Geometry of the Pauli maps and Pauli channels

Abstract

We analyze the geometrical properties of trace-preserving Pauli maps. Using the Choi-Jamio\lkowski isomorphism, we express the Hilbert-Schmidt line and volume elements in terms of the eigenvalues of the Pauli map. We analytically compute the volumes of positive, trace-preserving Pauli maps and Pauli channels. In particular, we find the relative volumes of the entanglement breaking Pauli channels, as well as the channels that can be generated by a time-local generator. Finally, we show what part of the Pauli channels are P and CP-divisible, which is related to the notion of Markovianity.

References in corpus (7)

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• Divisibility of qubit channels and dynamical maps
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Cited by in corpus (7)

• Beyond Shannon Limits: Quantum Communications through Quantum Paths
• Singularities, mixing and non-Markovianity of Pauli dynamical maps
• Log-Convex set of Lindblad semigroups acting on $N$-level system
• Geometry of generalized Pauli channels
• Geometry of symmetric and non-invertible Pauli channels
• Guaranteeing Completely Positive Quantum Evolution
• Entropic uncertainty under indefinite causal order and input-output direction