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arXiv:2606.02942

Maximizing Information Flow in Three-Coin Quantum Walk: from Initial Entanglement to Integrated Photonic Implementation

Seyed Mohsen Moosavi Khansari

quant-phSubmitted Jun 1, 2026• Announced Jun 3, 2026• 0 citations
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Abstract

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 $α\approx 0.71$ - 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.

Comments
11 pages, 3 figures

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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)I(C;P;t)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 ααα (amplitude of non-displacement states) and show that the GHZ state reaches a maximum of mutual information at α≈0.71α\approx 0.71α≈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 ααα can be tuned with nonlinear or electro-optic elements. A scalable numerical framework (Python code) for simulations up to t=5t = 5t=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.
This work investigates a discrete-time quantum walk on a one-dimensional lattice driven by three entangled coins, each initialized via a Hadamard operator. The walker moves only when all three coins yield identical outcomes (HHH or TTT), coupling an 8-dimensional coin Hilbert space to the position degree of freedom. We analyze fully separable, fully entangled, and intermediate initial coin states, computing the von Neumann entropy of reduced subsystems to derive the mutual information between coin and position over successive steps. Our results demonstrate that initial tripartite entanglement significantly accelerates the growth of mutual information and enhances coin-position correlations compared to separable initial conditions. Notably, GHZ-type entangled states exhibit non-monotonic short-time dynamics due to interference, yet ultimately yield up to 18% higher mutual information by the tenth step. These findings underscore the role of pre-walk entanglement as a resource for controlling information flow and spatial spreading in quantum-walk-based protocols, with implications for quantum transport, state transfer, and correlation engineering.
We experimentally show the first realization of the maximal entanglement under a ballistic quantum transport. An inhomogeneous ordered quantum walk is introduced to generate the maximal entanglement meanwhile maintaining the quadratic speedup, wherein the coin operations keep unchanged with time evolution but are varied according to positions in a deterministic way. Using a reconfigurable time-bin encoded optical network, we implement a 11-step ballistic quantum walk and obtain a maximal entanglement in which the von Neumann entropy of the coin state is close to 1. The construction of the maximal entanglement and the speedup of spreading signify a quadratic acceleration in producing entanglement with fast expansion of the Hilbert space, thus may stimulate the engineering of entanglement and the design of quantum algorithms.
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.
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.
We investigate quantum entanglement of three photons performing discrete-time quantum walk (DTQW) on the nearest-neighbor sites of a square lattice. Such a DTQW setup has already been proposed to be realizable using linear optical elements. Each lattice site corresponds to the sequential action of a half-wave plate and a polarizing beam splitter. Two-dimensional DTQW can be mapped to an effective one-dimensional DTQW with a four-sided coin that depends on the polarization and direction of motion of the photons. It is known that such a system is capable to spatially entangle two photons, prepared in a separable state initially. We generalize the result to the case of three photons to explore if distinct entanglement classes, namely W and GHZ states, can be produced by this setup. In addition to spatial entanglement, we analyze the possibility of entanglement in the polarization basis, too. Our results can be significant for a simple and fast generation of multipartite entangled photonic states demanded by practical quantum technology applications.
Quantum magic, which accounts for the nonstabilizer content of a state, is essential for universal quantum computation beyond classically simulable resources. However, the way magic builds up during structured unitary dynamics remains largely open. Here, we investigate the generation and evolution of quantum magic in discrete-time quantum walks (DTQWs)—a simple, tunable unitary model realizable on a wide range of architectures. We use stabilizer Rényi entropy as a measure of quantum magic and investigate single- and two-walker quantum walks on a one-dimensional lattice, considering a wide range of initial coin states. Our results reveal that DTQWs can dynamically generate significant magic, with the amount and structure dependent on the initial state of the coin. In the case of a single walker, we found a nontrivial and complementary relationship between magic and entanglement at long times. In the two-walker setting, even states close to stabilizer form can evolve into highly magical states when subjected to quantum walk protocols. The generation of magic can occur independently of entanglement growth, emphasizing its distinct role as a quantum resource. We further show that the dynamical magic generation is robust under realistic noise—specifically, decoherence in the coin degree of freedom—demonstrating that this process persists across noisy settings. Finally, we discuss an experimentally feasible scheme to measure magic using current technology. Our findings position DTQWs as accessible and controllable platforms for producing quantum magic, offering a fresh perspective on their role in quantum information processing and reliable quantum computation.