Quantum boomerang capacity
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Inspired by the power of abstraction in information theory, we consider quantum boomerang protocols as a way of providing a unifying perspective to deal with several information-processing tasks related to and extending quantum channel discrimination to the Shannon-theoretic regime. Such protocols, defined in the most general quantum-physical way possible, have been considered in the physical context of the DW model of quantum reading [Das and Wilde, arXiv:1703.03706]. In [Das, arXiv:1901.05895], it was discussed how such protocols apply in the different physical context of round-trip communication from one party to another and back. The common point for all quantum boomerang tasks is that the decoder himself has access to both the input and output of a randomly selected sequence of channels, and the goal is to determine a message encoded into the channel sequence. As employed in the DW model of quantum reading, the most general quantum-physical strategy that a decoder can employ is an adaptive strategy, in which general quantum operations are executed before and after each call to a channel in the sequence. We determine lower and upper bounds on the quantum boomerang capacities in various scenarios of interest, and we also discuss cases in which adaptive schemes provide an advantage over non-adaptive schemes in zero-error quantum boomerang protocols.
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