Entanglement is a key resource in many quantum information applications and achieving high values independently of the initial conditions is an important task. Here we address the problem of generating highly entangled states in a discrete time quantum walk irrespective of the initial state using two different approaches. First, we present and analyze a deterministic sequence of coin operators which produces high values of entanglement in a universal manner for a class of localized initial states. In a second approach, we optimize the discrete sequence of coin operators using a reinforcement learning algorithm. While the amount of entanglement produced by the deterministic sequence is fully independent of the initial states considered, the optimized sequences achieve in general higher average values of entanglement that do however depend on the initial state parameters. Our proposed sequence and optimization algorithm are especially useful in cases where the initial state is not fully known or entanglement has to be generated in a universal manner for a range of initial states.
Abstract Entanglement is a key resource in many quantum information applications and achieving high values independently of the initial conditions is an important task. Here we address the problem of generating highly entangled states in a discrete time quantum walk irrespective of the initial state using two different approaches. First, we present and analyze a deterministic sequence of coin operators which produces high values of entanglement in a universal manner for a class of localized initial states. In a second approach, we optimize the discrete sequence of coin operators using a reinforcement learning algorithm. While the amount of entanglement produced by the deterministic sequence is fully independent of the initial states considered, the optimized sequences achieve in general higher average values of entanglement that do however depend on the initial state parameters. Our proposed sequence and optimization algorithm are especially useful in cases where the initial state is not fully known or entanglement has to be generated in a universal manner for a range of initial states.
Quantum walks have been a platform for the study and modeling of many processes and physical systems, going from its application on the development of quantum algorithms to the study of energy transport in biological molecules.In the same way that in general aspects of quantum theory, it also aroused the necessity of studying the introduction of noise in the evolution of quantum walks, given that it is a major factor in experimental applications.In this context, in 2018 G. D. Molfetta et al. presented a quantum model of the classical elephant random walk, the elephant quantum walk, that analyzes a noisy unitary evolution.Posteriorly, M. A. Pires et al. generalized this walk into the generalized elephant quantum walk, showing to have an interesting property of controlling the diffusive behavior of the walker while maintaining the maximum generation of entanglement between its degrees of freedom, something unknown until then.In this work we proposed ourselves to study, through numerical experiments, the generation of entanglement in the generalized elephant quantum walk in general initial settings and evolutions.For such, first we introduce classical random walks, reviewing the necessary probability concepts.After, we approach quantum walks and restrict the description to coined discrete time quantum walks, the type of quantum walk to be studied.Our results indicate that this type of quantum walk potentially generates maximally entangled states for almost all initial states and evolutions, even with a low degree of noise.These results indicate that a dynamically random evolution, being it either in the coin operator, as previously studied for other authors, or in the shift operator as in this walk, generates maximally correlated states.
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 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.
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with one coin and two walkers whose purpose is to generate entanglement between walkers. We provide several classical computer simulations of our quantum algorithm in which we show that, although the asymptotical amount of entanglement generated between walkers does not reach the highest degree of entanglement possible at each step for either coin measurement outcome, the entanglement ratio (entanglement generated/highest value of entanglement possible, for each step) tends to converge, and the actual convergence value depends on the coin initial state and on the coin measurement outcome. Furthermore, our numerical simulations show that, for the quantum walks used in our algorithm, the value towards which entanglement ratio converges also depends on the position probability distribution symmetry of a quantum walk computed with one single walker and the same coin initial state employed in the corresponding quantum walk with two walkers.