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

arXiv:1605.05553 · Fortschritte der Physik

Does the measurement take place when nobody observes it?

Shmuel Gurvitz

Published Nov 8, 2016• 10 citations
arXivHTMLPDF

Abstract

We consider non‐selective continuous measurements of a particle tunneling to a reservoir of finite band‐width (Λ). The particle is continuously monitored by frequent projective measurements (“quantum trajectory”), separated by a time‐interval τ. A simple analytical expression for the decay rate has been obtained. For Markovian reservoirs ( ), no effect of the measurements is found. Otherwise for a finite Λ, the decay rate always depends on the measurement time τ. This result is compared with alternative calculations, with no intermediate measurements, but when the measurement device is included in the Schrödinger evolution. We found that the detector affects the system by the decoherence rate ( ), related to the detector's signal. Although both treatments are different, the final results become very close for . This τ corresponds to the minimal time for which the detector's signal can be distinguished by an “observer”. This indicates a fundamental role of information in quantum motion and can be used for the extension of the quantum trajectory method for non‐Markovian environments.

DOI
10.1002/prop.201600065

Related papers

Quantum transfer through a non-Markovian environment under frequent measurements and Zeno effect

Luting Xu, Yunshan Cao, Xin-Qi Li +2 more

We study transitions of a particle between two wells, separated by a reservoir, under the condition that the particle is not detected in the reservoir. Conventional quantum trajectory theory predicts that such no-result continuous measurement would not affect these transitions. We demonstrate that it holds only for Markovian reservoirs (infinite bandwidth $\ensuremath{\Lambda}$). In the case of finite $\ensuremath{\Lambda}$, the probability of the particle's interwell transition is a function of the ratio $\ensuremath{\Lambda}/\ensuremath{\nu}$, where $\ensuremath{\nu}$ is the frequency of measurements. This scaling tells us that in the limit $\ensuremath{\nu}\ensuremath{\rightarrow}\ensuremath{\infty}$, the measurement freezes the initial state (the quantum Zeno effect), whereas for $\ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ it does not affect the particle's transition across the reservoir. The scaling is proved analytically by deriving a simple formula, which displays two regimes, with the Zeno effect and without the Zeno effect. It also supports a simple explanation of the Zeno effect entirely in terms of the energy-time uncertainty relation, with no explicit use of the projection postulate. Experimental tests of our predictions are discussed.

arXiv:1401.3159•Physical Review A•Aug 11, 2014•12 citations

Influence of measurement on the lifetime and the linewidth of unstable systems

B. Elattari, S. A. Gurvitz

We investigate the quantum Zeno effect in the case of electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schr\"odinger equation for the whole system can be reduced to Bloch-type rate equations describing the combined time development of the detector and the measured system. Using these equations we find that continuous measurement of the unstable system does not affect its exponential decay to a reservoir with a constant density of states. The width of the energy distribution of the tunneling electron, however, is not equal to the inverse lifetime---it increases due to the decoherence generated by the detector. We extend the analysis to the case of a reservoir described by an energy-dependent density of states, and we show that continuous measurement of such quantum systems affects both the exponential decay rate and the energy distribution. The decay does not always slow down, but might be accelerated. The energy distribution of the tunneling electron may reveal the lines invisible before the measurement.

arXiv:quant-ph/0001020•Physical Review A•Aug 8, 2000•48 citations

Conditions for implementing projective measurements through continuous monitoring

Therese Karmstrand, Franco Nori, Clemens Gneiting

Projective measurements are foundational for quantum physics in general and quantum information tasks in particular. However, their direct implementation is often not warranted. Here, we investigate under what conditions continuous monitoring that manifests in quantum jump trajectories realises projective measurements over time. Considering finite-dimensional quantum systems and single, diagonalisable jump operators, we show if and how the detected quantum jump statistics force, and allow inferring, the convergence of individual quantum trajectories towards eigenstates of an observable in the long-time limit. We identify a necessary non-degeneracy condition that is related to the presence of a strong symmetry with non-degenerate symmetry sectors. We derive analytical expressions for the rate of convergence and the time-error relationship in finite-time measurements. Our results provide a transparent framework for understanding the emergence of projective measurements from continuous monitoring, with direct implications for the optimisation of quantum measurement protocols in experiments.

