Geometry of generalized Pauli channels
arXiv:2002.04657 · doi:10.1103/PhysRevA.101.062323
Abstract
We analyze the geometry of the generalized Pauli channels constructed from the mutually unbiased bases. The Choi-Jamiołkowski 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.
References in corpus (10)
- Assessing non-Markovian dynamics
- Detecting non-Markovianity of quantum evolution via spectra of dynamical maps
- Pauli Diagonal Channels Constant on Axes
- Divisibility of qubit channels and dynamical maps
- Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive
- Pauli semigroups and unistochastic quantum channels
- Geometry of the Pauli maps and Pauli channels
- Geometry on the manifold of Gaussian quantum channels
- Regularized maximal fidelity of the generalized Pauli channels
- Amplitude Damping for single-qubit System with single-qubit mixed-state Environment