Resource theories of communication with quantum superpositions of processes
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A novel approach to quantum communication has demonstrated that placing communication channels in a quantum superposition of alternative configurations can boost the amount of transmissible information beyond the limits of conventional quantum Shannon theory. Instances of this paradigm are the superposition of different causal orderings of communication devices [Ebler et al., Phys. Rev. Lett. 120, 120502 (2018); Salek et al., arXiv:1809.06655 (2018); Chiribella et al., arXiv:1810.10457 (2018)], or the superposition of information carriers' trajectories [Chiribella and Kristjánsson, Proc. R. Soc. A 475, 20180903 (2019); Gisin et al., Phys. Rev. A 72, 012338 (2005); Abbott et al., arXiv:1810.09826 (2018)]. Recently, it was argued that the communication advantages presented in the first three references above are not a genuine consequence of indefinite causal order but can be reproduced by the coherent control of devices [Abbott et al., arXiv:1810.09826 (2018); Guérin et al., Phys. Rev. A 99, 062317 (2019)]. Here, we point out that these arguments set up an uneven comparison between different types of quantum superpositions. To shed light on the discussion, we study communication as a resource theory, formally specifying the communication resources and the allowed operations on them. We argue that any reasonable resource theory of communication must prohibit the use of side-channels, which allow a sender and a receiver to communicate independently of the communication channels initially available to them. We show that the communication paradigms introduced in the first six references above are compatible with such a resource-theoretic framework, while the counterexamples proposed in [Guérin et al., Phys. Rev. A 99, 062317 (2019)] create side-channels.
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