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arXiv:2602.16391

Enhancing delocalization and entanglement in asymmetric discrete-time quantum walks

Hao Zhao, Qiyan He, Fengzhi Yang, Cui Kong, Huiyun Cao, Tianqi Yan, Bingrui Zhong, Kaikun Tian, Jiguo Wang, Chuanjia Shan, Jibing Liu

quant-phSubmitted Feb 18, 2026• Announced Feb 19, 2026• 0 citations
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Abstract

In this paper, we investigate the enhancement of delocalization and coin-position entanglement in asymmetric discrete-time quantum walks (DTQWs). The asymmetry results from asymmetric coin operations, asymmetric initial states, and asymmetric polarization-dependent losses. By varying these asymmetry factors, the inverse participation ratio and entanglement entropy of the walker are numerically calculated for different coin and loss parameters, both for symmetric and asymmetric initial states. We then experimentally implement a 16-step asymmetric DTQW using a time-multiplexing fiber loop structure. By choosing an asymmetric initial state, both coin-position entanglement and delocalization are simultaneously enhanced under specific coin parameters. Moreover, we observe that with finite asymmetric polarization-dependent loss, the photon probability on the left side decreases significantly, while that on the right side increases and becomes more localized. Interestingly, under specific coin parameters, the entanglement and delocalization exhibit improved robustness against polarization-dependent loss. These results demonstrate that the DTQWs constitute an ideal platform for investigating photonic delocalization and hybrid entanglement.

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Enhancing delocalization and entanglement in asymmetric discrete-time quantum walks

Hao Zhao, Qiyan He, Fengzhi Yang +8 more

In this paper, we investigate the enhancement of delocalization and coin-position entanglement in asymmetric discrete-time quantum walks (DTQWs). The asymmetry results from asymmetric coin operations, asymmetric initial states, and asymmetric polarization-dependent losses. By varying these asymmetry factors, the inverse participation ratio and entanglement entropy of the walker are numerically calculated for different coin and loss parameters, both for symmetric and asymmetric initial states. We then experimentally implement a 16-step asymmetric DTQW using a time-multiplexing fiber loop structure. By choosing an asymmetric initial state, both coin-position entanglement and delocalization are simultaneously enhanced under specific coin parameters. Moreover, we observe that with finite asymmetric polarization-dependent loss, the photon probability on the left side decreases significantly, while that on the right side increases and becomes more localized. Interestingly, under specific coin parameters, the entanglement and delocalization exhibit improved robustness against polarization-dependent loss. These results demonstrate that the DTQWs constitute an ideal platform for investigating photonic delocalization and hybrid entanglement.

Optics Express•Jun 11, 2026•0 citations

Maximal coin-position entanglement and non-Hermitian skin effect in discrete-time quantum walks

Ding Cheng, Yi Li, Hao Zhao +6 more

A distinctive feature of non-Hermitian systems is the skin effect, which has recently attracted widespread attention. Quantum walks provide a powerful platform for investigating the underlying mechanisms of the non-Hermitian skin effect. Additionally, hybrid entanglement generation in quantum walks is recognized as another crucial property. However, experimentally investigating the influence of skin effect on the evolution of entanglement dynamics in the non-Hermitian systems remains a challenge. In this paper, we present a flexible implementation of 20-step discrete-time quantum walks using an optimized time-multiplexed loop configuration. By optimizing the coin parameter, we achieve maximal coin-position entanglement after 20-step quantum walks. Moreover, we experimentally measure the polarization-averaged growth rates and the evolution of coin-position entanglement under specific coin and loss parameters. We observe the asymmetric Lyapunov exponent profiles and the entanglement suppression induced by the non-Hermitian skin effect. Interestingly, this entanglement suppression weakens with increasing coin parameters and enhances with increasing loss parameters and evolution steps. Our results demonstrate the potential of quantum walks as a powerful platform for investigating hybrid entanglement properties and skin effects in non-Hermitian systems.