quant-pharXiv:2608.09639•Physical Review Research•Aug 11, 2026•0 citations

Effect of Measurement on the Decay Rate of a Quantum System

B. Elattari, S. A. Gurvitz

We investigated the electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schrodinger equation for the whole system can be reduced to new Bloch-type rate equations describing the time development of the detector and the measured system at once. Using these equations we find that the continuous measurement of the unstable system does not affect its exponential decay, exp(-gammat), contrary to expectations based on the quantum Zeno effect. However, the width of the energy distribution of the tunneling electron is no longer gamma, but increases due to the decoherence, generated by the detector.

arXiv:quant-ph/9908054•Physical Review Letters•Mar 6, 2000•45 citations

Continuous measurement and non-Markovian quantum trajectories

Michael W. Jack, Matthew J. Collett

Based on a microscopic model of an open system consisting of a boson field coupled linearly to a system, we formulate quantum trajectories as continuous measurements of the output field from the system. We present a formulation for the case when the field quantity that is being monitored effectively commutes with itself at different times. In general, this results in a non-Markovian evolution for the reduced system conditioned on the measurements. Under the finite-memory time approximation this evolution can be numerically simulated. The generalization of the techniques of quantum trajectories to the non-Markovian regime is expected to contribute to our understanding of open system problems beyond the Born-Markov approximation.

Physical Review A•May 16, 2000•21 citations

The quantum Zeno and anti-Zeno effects with non-selective projective measurements

Mehwish Majeed, Adam Zaman Chaudhry

In studies of the quantum Zeno and anti-Zeno effects, it is usual to consider rapid projective measurements with equal time intervals being performed on the system to check whether or not the system is in the initial state. These projective measurements are selective measurements in the sense that the measurement results are read out and only the case where all the measurement results correspond to the initial state is considered in the analysis of the effect of the measurements. In this paper, we extend such a treatment to consider the effect of repeated non-selective projective measurements - only the final measurement is required to correspond to the initial state, while we do not know the results of the intermediate measurements. We present a general formalism to derive the effective decay rate of the initial quantum state with such nonselective measurements. Importantly, we show that there is a difference between using non-selective projective measurements and the usual approach of considering only selective measurements only if we go beyond the weak system-environment coupling regime in models other than the usual population decay models. As such, we then apply our formalism to investigate the quantum Zeno and anti-Zeno effects for three exactly solvable system-environment models: a single two-level system undergoing dephasing, a single two-level system interacting with an environment of two-level systems and a large spin undergoing dephasing. Our results show that the quantum Zeno and anti-Zeno effects in the presence of non-selective projective measurements can differ very significantly as compared to the repeated selective measurement scenario.

