Zeno subspace in quantum-walk dynamics

Journal Article · Mon Nov 15 04:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.052108· OSTI ID:21528565

Chandrashekar, C M ^[1]

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1. Quantum Science Center, The Institute of Mathematical Sciences, Chennai 600113 (India)

We investigate discrete-time quantum-walk evolution under the influence of 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}){sup n}. We show that P(0,{tau}){sup n}>P(0,t) leads to the quantum Zeno effect in position subspace when a parameter {theta} in the quantum coin operations and frequency of measurements is greater than the critical value, {theta}>{theta}{sub c} and n>n{sub c}. This Zeno effect in the subspace preserves the dynamics in coin Hilbert space of the walk dynamics and has the 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 that is highly transient in nature.

• OSTI ID: 21528565
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 82; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
EVOLUTION
HILBERT SPACE
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL EVOLUTION
MATHEMATICAL SPACE
MECHANICS
PARTICLES
PROBABILITY
QUANTUM MECHANICS
QUANTUM STATES
SPACE