Quantum informational properties of the Landau-Streater channel

TL;DR

This paper investigates the Landau-Streater quantum channel, analyzing its spectral properties, capacities, and entanglement behavior, revealing its covariance, non-Markovian nature, and capacity characteristics across different dimensions.

Contribution

It provides explicit spectral analysis, capacity calculations, and entanglement preservation properties of the Landau-Streater channel, including its covariance and non-Markovian features.

Findings

Spectrum and minimal output entropy explicitly derived.

Quantum capacity is zero for d=2,3 and positive for d≥4.

Channel preserves some entanglement for d≥3.

Abstract

We study the Landau--Streater quantum channel $\Phi: \mathcal{B}(\mathcal{H}_d) \mapsto \mathcal{B}(\mathcal{H}_d)$, whose Kraus operators are proportional to the irreducible unitary representation of $SU(2)$ generators of dimension $d$. We establish $SU(2)$ covariance for all $d$ and $U(3)$ covariance for $d=3$. Using the theory of angular momentum, we explicitly find the spectrum and the minimal output entropy of $\Phi$. Negative eigenvalues in the spectrum of $\Phi$ indicate that the channel cannot be obtained as a result of Hermitian Markovian quantum dynamics. Degradability and antidegradability of the Landau--Streater channel is fully analyzed. We calculate classical and entanglement-assisted capacities of $\Phi$. Quantum capacity of $\Phi$ vanishes if $d=2,3$ and is strictly positive if $d \geqslant 4$. We show that the channel $\Phi \otimes \Phi$ does not annihilate entanglement and preserves entanglement of some states with Schmidt rank $2$ if $d \geqslant 3$.