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arXiv:2005.00618 · Physical Review Letters

Quantum and Classical Data Transmission through Completely Depolarizing Channels in a Superposition of Cyclic Orders

Giulio Chiribella, Matthew Wilson, H. F. Chau

Published Nov 5, 2021• 49 citations

Abstract

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.

DOI: 10.1103/physrevlett.127.190502

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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.

If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit nonzero classical information. Here we study how well we can transmit classical information with

N

depolarizing channels put in superposition of

M

causal orders via a quantum switch. We calculate the Holevo quantity if the superposition uses only cyclic permutations of channels and find that it increases with

M

and it is independent of

N

. For a qubit it never reaches 1 if we are increasing

M

. On the other hand, the classical capacity decreases with the dimension

d

of the message system. Further, for

N=3

and 4 we studied the superposition of all causal orders and uniformly superposed causal orders belonging to different cosets created by a cyclic permutation subgroup.

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 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 \pm 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.

Noise fundamentally limits quantum communication capacity, completely preventing information transmission in fully depolarizing environments. While indefinite causal order theoretically circumvents this limitation, experimentally realizing multi-channel configurations for genuine quantum transmission remains challenging. Here we show the activation of quantum communication through completely depolarizing channels using a programmable silicon photonic chip. By implementing a superposition of cyclic orders across four completely depolarizing channels, we achieve an output state fidelity of 0.712 ± 0.013, which strictly exceeds the classical threshold of 2/3. This mechanism provides a powerful tool for overcoming extreme noise, offering broad potential for building robust quantum networks in highly decoherent environments. Noise severely limits quantum communication, particularly in completely depolarizing channels where information transmission is impossible. Here, the authors use a programmable silicon photonic chip to show quantum information transmission through multiple concatenated depolarizing channels by implementing a superposition of cyclic orders, achieving fidelities above the classical qubit threshold in a strongly noisy regime.