Steering of Quantum Walks through Coherent Control of High-dimensional Bi-photon Quantum Frequency Combs with Tunable State Entropies

Quantum walks are central to a wide range of applications such as quantum search, quantum information processing, and entanglement transport. Gaining control over the duration and the direction of quantum walks (QWs) is crucial to implementing dedicated processing. However, in current systems, it is cumbersome to achieve in a scalable format. High-dimensional quantum states, encoded in the photons' frequency degree of freedom in on-chip devices are great assets for the scalable generation and reliable manipulation of large-scale complex quantum systems. These states, viz. quantum frequency combs (QFCs) accommodating huge information in a single spatial mode, are intrinsically noise tolerant, and suitable for transmission through optical fibers, thereby promising to revolutionize quantum technologies. Existing literature aimed to generate maximally entangled QFCs excited from continuous-wave lasers either from nonlinear microcavities or from waveguides with the help of filter arrays. QWs with flexible depth/duration have been lately demonstrated from such QFCs. Here, instead of maximally-entangled QFCs, we generate high-dimensional quantum photonic states with tunable entropies from periodically poled lithium niobate waveguides by exploiting a novel pulsed excitation and filtering scheme. We confirm the generation of QFCs with normalized entropies from $\sim 0.35$ to $1$ by performing quantum tomography with high fidelities. These states can be an excellent testbed for several quantum computation and communication protocols in nonideal scenarios and enable artificial neural networks to classify unknown quantum states. Further, we experimentally demonstrate the steering and coherent control of the directionality of QWs initiated from such QFCs with tunable entropies. Our findings offer a new control mechanism for QWs as well as novel modification means for joint probability distributions.