We introduce a generalization of the Pauli channels using the mutually unbiased measurement operators. The resulting channels are bistochastic, but their eigenvectors are not unitary. We analyze the channel properties, such as complete positivity, entanglement breaking, and the multiplicativity of maximal output purity. We illustrate our results with the maps constructed from the Gell-Mann matrices and the Heisenberg-Weyl observables.

arXiv:2003.12570Physical Review ASep 3, 20206 citations

arXiv:2105.08831 · Quantum Information Processing

Mutually unbiased measurements with arbitrary purity

Mahdi Salehi, Seyed Javad Akhtarshenas, Mohsen Sarbishaei, Hakimeh Jaghouri

Published Nov 24, 2021• 8 citations

arXiv HTML PDF

DOI: 10.1007/s11128-021-03340-5

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Generalization of Pauli channels through mutually unbiased measurements

Katarzyna Siudzińska

arXiv:2003.12570Physical Review ASep 3, 20206 citations

We present marginal cumulative distribution functions (CDF) for density matrices

ρ

of fixed purity

\tfrac{1}{N}\leμ_N(ρ)=\textrm{Tr}[ρ^2]\le 1

for arbitrary dimension

N

. We give closed form analytic formulas for the cases

N=2

(trivial),

N=3

and

N=4

, and present a prescription for CDFs of higher arbitrary dimensions. These formulas allows one to uniformly sample density matrices at a user selected, fixed constant purity, and also detail how these density matrices are distributed nonlinearly in the range

μ_N(ρ)\in[\tfrac{1}{N}, 1]

. As an illustration of these formulas, we compare the logarithmic negativity and quantum discord to the (Wootter's) concurrence spanning a range of fixed purity values in

μ_4(ρ)\in[\tfrac{1}{4}, 1]

for the case of

N=4

(two qubits). We also investigate the distribution of eigenvalues of a reduced

N

-dimensional obtained by tracing out the reservoir of its higher-dimensional purification. Lastly, we numerically investigate a recently proposed complementary-quantum correlation conjecture which lower bounds the quantum mutual information of a bipartite system by the sum of classical mutual informations obtained from two pairs of mutually unbiased measurements. Finally, numerical implementation issues for the computation of the CDFs and inverse CDFs necessary for uniform sampling

ρ

for fixed purity at very high dimension are briefly discussed.