Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1802.02222 · Scientific Reports

Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks

Andrew K. Harter, Avadh Saxena, Yogesh N. Joglekar

Published Aug 7, 2018• 6 citations
arXivHTMLPDF

Abstract

Quantum walks often provide telling insights about the structure of the system on which they are performed. In [Formula: see text]-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization of the mean displacement of such a walker. We investigate the fragile aspects of a topological transition in these two dimer models. We find that the transition is sensitive to the initial state of the walker on the Bloch sphere, and the resultant mean displacement has a robust topological component and a quasiclassical component. In [Formula: see text] symmetric dimer lattices, we also show that the transition is smeared by nonlinear effects that become important in the [Formula: see text]-symmetry broken region. By carrying out consistency checks via analytical calculations, tight-binding results, and beam-propagation-method simulations, we show that our predictions are easily testable in today's experimental systems.

DOI
10.1038/s41598-018-30344-6

Related papers

Persistence of topological phases in non-Hermitian quantum walks

Vikash Mittal, Aswathy Raj, Sanjib Dey +1 more

Discrete-time quantum walks are known to exhibit exotic topological states and phases. Physical realization of quantum walks in a lossy environment may destroy these phases. We investigate the behaviour of topological states in quantum walks in the presence of a lossy environment. The environmental effects in the quantum walk dynamics are addressed using the non-Hermitian Hamiltonian approach. We show that the topological phases of the quantum walks are robust against moderate losses. The topological order in one-dimensional split-step quantum walk persists as long as the Hamiltonian respects exact [Formula: see text]-symmetry. Although the topological nature persists in two-dimensional quantum walks as well, the [Formula: see text]-symmetry has no role to play there. Furthermore, we observe topological phase transition in two-dimensional quantum walks that is induced by losses in the system.

arXiv:2007.15500•Scientific Reports•May 13, 2021•23 citations

Observation of dark edge states in parity-time-symmetric quantum dynamics

Peng Xue, Xingze Qiu, Kunkun Wang +2 more

Topological edge states arise in non-Hermitian parity-time ([Formula: see text])-symmetric systems, and manifest themselves as bright or dark edge states, depending on the imaginary components of their eigenenergies. As the spatial probabilities of dark edge states are suppressed during the non-unitary dynamics, it is a challenge to observe them experimentally. Here we report the experimental detection of dark edge states in photonic quantum walks with spontaneously broken [Formula: see text] symmetry, thus providing a complete description of the topological phenomena therein. We experimentally confirm that the global Berry phase in [Formula: see text]-symmetric quantum-walk dynamics unambiguously defines topological invariants of the system in both the [Formula: see text]-symmetry-unbroken and -broken regimes. Our results establish a unified framework for characterizing topology in [Formula: see text]-symmetric quantum-walk dynamics, and provide a useful method to observe topological phenomena in [Formula: see text]-symmetric non-Hermitian systems in general.

National Science Review•Jan 10, 2023•7 citations

Characterization of topological phases and selection of topological interface modes in the parity-time-symmetric quantum walk

Tian Chen, Bo Wang, Xiangdong Zhang

We present a method to detect topological invariants in nonunitary parity-time-symmetric (PT-symmetric) quantum walks (QWs). The topological phases of a PT-symmetric QW can be characterized by the mean position of the walk, which is an experimentally observable quantity. This method can also be applied to reveal topological phases in the unitary split-step QW and lattice model. We also explore the selection of topological interface modes in the PT-symmetric QW. The introduction of nonunitarity into the PT-symmetric QW can render the eigenvalue of the topological interface mode larger than the bulk region modes, which leads to the selective excitation of the corresponding topological interface mode during the evolution. Contrary to the Su--Schrieffer--Heeger (SSH) lattice model, in the PT-symmetric QW, the transition between the amplification and the suppression of the topological interface mode may not occur. Our study of the selection of topological interface modes in the PT-symmetric QW provides a route to realize the lasing of specific modes within the system.

Physical Review A•May 18, 2018•26 citations

Detecting Topological Invariants in Nonunitary Discrete-Time Quantum Walks

Xiang Zhan, Lei Xiao, Zhihao Bian +5 more

We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon, which effectively introduces loss to the dynamics. The topological invariant of the nonunitary quantum walk is manifested in the quantized average displacement of the walker, which is probed by monitoring the photon loss. We confirm the topological properties of the system by observing localized edge states at the boundary of regions with different topological invariants. We further demonstrate the robustness of both the topological properties and the measurement scheme of the topological invariants against disorder.

arXiv:1709.10287•Physical Review Letters•Sep 27, 2017•208 citations

Photonic quantum walks with symmetry protected topological phases

Andrea Blanco‐Redondo, Bryn A. Bell, Mordechai Segev +1 more

We experimentally study the effect of the lattice topology on photonic quantum walks. We generate correlated photon pairs in an array of silicon nanowaveguides making use of the high-nonlinearity available in the system. By using single-photon measurements and propagation simulations we demonstrate the transition between the characteristic path entanglement in random quantum walks and topological localization of the quantum states. Further, we show that this topological localization is robust against disorder that preserves the chiral symmetry of the system.

