Quantum walk for SU(1,1)
arXiv:2207.04511 · doi:10.1103/PhysRevA.107.022224
Abstract
We propose a scheme to implement the quantum walk for SU(1,1) in the phase space, which generalizes those associated with the Heisenberg-Weyl group. The movement of the walker described by the SU(1,1) coherent states can be visualized on the hyperboloid or the Poincaré disk. In both one-mode and two-mode realizations, we introduce the corresponding coin-flip and conditional-shift operators for the SU(1,1) group, whose relations with those for Heisenberg-Weyl group are analyzed. The probability distribution, standard deviation and the von Neumann entropy are employed to describe the walking process. The nonorthogonality of the SU(1,1) coherent states precludes the quantum walk for SU(1,1) from the idealized one. However, the overlap between different SU(1,1) coherent states can be reduced by increasing the Bargmann index , which indicates that the two-mode realization provides more possibilities to simulate the idealized quantum walk.
arXiv comment8 pages, 6 figures
References in corpus (45)
- Quantum random walks - an introductory overview
- Quantum Computation and Decision Trees
- Universal computation by quantum walk
- Quantum walks: a comprehensive review
- Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Observation of topologically protected bound states in a one dimensional photonic system
- Exploring Topological Phases With Quantum Walks
- Universal quantum computation using the discrete time quantum walk
- Anderson localization of entangled photons in an integrated quantum walk
- Quantum walk of a trapped ion in phase space
- Universal computation by multi-particle quantum walk
- Strongly Correlated Quantum Walks in Optical Lattices
- Decoherence and disorder in quantum walks: From ballistic spread to localization
- Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
- Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
- Implementing the quantum random walk
- Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
- Quantum harmonic oscillator state synthesis by reservoir engineering
- Simulating dynamic quantum phase transitions in photonic quantum walks
- The quantum to classical transition for random walks
- Quantum quincunx in cavity quantum electrodynamics
- Quantum random walks with decoherent coins
- Entanglement in coined quantum walks on regular graphs
- Quantum Entangled Interferometers
- Quantum walk on the line: entanglement and non-local initial conditions
- Topological quantum walks in momentum space with a Bose-Einstein condensate
- Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks
- Breakdown of an Electric-Field Driven System: a Mapping to a Quantum Walk
- Entanglement between a qubit and the environment in the spin-boson model
- Quantum Walk in Momentum Space with a Bose-Einstein Condensate
- Disordered Quantum Walks in one lattice dimension
- Explicit definition of symmetry for non-unitary quantum walks with gain and loss
- Detecting non-Bloch topological invariants in quantum dynamics
- Superposition of two-mode squeezed states for quantum information processing and quantum sensing
- Quantum harmonic oscillator state control in a squeezed Fock basis
- SU(1,1) echoes for breathers in quantum gases
- Many-Body Echo
- Experimental simulation and limitations of quantum walks with trapped ions
- Many-body Dynamics with Time-dependent Interaction
- Sub-Planck phase-space structure and sensitivity for SU(1,1) compass states
- Geometrizing quantum dynamics of a Bose-Einstein condensate
- Quantum walk on circles in phase space
- Quantum walk on the Bloch sphere
- Quantum walk on a toral phase space