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Discrete-Time Quantum Walk with Phase Disorder: Localization and Entanglement Entropy

Meng Zeng, Ee Hou Yong

Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic phase disorder following either binary or uniform distribution in both one and two dimensions. For one dimension, we consider the Hadamard coin; for two dimensions, we consider either a 2-level Hadamard coin (Hadamard walk) or a 4-level Grover coin (Grover walk) for the rotation in coin-space. We study the transport properties e.g. inverse participation ratio (IPR) and the standard deviation of the density function (σ) as well as the coin-position entanglement entropy (EE), due to the two types of phase disorders and the two types of coins. Our numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the DTQW. The distribution of the phase disorder has very minor effects on the quantum walk.

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Experimental demonstration of quantum walks with initial superposition states

Qi-Ping Su, Yu Zhang, Li Yu +9 more

Abstract The preparation of initial superposition states of discrete-time quantum walks (DTQWs) is necessary for the study and applications of DTQWs. Based on an encoding method, here, we propose a DTQW protocol in linear optics, which enables the preparation of arbitrary initial superposition states of the walker and the coin and enables to obtain the states of the DTQW in addition to the probability distribution of the walker. With this protocol, we experimentally demonstrate the DTQW in the polarization space with both the walker and the coin initially in superposition states, by using only passive linear-optical elements. The effects of the walker’s different initial superposition states on the spread speed of the DTQW and on the entanglement between the coin and the walker are also experimentally investigated, which have not been reported before. When the walker starts with superposition states, we show that the properties of DTQWs are very different from those of DTQWs starting with a single position. Our findings reveal different properties of DTQWs and pave an avenue to study DTQWs with arbitrary initial states. Moreover, this encoding method enables one to encode an arbitrary high-dimensional quantum state, using a single physical qubit, and may be adopted to implement other quantum information tasks.

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Alana Spak dos Santos, Thiago T. Tsutsui, Fabiano M. Andrade

In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantum-walk (DTQW) analog of a periodic array of point interactions of the Kronig-Penney type, where the walker's wavenumber serves as a continuous, physically transparent control parameter for the coin operation. We analyze the spectra and the dynamics of position probability and entanglement, yielding distinct results for specific energies and point interactions. We relate the spectral structure to the spatial probability distribution and explicitly characterize the long-time entanglement behavior for each point interaction. The transmission modulus determines the quasienergy gap, bandwidth, and maximum group velocity, while also controlling the long-time coin-position entanglement for the initial state considered. The four families of one-dimensional point interactions ($δ$, $δ'$, crossed and asymmetric) realize qualitatively distinct transmission profiles and span the full range of behavior, including enhanced or strongly suppressed spreading and oscillatory entanglement.

quant-pharXiv:2609.03272•Sep 4, 2026•0 citations

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

Seyed Mohsen Moosavi Khansari

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.

