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Quantum switch of quantum switches

Debarshi Das, Somshubhro Bandyopadhyay

Published Nov 16, 2021• 0 citations
OpenAlex

Abstract

Recent results have shown that quantum theory is compatible with novel causal structures where events happen without a definite causal order. In particular, the quantum switch describes a process in which two quantum channels act in a coherent superposition of their two possible orders. Furthermore, the quantum switch can perform communication tasks that are impossible within the framework of the standard quantum Shannon theory. The present paper considers the scenario of one-shot heralded qubit communication using a higher-order quantum switch constructed from two quantum switches. Specifically, we show that two quantum switches put in a superposition of their alternative causal orders can transmit a qubit, without any error, with a probability strictly higher than that achievable with each quantum switch. We discuss three examples that demonstrate this communication advantage. Notably, a higher-order quantum switch not only can outperform useful quantum switches but also becomes useful as a resource even if the quantum switches making it up are useless.

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Recent results have shown that quantum theory is compatible with novel causal structures where events happen without a definite causal order. In particular, the quantum switch describes a process in which two quantum channels act in a coherent superposition of their two possible orders. Furthermore, the quantum switch can perform communication tasks that are impossible within the framework of the standard quantum Shannon theory. The present paper considers the scenario of one-shot heralded qubit communication using a higher-order quantum switch constructed from two quantum switches. Specifically, we show that two quantum switches put in a superposition of their alternative causal orders can transmit a qubit, without any error, with a probability strictly higher than that achievable with each quantum switch. We discuss three examples that demonstrate this communication advantage. Notably, a higher-order quantum switch not only can outperform useful quantum switches but also becomes useful as a resource even if the quantum switches making it up are useless.
The quantum switch describes a quantum operation in which two or more quantum channels act on a quantum system with the order of application determined by the state of an order quantum system. And by suitably choosing the state of the order system, one can create a quantum superposition of the different orders of application, which can perform communication tasks impossible within the framework of the standard quantum Shannon theory. In this paper, we consider the scenario of one-shot heralded qubit communication and ask whether there are protocols using a given quantum switch or switches that could outperform the given ones. We answer this question in the affirmative. We define a higher-order quantum switch composed of two quantum switches, with their order of application controlled by another order quantum system. We then show that the quantum switches placed in a quantum superposition of their alternative orders can transmit a qubit, without any error, with a probability higher than that achievable with the quantum switches individually. We demonstrate this communication advantage over quantum switches that are useful as a resource and those that are useless. We also show that there are situations where there is no communication advantage over the individual quantum switches.
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 events to happen with no definite causal order: this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Here, we realize a photonic quantum switch, where two operations A[over ^] and B[over ^] act in a quantum superposition of their two possible orders. The operations are on the transverse spatial mode of the photons; polarization coherently controls their order. Our implementation ensures that the operations cannot be distinguished by spatial or temporal position-further it allows qudit encoding in the target. We confirm our quantum switch has no definite causal order by constructing a causal witness and measuring its value to be 18 standard deviations beyond the definite-order bound.
Abstract Applications of the quantum switch on quantum channels have recently become a topic of intense discussion. In the present work, we show that some useless (for communication) channels may provide useful communication under the action of quantum switch for several information-theoretic tasks: quantum random access codes, quantum steering, etc. We demonstrate that the quantum switch can also be useful in preventing the loss of coherence in a system when only coherence-breaking channels are the available channels for communication. We also show that if a useless quantum channel does not provide useful communication even after using a quantum switch, concatenating the channel with another suitable quantum channel, and subsequently using the switch, one may achieve useful communication. Finally, we discuss how the introduction of noise in the quantum switch can reduce the advantage that the switch provides.
In a recent series of works [Ebler et al., Phys. Rev. Lett. 120, 120502 (2018); arXiv:1809.06655v2; arXiv:1810.10457v2], it has been shown that the quantum superposition of causal order---the quantum switch---offers an enhancement of classical and quantum channel capacity through noisy channels, a phenomenon that was coined ``causal activation.'' In this paper, we attempt to clarify the nature of the advantage, by comparing the quantum switch to a class of processes that can be interpreted as quantum superposition of processes with the same causal order. We show that some of these processes can match or even outperform the quantum switch at enhancing classical and quantum channel capacity, and argue that they require the same resources as the switch. We conclude, in agreement with Abbott et al. [arXiv:1810.09826v1], that the aforementioned advantages appear to be attributable to the ability to coherently control quantum operations, and not to indefinite causal order per se.
Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication complexity. Recently, a novel quantum resource called the quantum switch-which creates a coherent superposition of the causal order of events, known as quantum causality-has been harnessed theoretically in a new protocol providing provable exponential separation. We experimentally demonstrate such an advantage by realizing a superposition of communication directions for a two-party distributed computation. Our photonic demonstration employs d-dimensional quantum systems, qudits, up to d=2^{13} dimensions and demonstrates a communication complexity advantage, requiring less than (0.696±0.006) times the communication of any causally ordered protocol. These results elucidate the crucial role of the coherence of communication direction in achieving the exponential separation for the one-way processing task, and open a new path for experimentally exploring the fundamentals and applications of advanced features of indefinite causal structures.