Measurement incompatibility is strictly stronger than disturbance (original) (raw)

Incompatibility is strictly stronger than disturbance

arXiv (Cornell University), 2023

The core of Heisenberg's heuristic argument for the uncertainty principle, involving the famous γ-ray microscope Gedankenexperiment, hinges upon the existence of measurements that irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. The argument was put forward to justify measurement incompatibility in quantum theory, namely, the existence of measurements that cannot be performed jointly-a feature that is now understood to be different from irreversibility of measurement disturbance, though related to it. In this Letter, on the one hand, we provide a compelling argument showing that measurement incompatibility is indeed a sufficient condition for irreversibility of measurement disturbance, while, on the other hand, we exhibit a toy theory that is a counterexample for the converse implication.

“No Information Without Disturbance”: Quantum Limitations of Measurement

Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle (eds. W.C. Myrvold, J. Christian), pp. 229-256, 2009

In this contribution I review rigorous formulations of a variety of limitations of measurability in quantum mechanics. To this end I begin with a brief presentation of the conceptual tools of modern measurement theory. I will make precise the notion that quantum measurements necessarily alter the system under investigation and elucidate its connection with the complementarity and uncertainty principles.

On the Heisenberg principle, namely on the information-disturbance trade-off in a quantum measurement

Fortschritte Der Physik-progress of Physics, 2003

Common misconceptions on the Heisenberg principle are reviewed, and the original spirit of the principle is reestablished in terms of the trade-off between information retrieved by a measurement and disturbance on the measured system. After analyzing the possibility of probabilistically reversible measurements, along with erasure of information and undoing of disturbance, general information-disturbance trade-offs are presented, where the disturbance of the measurement is related to the possibility in principle of undoing its effect. *

Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements

2012

While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as ''Heisenberg's uncertainty principle,''Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create. Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle.

Incompatibility robustness of quantum measurements: a unified framework

New Journal of Physics, 2019

In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible quantum measurements, i.e. measurements that cannot be simultaneously performed on a single copy of the system. It is then natural to ask what the most incompatible quantum measurements are. To answer this question, several measures have been proposed to quantify how incompatible a set of measurements is, however their properties are not well-understood. In this work, we develop a general framework that encompasses all the commonly used measures of incompatibility based on robustness to noise. Moreover, we propose several conditions that a measure of incompatibility should satisfy, and investigate whether the existing measures comply with them. We find that some of the widely used measures do not fulfil these basic requirements. We also show that when looking for the most incompatible pairs of measurements, we obtain different ans...

The Theory of Quantum Uncertainties and Quantum Measurements

  1. We shall discuss what modern interpretations say about the Heisenberg's uncertainties. These interpretations explain that a quantity begins to 'lose' meaning when a conjugate property begins to 'acquire' definite meaning. We know that a quantity losing meaning means that it has no fixed value and has an uncertainty . In this paper we look deeper into this interpretation and the outcome reveals more evidence of the quantity losing meaning. Newer insights appear. 2) We consider two extreme cases of hypothetical processes nature undergoes, without interference by a measurement: One, a system collapses to an energy eigenstate under the influence of a Hamiltonian instantaneously at a time ttt. This is thus what would happen if we would measure the system's energy. Next, when a particle becomes localised to a point at a time t_0t_0t_0 under the influence of a Hamiltonian. This is thus what would happen if we would measure the system's position. We shall prove th...

Interpretations of quantum mechanics, joint measurement of incompatible observables, and counterfactual definiteness

Foundations of Physics, 1994

The validity of the conclusion to the nonlocality of quantum mechanics, accepted widely today as the only reasonable solution to the EPR and Bell issues, is questioned and criticized. Arguments are presented which remove th o compelling character of this conclusion and make cleat" that it is not the most obvtuus solution. Alternative solutions are developed which are free of the contradictions related with the nonlocality conclusion. Firstly, the dependence on the adopted interpretation is shown, with the conclusion that the alleged nonlocality property of the quantum formalism may have been reached on the basis of an interpretation that is unnecessarily restrictive. Secondly, by extending the conventional quantum formalism along the lines of Ludwig and Davies it is shown that the Bell problem may be related to complementarity rather than to nonlocality. Finally, the dependence on counterfactual reason#lg is critically examhled. It appears that locality on the quantum level may still be retained provided one accepts a newly proposed principle of nonreproducibility at the individual quantum level as an alternative of quantum nonlocality. It is concluded that the locality principle can retain its general validity, in full conformity with all experimental data.

The Quantum Measurement Problem: State of Play

This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics. In it, I aim to review, in a way accessible to foundationally interested physicists as well as physics-informed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don’t advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the “traditional” formulation of the problem.

Preparation and measurement: two independent sources of uncertainty in quantum mechanics

1999

In the Copenhagen interpretation the Heisenberg uncertainty relation is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint measurement of incompatible observables. This interpretation has already been criticized by Ballentine a long time ago, and has recently been challenged in an experimental way. These criticisms can be substantiated by using the generalized formalism of positive operator-valued measures, from which a new inequality can be derived, precisely illustrating the Copenhagen concept of complementarity. The different roles of preparation and measurement in creating uncertainty in quantum mechanics are discussed.