AIP conference proceedings•Jan 1, 2017•1 citation

Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks

Zhi-Yu Tian, Yang Liu, Le Luo

Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk-boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity-time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems.

arXiv:2201.09593•Entropy•Aug 31, 2021•0 citations
Quantum walks often provide telling insights about the structure of the system on which they are performed. In [Formula: see text]-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization of the mean displacement of such a walker. We investigate the fragile aspects of a topological transition in these two dimer models. We find that the transition is sensitive to the initial state of the walker on the Bloch sphere, and the resultant mean displacement has a robust topological component and a quasiclassical component. In [Formula: see text] symmetric dimer lattices, we also show that the transition is smeared by nonlinear effects that become important in the [Formula: see text]-symmetry broken region. By carrying out consistency checks via analytical calculations, tight-binding results, and beam-propagation-method simulations, we show that our predictions are easily testable in today's experimental systems.
Discrete-time quantum walks are known to exhibit exotic topological states and phases. Physical realization of quantum walks in a lossy environment may destroy these phases. We investigate the behaviour of topological states in quantum walks in the presence of a lossy environment. The environmental effects in the quantum walk dynamics are addressed using the non-Hermitian Hamiltonian approach. We show that the topological phases of the quantum walks are robust against moderate losses. The topological order in one-dimensional split-step quantum walk persists as long as the Hamiltonian respects exact [Formula: see text]-symmetry. Although the topological nature persists in two-dimensional quantum walks as well, the [Formula: see text]-symmetry has no role to play there. Furthermore, we observe topological phase transition in two-dimensional quantum walks that is induced by losses in the system.
Topological edge states arise in non-Hermitian parity-time ([Formula: see text])-symmetric systems, and manifest themselves as bright or dark edge states, depending on the imaginary components of their eigenenergies. As the spatial probabilities of dark edge states are suppressed during the non-unitary dynamics, it is a challenge to observe them experimentally. Here we report the experimental detection of dark edge states in photonic quantum walks with spontaneously broken [Formula: see text] symmetry, thus providing a complete description of the topological phenomena therein. We experimentally confirm that the global Berry phase in [Formula: see text]-symmetric quantum-walk dynamics unambiguously defines topological invariants of the system in both the [Formula: see text]-symmetry-unbroken and -broken regimes. Our results establish a unified framework for characterizing topology in [Formula: see text]-symmetric quantum-walk dynamics, and provide a useful method to observe topological phenomena in [Formula: see text]-symmetric non-Hermitian systems in general.
We present a method to detect topological invariants in nonunitary parity-time-symmetric (PT-symmetric) quantum walks (QWs). The topological phases of a PT-symmetric QW can be characterized by the mean position of the walk, which is an experimentally observable quantity. This method can also be applied to reveal topological phases in the unitary split-step QW and lattice model. We also explore the selection of topological interface modes in the PT-symmetric QW. The introduction of nonunitarity into the PT-symmetric QW can render the eigenvalue of the topological interface mode larger than the bulk region modes, which leads to the selective excitation of the corresponding topological interface mode during the evolution. Contrary to the Su--Schrieffer--Heeger (SSH) lattice model, in the PT-symmetric QW, the transition between the amplification and the suppression of the topological interface mode may not occur. Our study of the selection of topological interface modes in the PT-symmetric QW provides a route to realize the lasing of specific modes within the system.
We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon, which effectively introduces loss to the dynamics. The topological invariant of the nonunitary quantum walk is manifested in the quantized average displacement of the walker, which is probed by monitoring the photon loss. We confirm the topological properties of the system by observing localized edge states at the boundary of regions with different topological invariants. We further demonstrate the robustness of both the topological properties and the measurement scheme of the topological invariants against disorder.
We experimentally study the effect of the lattice topology on photonic quantum walks. We generate correlated photon pairs in an array of silicon nanowaveguides making use of the high-nonlinearity available in the system. By using single-photon measurements and propagation simulations we demonstrate the transition between the characteristic path entanglement in random quantum walks and topological localization of the quantum states. Further, we show that this topological localization is robust against disorder that preserves the chiral symmetry of the system.
Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk-boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity-time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems.