Indefinite causal order enables perfect quantum communication with zero capacity channels

Abstract

Quantum mechanics is compatible with scenarios where the relative order between two events can be indefinite. Here we show that two independent instances of a noisy process can behave as a perfect quantum communication channel when used in a coherent superposition of two alternative orders. This phenomenon occurs even if the original process has zero capacity to transmit quantum information. In contrast, perfect quantum communication does not occur when the message is sent directly from the sender to the receiver through a superposition of alternative paths, with an independent noise process acting on each path. The possibility of perfect quantum communication through independent noisy channels highlights a fundamental difference between the superposition of orders in time and the superposition of paths in space.

Quantum Shannon theory with superpositions of trajectories

“…However, the map A + F • F † is proportional to a unitary gate if and only if the original channel A was a unitary gate itself. In fact, the same result holds for the superposition of two different channels A and B, and more generally, of N independent channels: superpositions of independent noisy channels never lead to a noiseless channel, as long as N is a finite number [16].…”

“…Another example arises when a particle visits a given set of regions in a superposition of multiple orders [10]. In this setting, the correlations arising from the memory in the environment can give rise to a noiseless transmission of quantum information through noisy channels, a phenomenon that cannot take place with the superposition of independent channels [16].…”

The Entanglement-Assisted Communication Capacity Over Quantum Trajectories

“…Consequently, the incorporation of auxiliary qubits in quantum error-correction codes increases the total number of quantum channel uses. By contrast, the utilization of the auxiliary qubit ω of (24) does not increase the number of quantum channel uses. In fact, as shown in [18], the encoding operation of (24) must be considered as a non-side-channel generating operation, since the control qubit ω does not carry -or embed in any waythe information from the source to the destination.…”

“…Thus, we can utilize the measurement result to our advantage for improving the performance of classical and quantum communication. Based on the formal description of the quantum trajectory in (24), indeed we require an additional auxiliary qubit ω to control the superposition of the causal orders of the quantum channels D(•) and E(•). Intuitively, we have the inclination to make a comparison between the advocated scheme presented in this treatise to another auxiliary-qubits assisted scheme, such as quantum error-correction codes [60], [61].…”

“…As counter-intuitive as it seems, the ability of information carrier traversing a superposition of classical trajectories has been experimentally verified using a quantum device called quantum switch [4]- [12]. Until recently, the alluring benefits of the indefinite casual order of quantum process have been reported for various aspects of quantum information processing, including quantum computation [13], [14], noiseless quantum teleportation [15], communication complexity [16], quantum resource theory [17], [18], quantum metrology [19], discrimination of quantum process [20], and ultimately for boosting the channel capacities of quantum and classical communications over quantum channels [21]- [24].…”