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:2001.03647 · Physical Review A

Protective measurement of open quantum systems

Maximilian Schlosshauer

Published Jan 10, 2020• 4 citations
arXivHTMLPDF

Abstract

We study protective quantum measurements in the presence of an environment and decoherence. We consider the model of a protectively measured qubit that also interacts with a spin environment during the measurement. We investigate how the coupling to the environment affects the two characteristic properties of a protective measurement, namely (i) the ability to leave the state of the system approximately unchanged and (ii) the transfer of information about expectation values to the apparatus pointer. We find that even when the interaction with the environment is weak enough not to lead to appreciable decoherence of the initial qubit state, it causes a significant broadening of the probability distribution for the position of the apparatus pointer at the conclusion of the measurement. This washing out of the pointer position crucially diminishes the accuracy with which the desired expectation values can be measured from a readout of the pointer. We additionally show that even when the coupling to the environment is chosen such that the state of the system is immune to decoherence, the environment may still detrimentally affect the pointer readout.

DOI
10.1103/physreva.101.012108

Related papers

Critique of protective measurements

N. D. Hari Dass, Tabish Qureshi

The recently proposed idea of ``protective'' measurement of a quantum state is critically examined, and generalized. Earlier criticisms of the idea are discussed, and their relevance to the proposal assessed. Several constraints on measuring apparatus required by ``protective'' measurements are discussed, with emphasis on how they may restrict their experimental feasibility. Though ``protective'' measurements result in an unchanged system state and a shift of the pointer proportional to the expectation value of the measured observable in the system state, the actual reading of the pointer position gives rise to several subtleties. We propose several schemes for reading the pointer position, both when the apparatus is treated as a classical system as well as when its quantum aspects are taken into account, that address these issues. The tiny entanglement which is always present due to deviation from extreme adiabaticity in realistic situations is argued to be the weakest aspect of the proposal. Because of this, one can never perform a protective measurement on a single quantum system with absolute certainty. This clearly precludes an ontological status for the wave function. Several other conceptual issues are also discussed.

arXiv:quant-ph/9805012•Physical Review A•Apr 1, 1999•48 citations

Decoherence bypass of macroscopic superpositions in quantum measurement

Dominique Spehner, Fritz Haake

We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that a distinct pointer position is tied to each eigenvalue of the measured object observable. Those different pointer positions mutually decohere under the influence of an environment. Overcoming limitations of previous approaches we (i) cope with initial correlations between pointer and environment by considering them initially in a metastable local thermal equilibrium, (ii) allow for object–pointer entanglement and environment-induced decoherence of distinct pointer readouts to proceed simultaneously, such that mixtures of macroscopically distinct object–pointer product states arise without intervening macroscopic superpositions, and (iii) go beyond the Markovian treatment of decoherence.

arXiv:0709.0469•Journal of Physics A Mathematical and Theoretical•Feb 5, 2008•5 citations

Decoherence and measurement in open quantum systems

Vladimir Privman A, Dima V. Mozyrsky

We review results of a recently developed model of a microscopic quantum system interacting with the macroscopic world components which are modeled by collections of bosonic modes. The interaction is via a general operator (Lambda) of the system, coupled to the creation and annihilation operators of the environment modes. We assume that in the process of a nearly instantaneous quantum measurement, the function of the environment involves two distinct parts: the pointer and the bath. Interaction of the system with the bath leads to decoherence such that the system and the pointer both evolve into a statistical mixture state described by the density matrix such that the system is in one of the eigenstates of (Lambda) with the correct quantum mechanical probability, whereas the expectation values of pointer operators retain amplified information on that eigenstate. We argue that this process represents the initial step of a quantum measurement.

arXiv:quant-ph/0003051•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 13, 2000•2 citations

Protecting a quantum state from environmental noise by an incompatible finite-time measurement

Carlos Alexandre Brasil, Leonardo Andreta de Castro, Reginaldo de Jesus Napolitano

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.

arXiv:1106.4537•Physical Review A•Aug 25, 2011•13 citations

State disturbance and pointer shift in protective quantum measurements

Maximilian Schlosshauer

We investigate the disturbance of the state of a quantum system in a protective measurement for finite measurement times and different choices of the time-dependent system-apparatus coupling function. The ability to minimize this state disturbance is essential to protective measurement. We show that for a coupling strength that remains constant during the measurement interaction of duration $T$, the state disturbance scales as ${T}^{\ensuremath{-}2}$, while a simple smoothing of the coupling function significantly improves the scaling behavior to ${T}^{\ensuremath{-}6}$. We also prove that the shift of the apparatus pointer in the course of a protective measurement is independent of the particular time dependence of the coupling function, suggesting that the guiding principle for choosing the coupling function should be the minimization of the state disturbance. Our results illuminate the dynamics of protective measurement under realistic circumstances and may aid in the experimental realization of such measurements.

arXiv:1411.2642•Physical Review A•Nov 10, 2014•7 citations

Does Decoherence Select the Pointer Basis of a Quantum Meter?

