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

Bulletin of the American Physical Society

Statistical and optimal behaviours of weak continuous quantum measurement using stochastic path integral formalism

Areeya Chantasri, Andrew N. Jordan

Published Mar 18, 2016• 0 citations
OpenAlex

Related papers

A Stochastic Path Integral Formulation for Continuous Quantum Measurement

Areeya Chantasri, Justin Dressel, Andrew N. Jordan

Bulletin of the American Physical Society•Mar 19, 2013•0 citations

Stochastic path-integral formalism for continuous quantum measurement

Areeya Chantasri, Andrew N. Jordan

We generalize and extend the stochastic path-integral formalism and action principle for continuous quantum measurement introduced in Chantasri, Dressel, and Jordan [Phys. Rev. A 88, 042110 (2013)], where the optimal dynamics, such as the most likely paths, is obtained by extremizing the action of the stochastic path integral. In this work, we apply exact functional methods as well as develop a perturbative approach to investigate the statistical behavior of continuous quantum measurement. Examples are given for the qubit case. For qubit measurement with zero-qubit Hamiltonian, we find analytic solutions for average trajectories and their variances while conditioning on fixed initial and final states. For qubit measurement with unitary evolution, we use the perturbation method to compute expectation values, variances, and multi-time-correlation functions of qubit trajectories in the short-time regime. Moreover, we consider continuous qubit measurement with feedback control, using the action principle to investigate the global dynamics of its most likely paths, and finding that in an ideal case, qubit state stabilization at any desired pure state is possible with linear feedback. We also illustrate the power of the functional method by computing correlation functions for the qubit trajectories with a feedback loop to stabilize the qubit Rabi frequency.

arXiv:1507.07016•Physical Review A•Sep 21, 2015•60 citations

Stochastic action principle approach to continuous quantum measurement

Andrew N. Jordan

Bulletin of the American Physical Society•Mar 3, 2015•0 citations

Stochastic Path-Integral Analysis of the Continuously Monitored Quantum Harmonic Oscillator

Tathagata Karmakar, Philippe Lewalle, Andrew N. Jordan

We consider the evolution of a quantum simple harmonic oscillator in a general Gaussian state under simultaneous time-continuous weak position and momentum measurements.We deduce the stochastic evolution equations for position and momentum expectation values and the covariance-matrix elements from the characteristic function of the system.By generalizing the Chantasri-Dressel-Jordan (CDJ) formalism (Chantasri et al., 2013(Chantasri et al., , 2015) ) to this continuous-variable system, we construct its stochastic Hamiltonian and action.Action extremization gives us the equations for the most likely readout paths and quantum trajectories.For steady states of the covariance-matrix elements, the analytical solutions for these most likely paths are obtained.Using the CDJ formalism, we calculate final-state probability densities exactly starting from any initial state.We also demonstrate the agreement between the optimal-path solutions and the averages of simulated clustered stochastic trajectories.Our results provide insights into the time dependence of the mechanical energy of the system during the measurement process, motivating their importance for quantum measurement-engine or refrigerator experiments.Although quantum mechanics fundamentally limits our ability to extract information via simultaneous measurements of noncommuting observables, insights into the dynamics of the system during such a process can lead to a deeper understanding of the physics of measurement.

arXiv:2103.06111•PRX Quantum•Feb 18, 2022•16 citations

Action principle for continuous quantum measurement

Areeya Chantasri, Justin Dressel, Andrew N. Jordan

We present a stochastic path integral formalism for continuous quantum measurement that enables the analysis of rare events using action methods. By doubling the quantum state space to a canonical phase space, we can write the joint probability density function of measurement outcomes and quantum state trajectories as a phase space path integral. Extremizing this action produces the most likely paths with boundary conditions defined by preselected and postselected states as solutions to a set of ordinary differential equations. As an application, we analyze continuous qubit measurement in detail and examine the structure of a quantum jump in the Zeno measurement regime.

arXiv:1305.5201•Physical Review A•Oct 14, 2013•88 citations

Stochastic processes and continual measurements in quantum mechanics

Alberto Barchielli

Lecture notes in physics•Jan 1, 1986•15 citations
We generalize and extend the stochastic path-integral formalism and action principle for continuous quantum measurement introduced in Chantasri, Dressel, and Jordan [Phys. Rev. A 88, 042110 (2013)], where the optimal dynamics, such as the most likely paths, is obtained by extremizing the action of the stochastic path integral. In this work, we apply exact functional methods as well as develop a perturbative approach to investigate the statistical behavior of continuous quantum measurement. Examples are given for the qubit case. For qubit measurement with zero-qubit Hamiltonian, we find analytic solutions for average trajectories and their variances while conditioning on fixed initial and final states. For qubit measurement with unitary evolution, we use the perturbation method to compute expectation values, variances, and multi-time-correlation functions of qubit trajectories in the short-time regime. Moreover, we consider continuous qubit measurement with feedback control, using the action principle to investigate the global dynamics of its most likely paths, and finding that in an ideal case, qubit state stabilization at any desired pure state is possible with linear feedback. We also illustrate the power of the functional method by computing correlation functions for the qubit trajectories with a feedback loop to stabilize the qubit Rabi frequency.
We consider the evolution of a quantum simple harmonic oscillator in a general Gaussian state under simultaneous time-continuous weak position and momentum measurements.We deduce the stochastic evolution equations for position and momentum expectation values and the covariance-matrix elements from the characteristic function of the system.By generalizing the Chantasri-Dressel-Jordan (CDJ) formalism (Chantasri et al., 2013(Chantasri et al., , 2015) ) to this continuous-variable system, we construct its stochastic Hamiltonian and action.Action extremization gives us the equations for the most likely readout paths and quantum trajectories.For steady states of the covariance-matrix elements, the analytical solutions for these most likely paths are obtained.Using the CDJ formalism, we calculate final-state probability densities exactly starting from any initial state.We also demonstrate the agreement between the optimal-path solutions and the averages of simulated clustered stochastic trajectories.Our results provide insights into the time dependence of the mechanical energy of the system during the measurement process, motivating their importance for quantum measurement-engine or refrigerator experiments.Although quantum mechanics fundamentally limits our ability to extract information via simultaneous measurements of noncommuting observables, insights into the dynamics of the system during such a process can lead to a deeper understanding of the physics of measurement.
We present a stochastic path integral formalism for continuous quantum measurement that enables the analysis of rare events using action methods. By doubling the quantum state space to a canonical phase space, we can write the joint probability density function of measurement outcomes and quantum state trajectories as a phase space path integral. Extremizing this action produces the most likely paths with boundary conditions defined by preselected and postselected states as solutions to a set of ordinary differential equations. As an application, we analyze continuous qubit measurement in detail and examine the structure of a quantum jump in the Zeno measurement regime.