Quantum Paths: A Quantum Walk Approach

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.