On the complementary quantum capacity of the depolarizing channel

Abstract

The qubit depolarizing channel with noise parameter $\eta$ transmits an input qubit perfectly with probability $1-\eta$, and outputs the completely mixed state with probability $\eta$. We show that its complementary channel has positive quantum capacity for all $\eta >0$. Thus, we find that there exists a single parameter family of channels having the peculiar property of having positive quantum capacity even when the outputs of these channels approach a fixed state independent of the input. Comparisons with other related channels, and implications on the difficulty of studying the quantum capacity of the depolarizing channel are discussed.

v4 corrects errors in equation (38)

References in corpus (5)

• The structure of degradable quantum channels
• Unbounded number of channel uses are required to see quantum capacity
• Private and Quantum Capacities of More Capable and Less Noisy Quantum Channels
• Quantum and private capacities of low-noise channels
• Detecting Incapacity

Cited by in corpus (10)

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• Entanglement cost and quantum channel simulation
• Quantum and private capacities of low-noise channels
• Semidefinite programming converse bounds for quantum communication
• Entropic singularities give rise to quantum transmission
• Evading noise in multiparameter quantum metrology with indefinite causal order
• Detecting positive quantum capacities of quantum channels
• Generalizations of $2$-dimensional diagonal quantum channels with constant Frobenius norm
• Quantum channels that destroy negative conditional entropy
• Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding