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Bulletin of the American Physical Society

Consecutive measurements on the same quantum system reveal that wavefunctions do not collapse

Christoph Adami, Davor Curic, Jennifer R. Glick, Lambert Giner, Jeff S. Lundeen

Published Mar 7, 2019• 0 citations
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Quantum Mechanics of Consecutive Measurements

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Consecutive quantum measurements performed on the same system can reveal fundamental insights into quantum theory's causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen interpretation, measurements affect the quantum system in such a way that the quantum superposition collapses after the measurement, erasing any knowledge of the prior state. We show that a sequence of measurements in a collapse picture is equivalent to a quantum Markov chain, and that considering the unitary evolution of quantum wavefunctions interacting consecutively with more than two detectors reveals an experimentally measurable difference between a collapse and unitary picture. The non-Markovian nature of sequential measurements that we report is consistent with earlier discoveries in optimal quantum state discrimination.

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Measurement in Quantum Field Theory

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The topic of measurement in relativistic quantum field theory is addressed in this article. Some of the long standing problems of this subject are highlighted, including the incompatibility of an instantaneous ``collapse of the wavefunction'' with relativity of simultaneity, and the difficulty of maintaining causality in the rules for measurement highlighted by ``impossible measurement'' scenarios. Thereafter, the issue is considered from the perspective of mathematical physics. To this end, quantum field theory is described in a model-independent, operator algebraic setting, on generic Lorentzian spacetime manifolds. The process of measurement is modelled by a localized dynamical coupling between a quantum field called the ``system'', and another quantum field, called the ``probe''. The result of the dynamical coupling is a scattering map, whereby measurements carried out on the probe can be interpreted as measurements of induced observables on the system. The localization of the dynamical coupling allows it to derive causal relations for the induced observables. It will be discussed how this approach leads to the concept of selective or non-selective system state updates conditioned on the result of probe measurements, which in turn allows it to obtain conditional probabilities for consecutive probe measurements consistent with relativistic causality and general covariance, without the need for a physical collapse of the wavefunction. In particular, the problem of impossible measurements is resolved. Finally, there is a brief discussion of accelerated detectors and other related work.

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Evidence of Uncollapsed Quantum Amplitudes After Consecutive Measurements

Christoph Adami, Lambert Giner, Jeff S. Lundeen +1 more

Two of the most common interpretations of quantum measurement disagree about the fate of quantum amplitudes after measurement, yet this disagreement has not previously led to experimentally distinguishable predictions. In the standard collapse picture, commonly linked to the Copenhagen interpretation of quantum mechanics, measurements eliminate unrealized amplitudes without leaving a memory. In contrast, in the unitary theory, the measurement device registers one of the possible outcomes while remaining part of an entangled state that continues to harbor the unrealized amplitudes. This persistence arises naturally under unitary evolution, since a measurement device that is part of an entangled system cannot serve as a faithful probe of the joint quantum state. Using single-photon measurements of a tunable quantum state, we experimentally show that these two theories make different predictions when three or more consecutive measurements are performed on the same quantum system. Analysis of the joint density matrix of the three measurements reveals coherence among them and supports the unitary theory of quantum measurement. When decoherence is explicitly introduced, the joint density matrix of the quantum system of interest and the apparatus becomes consistent with what a collapse theory would predict. This work clarifies the dynamics of consecutive quantum measurements and offers new insights into the interpretation of quantum measurements.

quant-pharXiv:2603.13974•Mar 17, 2026•0 citations

The collapse of a quantum state as a joint probability construction*

Peter Morgan

Abstract The collapse of a quantum state can be understood as a mathematical way to construct a joint probability density even for operators that do not commute . We can formalize that construction as a non-commutative, non-associative collapse product that is nonlinear in its left operand as a model for joint measurements at time-like separation, in part inspired by the sequential product for positive semi-definite operators. The familiar collapse picture , in which a quantum state collapses after each measurement as a way to construct a joint probability density for consecutive measurements, is equivalent to a no-collapse picture in which Lüders transformers applied to subsequent measurements construct a quantum-mechanics—free subsystem of quantum non-demolition operators, not as a dynamical process but as an alternative mathematical model for the same consecutive measurements. The no-collapse picture is particularly simpler when we apply signal analysis to millions or billions of consecutive measurements.

