Capacity Bounds for Quantum Communications through Quantum Trajectories
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In both classical and quantum Shannon's information theory, communication channels are generally assumed to combine through classical trajectories, so that the associated network path traversed by the information carrier is well-defined. Counter-intuitively, quantum mechanics enables a quantum information carrier to propagate through a quantum trajectory, i.e., through a path such that the causal order of the constituting communications channels becomes indefinite. Quantum trajectories exhibit astonishing features, such as providing non-null capacity even when no information can be sent through any classical trajectory. But the fundamental question of investigating the ultimate rates achievable with quantum trajectories is an open and crucial problem. To this aim, in this paper, we derive closed-form expressions for both the upper- and the lower-bound on the quantum capacity achievable via a quantum trajectory. The derived expressions depend, remarkably, on computable single-letter quantities. Our findings reveal the substantial advantage achievable with a quantum trajectory over any classical combination of the communications channels in terms of ultimate achievable communication rates. Furthermore, we identify the region where a quantum trajectory incontrovertibly outperforms the amount of transmissible information beyond the limits of conventional quantum Shannon theory, and we quantify this advantage over classical trajectories through a conservative estimate.
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