Quantum informational properties of the Landau-Streater channel

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 $d⩾4$. We show that the channel $\Phi \otimes \Phi$ does not annihilate entanglement and preserves entanglement of some states with Schmidt rank $2$ if $d⩾3$.

20 pages

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Cited by in corpus (9)

• Phase covariant qubit dynamics and divisibility
• Capacity of trace decreasing quantum operations and superadditivity of coherent information for a generalized erasure channel
• Capacities of the covariant Pauli channel
• Quasi-inversion of quantum and classical channels in finite dimensions
• The noisy Werner-Holevo channel and its properties
• Realization of the Werner-Holevo and Landau-Streater quantum channels for qutrits on quantum computers
• Capacities of a two-parameter family of noisy Werner-Holevo channels
• On quantum operations of photon subtraction and photon addition
• Strong symmetries in collision models and physical dilations of covariant quantum maps