Detecting positive quantum capacities of quantum channels

Abstract

Determining whether a noisy quantum channel can be used to reliably transmit quantum information at a non-zero rate is a challenging problem in quantum information theory. This is because it requires computation of the channel's coherent information for an unbounded number of copies of the channel. In this paper, we devise an elementary perturbative technique to solve this problem in a wide variety of circumstances. Our analysis reveals that a channel's ability to transmit information is intimately connected to the relative sizes of its input, output, and environment spaces. We exploit this link to develop easy tests which can be used to detect positivity of quantum channel capacities simply by comparing the channels' input, output, and environment dimensions. Several noteworthy examples, such as the depolarizing and transpose-depolarizing channels (including the Werner-Holevo channel), dephasing channels, generalized Pauli channels, multi-level amplitude damping channels, and (conjugate) diagonal unitary covariant channels, serve to aptly exhibit the utility of our method. Notably, in all these examples, the coherent information of a single copy of the channel turns out to be positive.

v2: Minor modifications with updated references. Closer to the published version

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Cited by in corpus (10)

• Resonant Multilevel Amplitude Damping Channels
• Bounding quantum capacities via partial orders and complementarity
• Parallel ergotropy: Maximum work extraction via parallel local unitary operations
• Transmission of quantum information through quantum fields in curved spacetimes
• Operational Interpretation of the Choi Rank Through k-State Exclusion
• Quantum channels that destroy negative conditional entropy
• Coherent information of a quantum channel or its complement is generically positive
• Fully undistillable quantum states are separable
• The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels
• Noise is resource-contextual in quantum communication