quant-pharXiv:2606.02942•Jun 3, 2026•0 citations
In this paper, we investigate the enhancement of delocalization and coin-position entanglement in asymmetric discrete-time quantum walks (DTQWs). The asymmetry results from asymmetric coin operations, asymmetric initial states, and asymmetric polarization-dependent losses. By varying these asymmetry factors, the inverse participation ratio and entanglement entropy of the walker are numerically calculated for different coin and loss parameters, both for symmetric and asymmetric initial states. We then experimentally implement a 16-step asymmetric DTQW using a time-multiplexing fiber loop structure. By choosing an asymmetric initial state, both coin-position entanglement and delocalization are simultaneously enhanced under specific coin parameters. Moreover, we observe that with finite asymmetric polarization-dependent loss, the photon probability on the left side decreases significantly, while that on the right side increases and becomes more localized. Interestingly, under specific coin parameters, the entanglement and delocalization exhibit improved robustness against polarization-dependent loss. These results demonstrate that the DTQWs constitute an ideal platform for investigating photonic delocalization and hybrid entanglement.
In this paper, we investigate the enhancement of delocalization and coin-position entanglement in asymmetric discrete-time quantum walks (DTQWs). The asymmetry results from asymmetric coin operations, asymmetric initial states, and asymmetric polarization-dependent losses. By varying these asymmetry factors, the inverse participation ratio and entanglement entropy of the walker are numerically calculated for different coin and loss parameters, both for symmetric and asymmetric initial states. We then experimentally implement a 16-step asymmetric DTQW using a time-multiplexing fiber loop structure. By choosing an asymmetric initial state, both coin-position entanglement and delocalization are simultaneously enhanced under specific coin parameters. Moreover, we observe that with finite asymmetric polarization-dependent loss, the photon probability on the left side decreases significantly, while that on the right side increases and becomes more localized. Interestingly, under specific coin parameters, the entanglement and delocalization exhibit improved robustness against polarization-dependent loss. These results demonstrate that the DTQWs constitute an ideal platform for investigating photonic delocalization and hybrid entanglement.
A distinctive feature of non-Hermitian systems is the skin effect, which has recently attracted widespread attention. Quantum walks provide a powerful platform for investigating the underlying mechanisms of the non-Hermitian skin effect. Additionally, hybrid entanglement generation in quantum walks is recognized as another crucial property. However, experimentally investigating the influence of skin effect on the evolution of entanglement dynamics in the non-Hermitian systems remains a challenge. In this paper, we present a flexible implementation of 20-step discrete-time quantum walks using an optimized time-multiplexed loop configuration. By optimizing the coin parameter, we achieve maximal coin-position entanglement after 20-step quantum walks. Moreover, we experimentally measure the polarization-averaged growth rates and the evolution of coin-position entanglement under specific coin and loss parameters. We observe the asymmetric Lyapunov exponent profiles and the entanglement suppression induced by the non-Hermitian skin effect. Interestingly, this entanglement suppression weakens with increasing coin parameters and enhances with increasing loss parameters and evolution steps. Our results demonstrate the potential of quantum walks as a powerful platform for investigating hybrid entanglement properties and skin effects in non-Hermitian systems.
Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic phase disorder following either binary or uniform distribution in both one and two dimensions. For one dimension, we consider the Hadamard coin; for two dimensions, we consider either a 2-level Hadamard coin (Hadamard walk) or a 4-level Grover coin (Grover walk) for the rotation in coin-space. We study the transport properties e.g. inverse participation ratio (IPR) and the standard deviation of the density function (σ) as well as the coin-position entanglement entropy (EE), due to the two types of phase disorders and the two types of coins. Our numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the DTQW. The distribution of the phase disorder has very minor effects on the quantum walk.
Abstract The preparation of initial superposition states of discrete-time quantum walks (DTQWs) is necessary for the study and applications of DTQWs. Based on an encoding method, here, we propose a DTQW protocol in linear optics, which enables the preparation of arbitrary initial superposition states of the walker and the coin and enables to obtain the states of the DTQW in addition to the probability distribution of the walker. With this protocol, we experimentally demonstrate the DTQW in the polarization space with both the walker and the coin initially in superposition states, by using only passive linear-optical elements. The effects of the walker’s different initial superposition states on the spread speed of the DTQW and on the entanglement between the coin and the walker are also experimentally investigated, which have not been reported before. When the walker starts with superposition states, we show that the properties of DTQWs are very different from those of DTQWs starting with a single position. Our findings reveal different properties of DTQWs and pave an avenue to study DTQWs with arbitrary initial states. Moreover, this encoding method enables one to encode an arbitrary high-dimensional quantum state, using a single physical qubit, and may be adopted to implement other quantum information tasks.
In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantum-walk (DTQW) analog of a periodic array of point interactions of the Kronig-Penney type, where the walker's wavenumber serves as a continuous, physically transparent control parameter for the coin operation. We analyze the spectra and the dynamics of position probability and entanglement, yielding distinct results for specific energies and point interactions. We relate the spectral structure to the spatial probability distribution and explicitly characterize the long-time entanglement behavior for each point interaction. The transmission modulus determines the quasienergy gap, bandwidth, and maximum group velocity, while also controlling the long-time coin-position entanglement for the initial state considered. The four families of one-dimensional point interactions (δδδ, δ′δ'δ′, crossed and asymmetric) realize qualitatively distinct transmission profiles and span the full range of behavior, including enhanced or strongly suppressed spreading and oscillatory entanglement.
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.