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arXiv:1809.06655

Quantum communication in a superposition of causal orders

Sina Salek, Daniel Ebler, Giulio Chiribella

Published Sep 18, 2018• 47 citations
arXivHTMLPDF

Abstract

Quantum mechanics allows for situations where the relative order between two processes is entangled with a quantum degree of freedom. Here we show that such entanglement can enhance the ability to transmit quantum information over noisy communication channels. We consider two completely dephasing channels, which in normal conditions are unable to transmit any quantum information. We show that, when the two channels are traversed in an indefinite order, a quantum bit sent through them has a 25% probability to reach the receiver without any error. For partially dephasing channels, a similar advantage takes place deterministically: the amount of quantum information that can travel through two channels in a superposition of orders can be larger than the amount of quantum information that can travel through each channel individually.

DOI
10.48550/arxiv.1809.06655

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Quantum mechanics allows for situations where the relative order between two processes is entangled with a quantum degree of freedom. Here we show that such entanglement can enhance the ability to transmit quantum information over noisy communication channels. We consider two completely dephasing channels, which in normal conditions are unable to transmit any quantum information. We show that, when the two channels are traversed in an indefinite order, a quantum bit sent through them has a 25% probability to reach the receiver without any error. For partially dephasing channels, a similar advantage takes place deterministically: the amount of quantum information that can travel through two channels in a superposition of orders can be larger than the amount of quantum information that can travel through each channel individually.
In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter, we relax the assumption that quantum channels are combined classically, showing that a quantum communication network where quantum channels are combined in a superposition of different orders can achieve tasks that are impossible in conventional quantum Shannon theory. In particular, we show that two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference. The failure of such intuition stems from the fact that a single noisy channel can be a random mixture of elementary, noncommuting processes, whose order (or lack thereof) can affect the ability to transmit information.
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.
Completely depolarizing channels are often regarded as the prototype of physical processes that are useless for communication: any message that passes through them along a well-defined trajectory is completely erased. When two such channels are used in a quantum superposition of two alternative orders, they become able to transmit some amount of classical information, but still no quantum information can pass through them. Here, we show that the ability to place N completely depolarizing channels in a superposition of N alternative causal orders enables a high-fidelity heralded transmission of quantum information with error vanishing as 1/N. This phenomenon highlights a fundamental difference with the N=2 case, where completely depolarizing channels are unable to transmit quantum data, even when placed in a superposition of causal orders. The ability to place quantum channels in a superposition of orders also leads to an increase of the classical communication capacity with N, which we rigorously prove by deriving an exact single-letter expression. Our results highlight the more complex patterns of correlations arising from multiple causal orders, which are similar to the more complex patterns of entanglement arising in multipartite quantum systems.
Classically, no information can be transmitted through a depolarising, which is a completely noisy, channel.We show that by combining a depolarising channel with another channel in an indefinite causal order-that is, when there is a superposition of the order that these two channels were applied-it becomes possible to transmit significant information.We consider two limiting cases.When both channels are fully depolarising, the ideal limit is communication of 0.049 bits; experimentally we achieve (3.4 ± 0.2) × 10 -2 bits.When one channel is fully depolarising, and the other is a known unitary, the ideal limit is communication of 1 bit.We experimentally achieve 0.64 ± 0.02 bits.Our results offer intriguing possibilities for future communication strategies beyond conventional quantum Shannon theory.
When a noisy communication channel is used multiple times, the errors occurring at different times generally exhibit correlations. Classically, these correlations do not affect the evolution of individual particles: a single classical particle can only traverse the channel at a definite moment of time, and its evolution is insensitive to the correlations between subsequent uses of the channel. In stark contrast, here we show that a single quantum particle can sense the correlations between multiple uses of a channel at different moments of time. Taking advantage of this phenomenon, it is possible to enhance the amount of information that the particle can reliably carry through the channel. In an extreme example, we show that a channel that outputs white noise whenever the particle is sent at a definite time can exhibit correlations that enable a perfect transmission of classical bits when the particle is sent at a superposition of two distinct times. In contrast, we show that, in the lack of correlations, a single particle sent at a superposition of two times undergoes an effective channel with classical capacity of at most 0.16 bits. When multiple transmission lines are available, time correlations can be used to simulate the application of quantum channels in a coherent superposition of alternative causal orders, and even to provide communication advantages that are not accessible through the superposition of causal orders.
Communication in a network generally takes place through a sequence of intermediate nodes connected by communication channels. In the standard theory of communication, it is assumed that the communication network is embedded in a classical spacetime, where the relative order of different nodes is well defined. In principle, a quantum theory of spacetime could allow the order of the intermediate points between sender and receiver to be in a coherent superposition. Here we experimentally realize a tabletop simulation of this exotic possibility on a photonic system, demonstrating high-fidelity transmission of quantum information over two noisy channels arranged in a superposition of two alternative causal orders.