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arXiv:1811.07526 · Physical Review Letters

Experimental Transmission of Quantum Information Using a Superposition of Causal Orders

Yu Guo, Xiao‐Min Hu, Zhibo Hou, Huan Cao, Jin‐Ming Cui, Bi‐Heng Liu, Yun‐Feng Huang, Chuan‐Feng Li, Guang‐Can Guo, Giulio Chiribella

Published Jan 24, 2020• 129 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.124.030502

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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.
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.
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.
Quantum mechanics allows for the superposition of quantum states, thereby bringing about the great success of quantum communications. Recently, in the so-called quantum switch, the relative orders between quantum operations can also be coherently controlled with the help of an auxiliary system. In conventional quantum Shannon theory, however, communication channels are assumed to be combined in a classical way. Relaxing this assumption, it was shown theoretically that one can transmit information through a quantum switch. Here, we experimentally demonstrate this enhancement on the rates of communication for both classical and quantum information with the help of an optical quantum switch. Our results present evidence of the advantages of the superposition of causal orders in the communications domain.
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.
A major challenge in quantum communication is addressing the negative effects of noise on channel capacity, especially for completely depolarizing channels, where information transmission is inherently impossible. The concept of indefinite causal order provides a promising solution by allowing control over the sequence in which channels are applied. We experimentally demonstrate the activation of quantum communication through completely depolarizing channels using a programmable silicon photonic quantum chip. By implementing configurations based on the superposition of cyclic orders, a form of indefinite causal order, we report the first experimental realization of genuine quantum information transmission across multiple concatenated completely depolarizing channels. Our results show that when four completely depolarizing channels are combined using the superposition of cyclic orders, the fidelity of the output state is 0.712±0.0130.712 \pm 0.0130.712±0.013, significantly exceeding the classical threshold of 2/3. Our work establishes indefinite causal order as a powerful tool for overcoming noise-induced limitations in quantum communication, demonstrating its potential in high-noise environments and opening new possibilities for building robust quantum networks.