Communication through coherent control of quantum channels

TL;DR

This paper demonstrates that coherent control of quantum channels enables information transmission through depolarising channels without relying on indefinite causal order, revealing new insights into quantum channel implementation and control.

Contribution

It introduces a scenario where coherent control over identical depolarising channels allows information transfer without causal indefiniteness, and highlights the importance of the implementation details in quantum channels.

Findings

Information can be transmitted through depolarising channels via coherent control.

Implementation details of channels affect the output state and distinguishability.

A new 'transformation matrix' is needed to fully describe coherently controlled channels.

Abstract

A completely depolarising quantum channel always outputs a fully mixed state and thus cannot transmit any information. In a recent Letter [D. Ebler et al., Phys. Rev. Lett. 120, 120502 (2018)], it was however shown that if a quantum state passes through two such channels in a quantum superposition of different orders - a setup known as the "quantum switch" - then information can nevertheless be transmitted through the channels. Here, we show that a similar effect can be obtained when one coherently controls between sending a target system through one of two identical depolarising channels. Whereas it is tempting to attribute this effect in the quantum switch to the indefinite causal order between the channels, causal indefiniteness plays no role in this new scenario. This raises questions about its role in the corresponding effect in the quantum switch. We study this new scenario in detail and we see that, when quantum channels are controlled coherently, information about their specific implementation is accessible in the output state of the joint control-target system. This allows two different implementations of what is usually considered to be the same channel to therefore be differentiated. More generally, we find that to completely describe the action of a coherently controlled quantum channel, one needs to specify not only a description of the channel (e.g., in terms of Kraus operators), but an additional "transformation matrix" depending on its implementation.