Communication through coherent control of quantum channels

Abstract

A completely depolarising quantum channel always outputs a fully mixed state and thus cannot transmit any information. In a recent Letter\cite{ebler18}, 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.

Quantum Shannon theory with superpositions of trajectories

“…The ability to propagate along multiple paths allows quantum particles to experience coherent superpositions of alternative evolutions [8,9], or to experience a set of evolutions in a superposition of alternative orders [10,11]. When a particle travels along alternative paths, the interference of noisy processes taking place on different paths can result in cleaner communication channels overall [12,13]. Similarly, when a particle experiences noisy processes in a superposition of orders, the interference between alternative orderings can boost the capacity to communicate classical and quantum bits [14][15][16].…”

Routed quantum circuits

“…Indeed, the features of this example are common in quantum optics, in which sending a photon in a superposition of trajectories, and applying operations which do not modify the number of photons (such as waveplates) are standard protocols. This point has, in particular, been encountered in different guises in the literature discussing the possibility of coherently controlling unknown unitaries [15,17,18,19] or quantum channels [11,12,13,14,20,23,24,21]: no-go theorems forbid such coherent control in standard quantum circuits, yet it is achievable in 2 In technical terms, this means that they cannot be adequately described using the categories FHilb or CPM [FHilb]. In Appendix B, we extend this discussion to the case of other standard categorical constructions such as CP* [FHilb] and the Karoubi envelope of CPM [FHilb].…”

“…The goal of Refs. [23,24] was to study the communication advantages that using such scenarios can lead to. In a similar spirit, several recent works have investigated the use in quantum computation of controlling unknown 'black box' quantum operations, where a quantum control system determines if one unknown operation is used, or another, or both in a superposition [15,16,17,18,19,20,21].…”

“…Here, we will describe the challenges that these works raise in terms of mathematical formalisation. To do so, we will focus on a paradigmatic example of communication in a superposition of trajectories, the 'one particle in two trajectories' scenario [24,23], focusing specifically on the perspective of Ref. [24].…”

“…The coherent control of quantum channels generalises the 'if' clause in classical computation to the quantum level, where the use or not of a given quantum channel is determined by the value of another quantum system -enabling the possibility of using multiple quantum channels in a superposition. This idea can be applied equally to computation, where it is often referred to as control of unknown unitaries (or channels) [15,16,17,18,19,20,21] and communication, where it takes the form of communication in a superposition of trajectories [22,23,24,25,26,27,28]. We shall describe superpositions of quantum channels in depth in Section 2.1, focusing on the communication perspective of Ref.…”