Edge State Transfer in Nonunitary Quantum Walk

Floquet Topological Phases Driven by $\mathcal{PT}$ Symmetric Nonunitary Time EvolutionFloquet Topological Phases Driven by $\mathcal{PT}$ Symmetric Nonunitary Time Evolution

Dakyeong Kim, Ken Mochizuki, Norio Kawakami +1 more

We study Floquet topological phases driven by $\mathcal{PT}$ symmetric nonunitary time evolution in one dimension, based on an experimental setup of discrete-time quantum walks. We develop, for nonunitary time-evolution operators, a procedure to calculate topological invariants for Floquet topological phases and find that the bulk-edge correspondence gives correct predictions of the emergent edge states. These edge states make exponential growth of wavefunction amplitudes at specific positions with time controllable. Hereby, we propose that these phenomena inherent in open quantum systems are feasibly observed by present experiments of quantum walks in both classical and quantum regimes.We study Floquet topological phases driven by $\mathcal{PT}$ symmetric nonunitary time evolution in one dimension, based on an experimental setup of discrete-time quantum walks. We develop, for nonunitary time-evolution operators, a procedure to calculate topological invariants for Floquet topological phases and find that the bulk-edge correspondence gives correct predictions of the emergent edge states. These edge states make exponential growth of wavefunction amplitudes at specific positions with time controllable. Hereby, we propose that these phenomena inherent in open quantum systems are feasibly observed by present experiments of quantum walks in both classical and quantum regimes.

Sep 30, 20160 citations

Zero transfer in continuous-time quantum walks

A. Sett, Haining Pan, Peter E. Falloon +1 more

arXiv:1902.11115Quantum Information ProcessingApr 10, 201916 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.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:1709.10287Physical Review LettersSep 27, 2017208 citations

Dynamical properties and applications of discrete time nonunitary quantum walks

Lihao Xu, Meng Li, Xiaoming Sun

Most existing studies of quantum walk focus on unitary closed systems, while the nonunitary counterpart, relevant to open quantum systems, remains relatively unexplored. This paper analyzes the position distribution and variance of quantum walk under the specific nonunitary evolution operator. Our results reveal that the variance exhibits distinct dynamical behavior depending on angular parameters, spatial dimensions, and initial states. In particular, for the one-dimensional non-Hermitian two-band lattice model, we demonstrate that the variance grows quadratically with time steps in the short-time regime, indicating faster diffusion than classical random walk. Leveraging this acceleration, we further propose a teleportation protocol based on nonunitary quantum walk, which eliminates the need for entangled state preparation and thereby reduces resource overhead while enhancing information transfer efficiency.Most existing studies of quantum walk focus on unitary closed systems, while the nonunitary counterpart, relevant to open quantum systems, remains relatively unexplored. This paper analyzes the position distribution and variance of quantum walk under the specific nonunitary evolution operator. Our results reveal that the variance exhibits distinct dynamical behavior depending on angular parameters, spatial dimensions, and initial states. In particular, for the one-dimensional non-Hermitian two-band lattice model, we demonstrate that the variance grows quadratically with time steps in the short-time regime, indicating faster diffusion than classical random walk. Leveraging this acceleration, we further propose a teleportation protocol based on nonunitary quantum walk, which eliminates the need for entangled state preparation and thereby reduces resource overhead while enhancing information transfer efficiency.

Physical Review ANov 3, 20250 citations

Floquet Topological Phases Driven by

\mathcal{PT}

Symmetric Nonunitary Time Evolution

We study Floquet topological phases driven by

\mathcal{PT}

symmetric nonunitary time evolution in one dimension, based on an experimental setup of discrete-time quantum walks. We develop, for nonunitary time-evolution operators, a procedure to calculate topological invariants for Floquet topological phases and find that the bulk-edge correspondence gives correct predictions of the emergent edge states. These edge states make exponential growth of wavefunction amplitudes at specific positions with time controllable. Hereby, we propose that these phenomena inherent in open quantum systems are feasibly observed by present experiments of quantum walks in both classical and quantum regimes.