Detecting positive quantum capacities of quantum channels

Can a noisy quantum channel be used to transmit quantum information reliably from a sender to a receiver? Answering this fundamental question has proved to be extremely difficult, despite years of research. Some noisy channels are known to have zero quantum capacity, i.e., it is impossible to send any quantum information reliably through them. However, our poor understanding of the set of zero capacity quantum channels, and the lack of a systematic procedure to determine whether a given channel has positive capacity, has led to the intractability of the above question. Satvik Singh (a CCIMI PhD student) along with his supervisor Nilanjana Datta at Cambridge have attempted to solve the stated problem by devising a simple perturbative strategy to detect positive quantum capacities of quantum channels. Their analysis reveal that a channel’s ability to transmit information is intimately connected to the relative sizes of its input, output, and environment spaces. They have exploited 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.

1) Singh, S., Datta, N. Detecting positive quantum capacities of quantum channels. npj Quantum Inf 8, 50 (2022). https://doi.org/10.1038/s41534-022-00550-2

2) Singh, S., Datta, N. Coherent information of a quantum channel or its complement is generically positive. Quantum 6, 775 (2022). https://doi.org/10.22331/q-2022-08-11-775

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