Classical random walk involves the erratic motion of walkers along some random routes or areas, such as pollen's Brownian motion. Meanwhile, quantum walk is an extension of classical random walk in the quantum realm, and compared with the classical case, it is characterized by quantum superposition and entanglement. The diffusive quantum walk speed increases quadratically rather than linearly as in classical random walk, demonstrating an advantage over classical diffusion by spreading quantum information at a faster rate. Thus, quantum walk can be utilized to develop such quantum algorithms as quantum searching. Compared with classical algorithms, quantum-walk-based algorithms can provide quadratic enhancement. Additionally, as an effective model for describing micro-particle dynamics, quantum walk can serve as a universal platform to achieve arbitrary unitary evolutions, quantum state preparation, quantum logic gate operations, quantum measurements, etc. Finally, quantum walk can realize all key steps in quantum information processing.

Recently, many efforts have been devoted to exploring new mechanisms and applications of quantum walk. During a quantum walk, the walker carries quantum information and evolves in different positions. Thus, quantum walk is an effective way to achieve quantum communication and is extensively employed for developing quantum algorithms and achieving universal quantum computation. In addition, quantum walk can realize positive operator measurement and can be applied to quantum precision measurement.

Specifically, by controlling various parameters like position, phase, and evolution time across multiple degrees of freedom during the quantum walk, the coin state can be restored to its initial state after a specific evolution time. This approach can be utilized for implementing quantum state transfer. Any arbitrarily high-dimensional quantum state can be prepared by loading a high-dimensional system state onto the walker position state and employing a position-dependent quantum-walk process. This can be adopted for high-dimensional quantum communication purposes. Additionally, quantum walk can also be employed for quantum secure communication, random number generation, and direct quantum communication.

For quantum computation applications, both continuous-time quantum walks and discrete-time quantum walks have been proven to be applicable to universal quantum computation. Among them, continuous-time quantum walks have intuitive correspondences and natural advantages in solving such problems as searching for marked points on graphs. The presence of coin degrees of freedom in discrete-time quantum walks makes the dynamic evolution process easier to control. Therefore, discrete-time quantum walks also have unique advantages and wide applications in designing quantum algorithms. Meanwhile, quantum walk is universal in constructing different Hamiltonian and can be utilized for quantum simulation.

By performing the orthogonal measurements on walker positions, the quantum walk can achieve coin state positive operator-valued measurements. This greatly reduces the experimental difficulty in implementing positive operator-valued measurements and improves their feasibility and scalability. During the quantum walk, the walker carrying coin states evolves at different positions, causing entanglement between coin states and different paths. Entanglement is an effective quantum resource for implementing precise quantum measurements, which makes quantum walk have great potential for applications in quantum metrology.

Quantum walks provide a programmable and simple model for implementing many key steps in quantum information processing. In summary, quantum walk can be widely applied to quantum communications, quantum computation, and quantum measurements. The new mechanisms and applications of quantum walks attract the attention of many researchers in quantum information processing.