Communication through quantum-controlled noise

In a recent series of works [Ebler et al., Phys. Rev. Lett. 120, 120502 (2018); arXiv:1809.06655v2; arXiv:1810.10457v2], it has been shown that the quantum superposition of causal order—the quantum switch—offers an enhancement of classical and quantum channel capacity through noisy channels, a phenomenon that was coined “causal activation.” In this paper, we attempt to clarify the nature of the advantage, by comparing the quantum switch to a class of processes that can be interpreted as quantum superposition of processes with the same causal order. We show that some of these processes can match or even outperform the quantum switch at enhancing classical and quantum channel capacity, and argue that they require the same resources as the switch. We conclude, in agreement with Abbott et al. [arXiv:1810.09826v1], that the aforementioned advantages appear to be attributable to the ability to coherently control quantum operations, and not to indefinite causal order per se.

Figure 1

Comparison of the space-time diagrams corresponding to implementations of the quantum switch (left), and the SDPP of Eq. (6) (right). The small gray squares are beam splitters, and the dashed red and solid blue lines represent the two paths that are taken in an equal superposition by the photon. The noisy channels ${\mathcal{M}}_A,{\mathcal{M}}_B$, and the Pauli-$X$ unitary act on the polarization degree of freedom of the photon. There exists inertial reference frames in which the gate $X$ occurs at a later (or earlier) time than the first application of ${\mathcal{M}}_A$, which makes it impossible to assign a temporal order between the application of ${\mathcal{M}}_A$ on one side of the superposition and that of $X$ on the other side. Whether the action of $X$ is part of the initial encoding or of the propagation channel depends on the reference frame.