Qubits through Queues: The Capacity of Channels with Waiting Time Dependent Errors. (arXiv:1804.00906v3 [cs.IT] UPDATED)

We consider a setting where qubits are processed sequentially, and derive
fundamental limits on the rate at which classical information can be
transmitted using quantum states that decohere in time. Specifically, we model
the sequential processing of qubits using a single server queue, and derive
explicit expressions for the capacity of such a `queue-channel.' We also
demonstrate a sweet-spot phenomenon with respect to the arrival rate to the
queue, i.e., we show that there exists a value of the arrival rate of the
qubits at which the rate of information transmission (in bits/sec) through the
queue-channel is maximized. Next, we consider a setting where the average rate
of processing qubits is fixed, and show that the capacity of the queue-channel
is maximized when the processing time is deterministic. We also discuss design
implications of these results on quantum information processing systems.

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