Zeno subspace in quantum-walk dynamics

Abstract

We investigate the discrete-time quantum walk evolution under the influence of the periodic measurements in position subspace. The undisturbed survival probability of the particle at the position subspace, $P(0,t)$ is compared with the survival probability after frequent ($n$) measurements at interval $\tau =t/n$, $P(0,\tau {)}^n$. We show that $P(0,\tau {)}^n>P(0,t)$ leading to the quantum Zeno effect in the position subspace when a parameter $\theta$ in the quantum coin operations and frequency of measurements is greater than the critical value, $\theta >{\theta }_c$ and $n>n_c$. This Zeno effect in the subspace preserves the dynamics in coin Hilbert space of the walk dynamics and has a potential to play a significant role in quantum tasks such as, preserving the quantum state of the particle at any particular position and to understand the Zeno dynamics in a multidimensional system which is highly transient in nature.

5 pages, 5 figures, Published version

References in corpus (31)

• Quantum Computation and Decision Trees
• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• A Quantum Random Walk Search Algorithm
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Photons Walking the Line: A quantum walk with adjustable coin operations
• Quantum Zeno subspaces
• From quantum cellular automata to quantum lattice gases
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Realization of a quantum walk with one and two trapped ions
• Quantum walk of a trapped ion in phase space
• Discrete single-photon quantum walks with tunable decoherence
• Quantum Zeno dynamics: mathematical and physical aspects
• Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
• Quantum random walks in optical lattices
• Experimental Implementation of the Quantum Random-Walk Algorithm
• Quantum Zeno effect by general measurements
• Quantum Simulations of Classical Annealing Processes
• Quantum Zeno Dynamics
• Optimizing the discrete time quantum walk using a SU(2) coin
• Recurrence and Pólya number of quantum walks
• Breakdown of an Electric-Field Driven System: a Mapping to a Quantum Walk
• Temporal behavior and quantum Zeno time of an excited state of the hydrogen atom
• Zeno dynamics yields ordinary constraints
• One- and two-dimensional quantum walks in arrays of optical traps
• Decoherence in Quantum Walks on the Hypercube
• Implementing the one-dimensional quantum (Hadamard) walk using a Bose-Einstein Condensate
• Hitting time for the continuous quantum walk
• Quantum phase transition using quantum walks in an optical lattice
• Quantum Zeno Effect with the Feynman-Mensky Path-Integral Approach
• Reflection and Transmission in a Neutron-Spin Test of the Quantum Zeno Effect
• Fractional recurrence in discrete-time quantum walk

Cited by in corpus (7)

• Quantum walks: a comprehensive review
• Confined quantum Zeno dynamics of a watched atomic arrow
• Deterministic generation of multiparticle entanglement by quantum Zeno dynamics
• Quantum Zeno effects across a parity-time symmetry breaking transition in atomic momentum space
• Survival probability in a one-dimensional quantum walk on a trapped lattice
• Quantized recurrence time in iterated open quantum dynamics
• Quantum Zeno dynamics of a matter-wave bright soliton