Geometry of generalized Pauli channels

• URL: http://arxiv.org/abs/2002.04657v2
• Date: Wed, 15 Apr 2020 21:48:17 GMT
• Title: Geometry of generalized Pauli channels
• Authors: Katarzyna Siudzi\'nska
• Abstract summary: Choi-Jamiolkowski isomorphism allows us to express the Hilbert-Schmidt line and volume elements in terms of the eigenvalues of the generalized Pauli maps. We analytically compute the volume of generalized Pauli channels and their important subclasses.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We analyze the geometry of the generalized Pauli channels constructed from the mutually unbiased bases. The Choi-Jamio{\l}kowski isomorphism allows us to express the Hilbert-Schmidt line and volume elements in terms of the eigenvalues of the generalized Pauli maps. After determining appropriate regions of integration, we analytically compute the volume of generalized Pauli channels and their important subclasses. In particular, we obtain the volumes of the generalized Pauli channels that can be generated by a legitimate generator and are entanglement breaking. We also provide the upper bound for the volume of positive, trace-preserving generalized Pauli maps.

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