arXiv:2101.10931•Journal of Physics A Mathematical and Theoretical•May 12, 2022•5 citations
Consecutive quantum measurements performed on the same system can reveal fundamental insights into quantum theory's causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen interpretation, measurements affect the quantum system in such a way that the quantum superposition collapses after the measurement, erasing any knowledge of the prior state. We show that a sequence of measurements in a collapse picture is equivalent to a quantum Markov chain, and that considering the unitary evolution of quantum wavefunctions interacting consecutively with more than two detectors reveals an experimentally measurable difference between a collapse and unitary picture. The non-Markovian nature of sequential measurements that we report is consistent with earlier discoveries in optimal quantum state discrimination.
The topic of measurement in relativistic quantum field theory is addressed in this article. Some of the long standing problems of this subject are highlighted, including the incompatibility of an instantaneous ``collapse of the wavefunction'' with relativity of simultaneity, and the difficulty of maintaining causality in the rules for measurement highlighted by ``impossible measurement'' scenarios. Thereafter, the issue is considered from the perspective of mathematical physics. To this end, quantum field theory is described in a model-independent, operator algebraic setting, on generic Lorentzian spacetime manifolds. The process of measurement is modelled by a localized dynamical coupling between a quantum field called the ``system'', and another quantum field, called the ``probe''. The result of the dynamical coupling is a scattering map, whereby measurements carried out on the probe can be interpreted as measurements of induced observables on the system. The localization of the dynamical coupling allows it to derive causal relations for the induced observables. It will be discussed how this approach leads to the concept of selective or non-selective system state updates conditioned on the result of probe measurements, which in turn allows it to obtain conditional probabilities for consecutive probe measurements consistent with relativistic causality and general covariance, without the need for a physical collapse of the wavefunction. In particular, the problem of impossible measurements is resolved. Finally, there is a brief discussion of accelerated detectors and other related work.
Two of the most common interpretations of quantum measurement disagree about the fate of quantum amplitudes after measurement, yet this disagreement has not previously led to experimentally distinguishable predictions. In the standard collapse picture, commonly linked to the Copenhagen interpretation of quantum mechanics, measurements eliminate unrealized amplitudes without leaving a memory. In contrast, in the unitary theory, the measurement device registers one of the possible outcomes while remaining part of an entangled state that continues to harbor the unrealized amplitudes. This persistence arises naturally under unitary evolution, since a measurement device that is part of an entangled system cannot serve as a faithful probe of the joint quantum state. Using single-photon measurements of a tunable quantum state, we experimentally show that these two theories make different predictions when three or more consecutive measurements are performed on the same quantum system. Analysis of the joint density matrix of the three measurements reveals coherence among them and supports the unitary theory of quantum measurement. When decoherence is explicitly introduced, the joint density matrix of the quantum system of interest and the apparatus becomes consistent with what a collapse theory would predict. This work clarifies the dynamics of consecutive quantum measurements and offers new insights into the interpretation of quantum measurements.
Abstract The collapse of a quantum state can be understood as a mathematical way to construct a joint probability density even for operators that do not commute . We can formalize that construction as a non-commutative, non-associative collapse product that is nonlinear in its left operand as a model for joint measurements at time-like separation, in part inspired by the sequential product for positive semi-definite operators. The familiar collapse picture , in which a quantum state collapses after each measurement as a way to construct a joint probability density for consecutive measurements, is equivalent to a no-collapse picture in which Lüders transformers applied to subsequent measurements construct a quantum-mechanics—free subsystem of quantum non-demolition operators, not as a dynamical process but as an alternative mathematical model for the same consecutive measurements. The no-collapse picture is particularly simpler when we apply signal analysis to millions or billions of consecutive measurements.