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arXiv:1807.07383 · Physical Review Research

Increasing communication capacity via superposition of order

Kaumudibikash Goswami, Y. Cao, Gerardo A. Paz-Silva, Jacquiline Romero, A. G. White

Published Aug 24, 2020• 90 citations
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Abstract

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.

DOI
10.1103/physrevresearch.2.033292

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•Jan 1, 2018•81 citations
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.
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.
In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number N of channels with arbitrary individual capacity i.e., information preservation characteristics in the case of indefinite causal order. We propose a formalism to assess information transmission in the most general case of N channels in an indefinite causal order scenario yielding the output of such transmission. Then, we explicitly derive the quantum switch output and the associated Holevo limit of the information transmission for N = 2 , N = 3 as a function of all involved parameters. We find in the case N = 3 that the transmission of information for three channels is twice that of transmission of the two-channel case when a full superposition of all possible causal orders is used.
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.
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 NNN depolarizing channels put in superposition of MMM 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 MMM and it is independent of NNN. For a qubit it never reaches 1 if we are increasing MMM. On the other hand, the classical capacity decreases with the dimension ddd of the message system. Further, for N=3N=3N=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.
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.
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.