Abstract
We introduce Partially Coherent Direct Sum (PCDS) quantum channels, as a generalization of the already known Direct Sum quantum channels. We derive necessary and sufficient conditions to identify the subset of those maps which are degradable, and provide a simplified expression for their quantum capacities. Interestingly, the special structure of PCDS allows us to extend the computation of the quantum capacity formula also for quantum channels which are explicitly not degradable (nor antidegradable). We show instances of applications of the results to dephasing channels, amplitude damping channels and combinations of the two.
Highlights
Since the seminal work of Shannon [1] the performance analysis of means of communication has been rephrased into the search of the maximum information transmission rates achievable by noisy channels
Again from data-processing inequality (DPI), it follows that the quantum capacity of Ω[CγC](κ) is always smaller than or equal to the corresponding value associated with the multi-level amplitude damping (MAD) channel Ω[CγC], as well as the quantum capacity of ∆(CκC) we computed in Sec. 5.1, i.e
We firstly introduced the new class of Partially Coherent Direct Sum channels
Summary
Since the seminal work of Shannon [1] the performance analysis of means of communication has been rephrased into the search of the maximum information transmission rates achievable by noisy channels. The approach to the evaluation of channel capacities was directed towards noisy quantum channels, opening the road to the field of quantum communication [2, 3, 4, 5]. PCDS appear to be interesting because their capacity is in principle exactly computable with reduced complexity for high dimensional systems. In this sense, the knowledge already acquired about low dimensional quantum channels can be exploited to compose new PCDS channels. At the same time the introduction of the PCDS can push the study of all accessible zoology of low dimensional channels.
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