Quantum Paths: a Quantum Walk approach

TL;DR

The paper addresses the challenge of implementing the quantum switch for noiseless communications by proposing a hybrid framework that combines spatial superposition of quantum channels with discrete-time quantum walk dynamics. It demonstrates that a two-hop evolution within this hybrid setup can reproduce the input-output behavior of a quantum switch for unitary channels, and identifies conditions under which non-unitary channels can be accommodated. This approach suggests a more feasible experimental route to realize switch-like advantages and provides a clearer interpretive link between spatial channel superposition, quantum walks, and causal-order superposition. Overall, the work opens new possibilities for scalable quantum networking by emulating the quantum switch through spatial superposition and walk-based dynamics.

Abstract

The quantum switch, a process enabling a coherent superposition of different orders of quantum channels, has garnered significant attention due to its ability to enable noiseless communications through noisy channels, such as entanglement-breaking channels. However, its practical implementation and scalability remain challenging. In contrast, the spatial superposition of quantum channels is more accessible experimentally and has been shown to enhance channel capacity, although it does not match the performance of the quantum switch. In this work, we present preliminary theoretical results demonstrating that, by applying tools of the quantum random walk framework to the spatial superposition of channels, it is possible to replicate the output of a quantum switch. These findings suggest a promising and more feasible route to emulate the quantum switch, offering both practical advantages and interpretative clarity.

Figures (3)

• Figure 1: Pictorial representation of the main result of this work: mimicking the quantum switch behavior via spatial superposition. Specifically, the network nodes are connected via two-hops. The evolution of the state of the information carrier through the two-hops spatial superposition of the quantum channels $\mathcal{E}$ and $\mathcal{D}$ is equivalent to the output of the quantum switch, exploiting the causal-order superposition of the considered channels.
• Figure 2: Pictorial representation of the spatial superposition of quantum channels. Based on the state of the control qubit, the quantum carrier can go either through one of the channels ($\mathcal{E}$ or $\mathcal{D}$) or through a quantum superposition of the two channels. Specifically, if the control qubit is initialized in $\ket{0}\bra{0}$ ($\ket{1}\bra{1}$), the information carrier propagates through channel $\mathcal{E}$ (channel $\mathcal{D}$), but if the control qubit is prepared in $\ket{+}\bra{+}$ ($\ket{-}\bra{-}$) then the information carrier propagates through a spatial superposition of both the channels.
• Figure 3: Pictorial representation of the quantum switch. The information carrier is sent through a superposition of different causal orders. Based on the quantum state of the control qubit, the informational carrier can go through an ordered sequence of channels $\mathcal{E}\rightarrow\mathcal{D}$ (equivalently $\mathcal{D}\rightarrow\mathcal{E}$) or a quantum superposition of the two orders.