Scientific Reports•Oct 1, 2018•13 citations
We consider non‐selective continuous measurements of a particle tunneling to a reservoir of finite band‐width (Λ). The particle is continuously monitored by frequent projective measurements (“quantum trajectory”), separated by a time‐interval τ. A simple analytical expression for the decay rate has been obtained. For Markovian reservoirs ( ), no effect of the measurements is found. Otherwise for a finite Λ, the decay rate always depends on the measurement time τ. This result is compared with alternative calculations, with no intermediate measurements, but when the measurement device is included in the Schrödinger evolution. We found that the detector affects the system by the decoherence rate ( ), related to the detector's signal. Although both treatments are different, the final results become very close for . This τ corresponds to the minimal time for which the detector's signal can be distinguished by an “observer”. This indicates a fundamental role of information in quantum motion and can be used for the extension of the quantum trajectory method for non‐Markovian environments.
We study transitions of a particle between two wells, separated by a reservoir, under the condition that the particle is not detected in the reservoir. Conventional quantum trajectory theory predicts that such no-result continuous measurement would not affect these transitions. We demonstrate that it holds only for Markovian reservoirs (infinite bandwidth $\ensuremath{\Lambda}$). In the case of finite $\ensuremath{\Lambda}$, the probability of the particle's interwell transition is a function of the ratio $\ensuremath{\Lambda}/\ensuremath{\nu}$, where $\ensuremath{\nu}$ is the frequency of measurements. This scaling tells us that in the limit $\ensuremath{\nu}\ensuremath{\rightarrow}\ensuremath{\infty}$, the measurement freezes the initial state (the quantum Zeno effect), whereas for $\ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ it does not affect the particle's transition across the reservoir. The scaling is proved analytically by deriving a simple formula, which displays two regimes, with the Zeno effect and without the Zeno effect. It also supports a simple explanation of the Zeno effect entirely in terms of the energy-time uncertainty relation, with no explicit use of the projection postulate. Experimental tests of our predictions are discussed.
We investigate the quantum Zeno effect in the case of electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schr\"odinger equation for the whole system can be reduced to Bloch-type rate equations describing the combined time development of the detector and the measured system. Using these equations we find that continuous measurement of the unstable system does not affect its exponential decay to a reservoir with a constant density of states. The width of the energy distribution of the tunneling electron, however, is not equal to the inverse lifetime---it increases due to the decoherence generated by the detector. We extend the analysis to the case of a reservoir described by an energy-dependent density of states, and we show that continuous measurement of such quantum systems affects both the exponential decay rate and the energy distribution. The decay does not always slow down, but might be accelerated. The energy distribution of the tunneling electron may reveal the lines invisible before the measurement.
Projective measurements are foundational for quantum physics in general and quantum information tasks in particular. However, their direct implementation is often not warranted. Here, we investigate under what conditions continuous monitoring that manifests in quantum jump trajectories realises projective measurements over time. Considering finite-dimensional quantum systems and single, diagonalisable jump operators, we show if and how the detected quantum jump statistics force, and allow inferring, the convergence of individual quantum trajectories towards eigenstates of an observable in the long-time limit. We identify a necessary non-degeneracy condition that is related to the presence of a strong symmetry with non-degenerate symmetry sectors. We derive analytical expressions for the rate of convergence and the time-error relationship in finite-time measurements. Our results provide a transparent framework for understanding the emergence of projective measurements from continuous monitoring, with direct implications for the optimisation of quantum measurement protocols in experiments.
We investigated the electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schrodinger equation for the whole system can be reduced to new Bloch-type rate equations describing the time development of the detector and the measured system at once. Using these equations we find that the continuous measurement of the unstable system does not affect its exponential decay, exp(-gammat), contrary to expectations based on the quantum Zeno effect. However, the width of the energy distribution of the tunneling electron is no longer gamma, but increases due to the decoherence, generated by the detector.
Based on a microscopic model of an open system consisting of a boson field coupled linearly to a system, we formulate quantum trajectories as continuous measurements of the output field from the system. We present a formulation for the case when the field quantity that is being monitored effectively commutes with itself at different times. In general, this results in a non-Markovian evolution for the reduced system conditioned on the measurements. Under the finite-memory time approximation this evolution can be numerically simulated. The generalization of the techniques of quantum trajectories to the non-Markovian regime is expected to contribute to our understanding of open system problems beyond the Born-Markov approximation.
In studies of the quantum Zeno and anti-Zeno effects, it is usual to consider rapid projective measurements with equal time intervals being performed on the system to check whether or not the system is in the initial state. These projective measurements are selective measurements in the sense that the measurement results are read out and only the case where all the measurement results correspond to the initial state is considered in the analysis of the effect of the measurements. In this paper, we extend such a treatment to consider the effect of repeated non-selective projective measurements - only the final measurement is required to correspond to the initial state, while we do not know the results of the intermediate measurements. We present a general formalism to derive the effective decay rate of the initial quantum state with such nonselective measurements. Importantly, we show that there is a difference between using non-selective projective measurements and the usual approach of considering only selective measurements only if we go beyond the weak system-environment coupling regime in models other than the usual population decay models. As such, we then apply our formalism to investigate the quantum Zeno and anti-Zeno effects for three exactly solvable system-environment models: a single two-level system undergoing dephasing, a single two-level system interacting with an environment of two-level systems and a large spin undergoing dephasing. Our results show that the quantum Zeno and anti-Zeno effects in the presence of non-selective projective measurements can differ very significantly as compared to the repeated selective measurement scenario.