Abraham G. Kofman, Gershon Kurizki

The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The latter statement means that the environment monitors (measures) selected observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the “pointer states” that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer’s choices play an indispensable role in quantum mechanics.

Entropy•Jan 10, 2022•3 citations
We study protective quantum measurements in the presence of an environment and decoherence. We consider the model of a protectively measured qubit that also interacts with a spin environment during the measurement. We investigate how the coupling to the environment affects the two characteristic properties of a protective measurement, namely (i) the ability to leave the state of the system approximately unchanged and (ii) the transfer of information about expectation values to the apparatus pointer. We find that even when the interaction with the environment is weak enough not to lead to appreciable decoherence of the initial qubit state, it causes a significant broadening of the probability distribution for the position of the apparatus pointer at the conclusion of the measurement. This washing out of the pointer position crucially diminishes the accuracy with which the desired expectation values can be measured from a readout of the pointer. We additionally show that even when the coupling to the environment is chosen such that the state of the system is immune to decoherence, the environment may still detrimentally affect the pointer readout.
The recently proposed idea of ``protective'' measurement of a quantum state is critically examined, and generalized. Earlier criticisms of the idea are discussed, and their relevance to the proposal assessed. Several constraints on measuring apparatus required by ``protective'' measurements are discussed, with emphasis on how they may restrict their experimental feasibility. Though ``protective'' measurements result in an unchanged system state and a shift of the pointer proportional to the expectation value of the measured observable in the system state, the actual reading of the pointer position gives rise to several subtleties. We propose several schemes for reading the pointer position, both when the apparatus is treated as a classical system as well as when its quantum aspects are taken into account, that address these issues. The tiny entanglement which is always present due to deviation from extreme adiabaticity in realistic situations is argued to be the weakest aspect of the proposal. Because of this, one can never perform a protective measurement on a single quantum system with absolute certainty. This clearly precludes an ontological status for the wave function. Several other conceptual issues are also discussed.
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that a distinct pointer position is tied to each eigenvalue of the measured object observable. Those different pointer positions mutually decohere under the influence of an environment. Overcoming limitations of previous approaches we (i) cope with initial correlations between pointer and environment by considering them initially in a metastable local thermal equilibrium, (ii) allow for object–pointer entanglement and environment-induced decoherence of distinct pointer readouts to proceed simultaneously, such that mixtures of macroscopically distinct object–pointer product states arise without intervening macroscopic superpositions, and (iii) go beyond the Markovian treatment of decoherence.
We review results of a recently developed model of a microscopic quantum system interacting with the macroscopic world components which are modeled by collections of bosonic modes. The interaction is via a general operator (Lambda) of the system, coupled to the creation and annihilation operators of the environment modes. We assume that in the process of a nearly instantaneous quantum measurement, the function of the environment involves two distinct parts: the pointer and the bath. Interaction of the system with the bath leads to decoherence such that the system and the pointer both evolve into a statistical mixture state described by the density matrix such that the system is in one of the eigenstates of (Lambda) with the correct quantum mechanical probability, whereas the expectation values of pointer operators retain amplified information on that eigenstate. We argue that this process represents the initial step of a quantum measurement.
We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.
We investigate the disturbance of the state of a quantum system in a protective measurement for finite measurement times and different choices of the time-dependent system-apparatus coupling function. The ability to minimize this state disturbance is essential to protective measurement. We show that for a coupling strength that remains constant during the measurement interaction of duration TTT, the state disturbance scales as ${T}^{\ensuremath{-}2}$, while a simple smoothing of the coupling function significantly improves the scaling behavior to ${T}^{\ensuremath{-}6}$. We also prove that the shift of the apparatus pointer in the course of a protective measurement is independent of the particular time dependence of the coupling function, suggesting that the guiding principle for choosing the coupling function should be the minimization of the state disturbance. Our results illuminate the dynamics of protective measurement under realistic circumstances and may aid in the experimental realization of such measurements.
The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The latter statement means that the environment monitors (measures) selected observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the “pointer states” that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer’s choices play an indispensable role in quantum mechanics.