We report that the position-inhomogeneous quantum walk (IQW) can be utilized to produce the maximal high-dimensional entanglement while maintaining the quadratic speedup spread of the wave function. Our calculations show that the maximal coin-walker entanglement can be generated in any odd steps or asymptotically in even steps, and the nearly maximal entanglement can be obtained in even steps after 2. We implement the IQW by a stable resource-saving time-bin optical network, in which a polarization Sagnac loop is employed to realize the precisely tunable phase shift. Our approach opens up an efficient way for high-dimensional entanglement engineering as well as promotes investigations on the role of coin-walker interactions in QW-based applications.
Discrete-time quantum walks are powerful platforms for simulating quantum transport and information processing. Here we introduce a walker on a one-dimensional lattice whose motion is controlled by three entangled coins, each initialized with the Hadamard gate, aiming to maximize information flow. The walker moves only when all three coins yield the same outcome (HHH or TTT), thus coupling the 8-dimensional coin Hilbert space to the position degree of freedom. By analyzing fully separable, fully entangled (GHZ-type) and intermediate initial states, and using the von Neumann entropy of reduced subsystems, we compute the mutual information
I(C;P;t) between coin and position. The results show that initial three-partite entanglement accelerates the growth of mutual information by up to 18\% after ten steps (when compared to the lower of the two separable states), although it exhibits short-term non-monotonic dynamics due to quantum interference. For the first time, we introduce a tunable parameter
α (amplitude of non-displacement states) and show that the GHZ state reaches a maximum of mutual information at
α≈0.71 - a key finding for optimal control of information flow. Finally, an integrated photonic implementation using polarization, spatial modes and time bins is proposed, where
α can be tuned with nonlinear or electro-optic elements. A scalable numerical framework (Python code) for simulations up to
t=5 steps is provided. Our findings establish three-partite entanglement as a dynamical resource for maximizing information flow and spatial spreading, with direct applications in quantum state transfer, entanglement-assisted sensing and programmable photonic quantum processors.
We study maximal coin-position entanglement generation via a discrete-time quantum walk, in which the coin operation is randomly selected from one of two coin operators set at each step. We solve maximal entanglement generation as an optimization problem with quantum process fidelity as the cost function. Then we determine the maximal entanglement that can be rigorously generated for any step beyond the second regardless of initial conditions with appropriate coin sequences. The simplest coin sequence comprising Hadamard and identity operations is equivalent to the generalized elephant quantum walk, which exhibits an increasingly faster spreading in terms of probability distribution. Experimentally, we demonstrate a ten-step quantum walk driven by such coin sequences with linear optics and thereby show the desired high-dimensional bipartite entanglement as well as the transport behavior of faster spreading.
Abstract. The coin-position entanglement generated by the evolution operator of a discrete–time quantum walk is quantified, using the von Neumann entropy of the reduced density operator (entropy of entanglement). In the case of a single walker, the entropy of entanglement converges, in the long time limit, to a well defined value which depends on the initial state. Exact expressions are obtained for local and non-local initial conditions. We also discuss the asymptotic bi-partite entanglement generated by non-separable coin operations for two coherent quantum walkers. In this case, the entropy of entanglement is observed to increase logarithmically with time. 1.
We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value asymptotically in the number of steps, outperforming the entanglement attained by using ordered QRW. The disorder is modeled by introducing an extra random aspect to QRW, a classical coin that randomly dictates which quantum coin drives the system's time evolution. We also show that maximal entanglement is achieved independently of the initial state of the walker, study the number of steps the system must move to be within a small fixed neighborhood of its asymptotic limit, and propose two experiments where these ideas can be tested.
We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value asymptotically in the number of steps, outperforming the entanglement attained by using ordered QRW. The disorder is modeled by introducing an extra random aspect to QRW, a classical coin that randomly dictates which quantum coin drives the system's time evolution. We also show that maximal entanglement is achieved independently of the initial state of the walker, study the number of steps the system must move to be within a small fixed neighborhood of its asymptotic limit, and propose two experiments where these ideas can be tested.