Enhanced communication with the assistance of indefinite causal order (1711.10165v2)

Abstract: 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, non-commuting processes, whose order (or lack thereof) can affect the ability to transmit information.

• The paper introduces a quantum SWITCH operation that leverages indefinite causal order to activate channels that are otherwise unable to transmit information.
• It demonstrates that two identical completely depolarizing channels can achieve positive Holevo capacity for qubit communications when arranged in a superposition of orders.
• The study challenges classical assumptions in quantum Shannon theory and offers new insights for designing efficient quantum communication networks.

Enhanced Communication With the Assistance of Indefinite Causal Order

The paper "Enhanced Communication With the Assistance of Indefinite Causal Order" proposes a novel framework within quantum Shannon theory, illustrating how quantum communication can be enhanced by utilizing quantum channels in a superposition of different orders. Authors Daniel Ebler, Sina Salek, and Giulio Chiribella explore the boundaries of classical assumptions within quantum communication networks, presenting compelling arguments and results that challenge established intuition regarding channel order.

Key Insights and Contributions

This research highlights several pivotal concepts:

1. Indefinite Causal Order and Quantum SWITCH: At the heart of the paper is the concept of quantum SWITCH, a higher-order operation that enables channels to be used in a superposition of orders. This means that quantum channels do not necessarily follow a fixed sequence, defying classical constraints on channel organization. The SWITCH operation induces a quantum superposition of two alternative orders of channels without realizing any classical mixture of orders.
2. Causal Activation: A significant result is that communication channels typically deemed ineffective, such as two identical completely depolarizing channels, can become active information carriers when combined through a quantum SWITCH. The phenomena termed "causal activation" imply that the order of channel operations fundamentally impacts their capability to convey information.
3. Analysis of Holevo Capacity: The paper proceeds to derive an expression for the Holevo capacity of two causally activated depolarizing channels. Contrary to classical expectation, the paper finds that when the quantum SWITCH is employed, these otherwise zero-capacity channels can independently support classical information transmission. Importantly, the derived expression reveals that the unique configuration achieves maximum communication efficiency for qubits and demonstrates a decrease with higher dimensions, underscoring non-intuitive quantum behaviors.
4. Non-commutativity and Self-switching: The phenomenon’s roots lie in the non-commutative nature of quantum processes. The paper points out that while switching identical channels classically does not alter outcomes, in the quantum field, switching yields distinct results when those channels comprise non-commuting operations.

Implications and Future Research

The implications of these findings are manifold for theoretical approaches in quantum information science. At a practical level, the insights gained could inform the design of more efficient quantum communication networks, suggesting that employing an indefinite causal structure in network configurations may unlock heretofore inaccessible communication enhancements.

The theoretical implications are equally profound. This research challenges the foundational assumptions in traditional quantum Shannon theory, providing a new lens through which the potential of quantum communication can be realized. These results may also serve to inform theoretical developments in emergent quantum gravity theories, where the causal structure is naturally indefinite.

The research opens several avenues for future exploration. Investigations could extend to assessing the non-additivity of the overall mapping generated by switching multiple depolarizing channels, potentially revealing further capabilities for quantum information transport. Additionally, practical implementations of indefinite causal order, such as through photonic systems or trapped ion configurations, offer rich potential but require further exploration regarding resource demands and technological feasibility.

In conclusion, this paper contributes an innovative perspective on quantum communication, demonstrating that the manipulation of channel order can substantially alter the communicative properties of quantum systems. As experimental techniques advance, these insights hold transformative potential for both quantum communication and the broader understanding of quantum information science.