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

Quantum Zeno region in quantum walk dynamics

C. M. Chandrashekar

Published Jul 8, 2010• 0 citations
OpenAlex

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.

Related papers

Zeno subspace in quantum-walk dynamics

C. M. Chandrashekar

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 $\ensuremath{\tau}=t/n$, $P(0,\ensuremath{\tau}){}^{n}$. We show that $P(0,\ensuremath{\tau}){}^{n}>P(0,t)$ leads to the quantum Zeno effect in position subspace when a parameter $\ensuremath{\theta}$ in the quantum coin operations and frequency of measurements is greater than the critical value, $\ensuremath{\theta}>{\ensuremath{\theta}}_{c}$ and $n>{n}_{c}$. This Zeno effect in the subspace preserves the dynamics in coin Hilbert space of the walk dynamics and has 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.

arXiv:1007.1303•Physical Review A•Nov 9, 2010•11 citations

Quantum Zeno dynamics: mathematical and physical aspects

P Facchi, S Pascazio

If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected "quantum Zeno subspace" is called "quantum Zeno dynamics:" for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.

arXiv:0903.3297•Journal of Physics A Mathematical and Theoretical•Oct 29, 2008•391 citations

Quantum Zeno dynamics: mathematical and physical aspects

Paolo Facchi A, Saverio Pascazio

Abstract. If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected “quantum Zeno subspace ” is called “quantum Zeno dynamics: ” for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.

•Nov 20, 2012•336 citations

Large-time limit of the quantum Zeno effect

Paolo Facchi A, Marilena Ligabò

If very frequent periodic measurements ascertain whether a quantum system is still in its initial state, its evolution is hindered. This peculiar phenomenon is called quantum Zeno effect. We investigate the large-time limit of the survival probability as the total observation time scales as a power of the measurement frequency, t∝Nα. The limit survival probability exhibits a sudden jump from 1 to 0 at α=1/2, the threshold between the quantum Zeno effect and a diffusive behavior. Moreover, we show that for α≥1, the limit probability becomes sensitive to the spectral properties of the initial state and to the arithmetic properties of the measurement periods.

arXiv:1702.04284•Journal of Mathematical Physics•Mar 1, 2017•6 citations

Quantum Zeno Dynamics

The evolution of a quantum system undergoing very frequent measurements takes place in a subspace of the total Hilbert space (quantum Zeno effect). The dynamical properties A quantum system, prepared in a state that does not belong to an eigenvalue of its total Hamiltonian, starts to evolve quadratically in time [1, 2]. This behavior leads to the so-called quantum Zeno phenomenon: by performing frequent measurements on the system, in order to check whether it is still in its initial state, one can “slow

•Jan 1, 2000•0 citations

Quantum Zeno Dynamics of two interacting particles

Varqa Abyaneh, Parsa Hossein Ghorbani

According to quantum Zeno dynamics (QZD), the evolution of a quantum system can be restricted to a subspace of its Hilbert space by frequent measurements. A crucial question in QZD of a particle's position is: how short the time interval between successive measurements should be, in order to confine the particle in its initial spatial region? To address this question, we consider a toy model with two ions initially known to be, for simplicity, in a one-dimensional spatial region. By simulating the evolution of this two-body quantum system, we estimate the measurement frequency needed to keep the ions within their initial confined region at a desired confidence level. Two key parameters we employ in our calculations are the Zeno time and the leakage probability of the quantum system. The measurement frequencies are calculated and compared when ions are located initially at different spatial regions. For our simulation, we introduce the Python code 2IonQZD.

arXiv:2402.06398•Scientific Reports•Sep 29, 2025•1 citation
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)P(0, t)P(0,t) is compared with the survival probability after frequent (nnn) measurements at interval τ=t/n\tau = t/nτ=t/n, P(0,τ)nP(0, \tau)^nP(0,τ)n. We show that P(0,τ)n>P(0,t)P(0, \tau)^n > P(0, t)P(0,τ)n>P(0,t) leading to the quantum Zeno effect in the position subspace when a parameter θ\thetaθ in the quantum coin operations and frequency of measurements is greater than the critical value, θ>θc\theta > \theta_{c}θ>θc​ and n>ncn>n_{c}n>nc​. 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.
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)P(0,t)P(0,t) is compared with the survival probability after frequent (nnn) measurements at interval $\ensuremath{\tau}=t/n$, $P(0,\ensuremath{\tau}){}^{n}$. We show that $P(0,\ensuremath{\tau}){}^{n}>P(0,t)$ leads to the quantum Zeno effect in position subspace when a parameter $\ensuremath{\theta}$ in the quantum coin operations and frequency of measurements is greater than the critical value, $\ensuremath{\theta}>{\ensuremath{\theta}}_{c}$ and n>ncn>{n}_{c}n>nc​. 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.
If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected "quantum Zeno subspace" is called "quantum Zeno dynamics:" for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.
Abstract. If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected “quantum Zeno subspace ” is called “quantum Zeno dynamics: ” for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.
If very frequent periodic measurements ascertain whether a quantum system is still in its initial state, its evolution is hindered. This peculiar phenomenon is called quantum Zeno effect. We investigate the large-time limit of the survival probability as the total observation time scales as a power of the measurement frequency, t∝Nα. The limit survival probability exhibits a sudden jump from 1 to 0 at α=1/2, the threshold between the quantum Zeno effect and a diffusive behavior. Moreover, we show that for α≥1, the limit probability becomes sensitive to the spectral properties of the initial state and to the arithmetic properties of the measurement periods.
The evolution of a quantum system undergoing very frequent measurements takes place in a subspace of the total Hilbert space (quantum Zeno effect). The dynamical properties A quantum system, prepared in a state that does not belong to an eigenvalue of its total Hamiltonian, starts to evolve quadratically in time [1, 2]. This behavior leads to the so-called quantum Zeno phenomenon: by performing frequent measurements on the system, in order to check whether it is still in its initial state, one can “slow
According to quantum Zeno dynamics (QZD), the evolution of a quantum system can be restricted to a subspace of its Hilbert space by frequent measurements. A crucial question in QZD of a particle's position is: how short the time interval between successive measurements should be, in order to confine the particle in its initial spatial region? To address this question, we consider a toy model with two ions initially known to be, for simplicity, in a one-dimensional spatial region. By simulating the evolution of this two-body quantum system, we estimate the measurement frequency needed to keep the ions within their initial confined region at a desired confidence level. Two key parameters we employ in our calculations are the Zeno time and the leakage probability of the quantum system. The measurement frequencies are calculated and compared when ions are located initially at different spatial regions. For our simulation, we introduce the Python code 2IonQZD.