16 Jan 2022 13:48:22 GMT
• Title: On quantum tomography on locally compact groups
• Authors: Grigori Amosov
• Abstract summary: We introduce quantum tomography on locally compact Abelian groups $G$. We provide three examples in which $G=mathbb R$ (the optical tomography), $G=mathbb Z_n$ (corresponding to measurements in mutually unbiased bases) and $G=mathbb T$ (the tomography of the phase) As an application we have calculated the quantum tomogram for the output states of quantum Weyl channels.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce quantum tomography on locally compact Abelian groups $G$. A linear map from the set of quantum states on the $C^*$-algebra $A(G)$ generated by the projective unitary representation of $G$ to the space of characteristic functions is constructed. The dual map determining symbols of quantum observables from $A(G)$ is derived. Given a characteristic function of a state the quantum tomogram consisting a set of probability distributions is introduced. We provide three examples in which $G={\mathbb R}$ (the optical tomography), $G={\mathbb Z}_n$ (corresponding to measurements in mutually unbiased bases) and $G={\mathbb T}$ (the tomography of the phase). As an application we have calculated the quantum tomogram for the output states of quantum Weyl channels.

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