Geometry of generalized Pauli channels

@article{Siudzinska2020GeometryOG,
  title={Geometry of generalized Pauli channels},
  author={Katarzyna Siudzi'nska},
  journal={Physical Review A},
  year={2020}
}
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… 
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References

SHOWING 1-10 OF 53 REFERENCES
Geometry of Pauli maps and Pauli channels
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…
Geometry on the manifold of Gaussian quantum channels
In the space of quantum channels, we establish the geometry that allows us to make statistical predictions about relative volumes of entanglement breaking channels among all the Gaussian quantum…
Pauli semigroups and unistochastic quantum channels
Regularized maximal fidelity of the generalized Pauli channels
TLDR
The asymptotic regularization of the maximal fidelity for the generalized Pauli channels is considered, and the formulas for the extremal channel fidelities and the maximal output $\infty$-norm are found.
Pauli Diagonal Channels Constant on Axes
TLDR
The convex structure of this class of channels is described and it is shown that the multiplicativity conjecture for maximal output p-norm holds for p = 2, providing new numerical evidence for the additivity of minimal output entropy.
Generalized Pauli channels and a class of non-Markovian quantum evolution
We analyze the quantum evolution represented by a time-dependent family of generalized Pauli channels. This evolution is provided by the random decoherence channels with respect to the maximal number…
Volume of the space of qubit-qubit channels and state transformations under random quantum channels
The simplest building blocks for quantum computations are the qubit-qubit quantum channels. In this paper, we analyze the structure of these channels via their Choi representation. The restriction of…
Volume of the set of locally diagonalizable bipartite states
The purpose of this article is to investigate the geometry of the set of locally diagonalizable bipartite quantum states. We have the following new results: the Hilbert–Schmidt volume of all locally…
Bures volume of the set of mixed quantum states
We compute the volume of the (N2 − 1)-dimensional set N of density matrices of size N with respect to the Bures measure and show that it is equal to that of an (N2 − 1)-dimensional hyper-hemisphere…
Relative volume of separable bipartite states
Every choice of an orthonormal frame in the d-dimensional Hilbert space of a system corresponds to one set of all mutually commuting density matrices or, equivalently, a classical statistical state…
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