Measurements Incompatible in Quantum Theory Cannot Be Measured Jointly in Any Other No-Signaling Theory (original) (raw)
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The Bell inequalities and the joint measurement of incompatible observables
Foundations of Physics Letters, 1992
On the basis of a theory of the joint nonideal (or inaccurate) measurement of incompatible observables an experiment is proposed in which all four observables that are involved in the Bell inequalities are measured jointly. It is demonstrated that the difference between violation and satisfaction ofthe Bell inequalities can be accounted for in a local way.
Joint measurement of incompatible observables and the bell inequalities
Physics Letters A, 1989
On the basis of a theory of the joint nonideal (or inaccurate) measurementsof incompatible observables an experiment is proposed in which all four observables that are involved in the Bell inequalities are measured jointly. It is demonstrated that the difference between violation and satisfaction of the Bell inequalities can be accounted for in a local way.
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.
Joint measurements and Bell inequalities
Physical Review A, 2005
Joint quantum measurements of non-commuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution for all involved observables exists. We investigate the connections between Bell inequalities and conditions for joint quantum measurements to be possible. Mermin's inequality for the threeparticle Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition for a joint measurement on two out of the three quantum systems to exist. Gisin's Bell inequality for three co-planar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement.
Notes on Joint Measurability of Quantum Observables
Foundations of Physics, 2008
For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly measurable, then their joint observable is unique and it gives the greatest lower bound for the effects corresponding to the observables; (iii) if we have two sharp observables and their every possible two outcome partitionings are jointly measurable, then the observables themselves are jointly measurable. We show that, in general, these properties do not hold. Also some possible candidates which would accompany joint measurability and generalize these apparently useful properties are discussed.
“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.
The Relational Dissolution of the Quantum Measurement Problems
2022
The Quantum Measurement Problem is arguably one of the most debated issues in the philosophy of Quantum Mechanics, since it represents not only a technical difficulty for the standard formulation of the theory, but also a source of interpretational disputes concerning the meaning of the quantum postulates. Another conundrum intimately connected with the QMP is the Wigner friend paradox, a thought experiment underlining the incoherence between the two dynamical laws governing the behavior of quantum systems, i.e the Schrödinger equation and the projection rule. Thus, every alternative interpretation aiming to be considered a sound formulation of QM must provide an explanation to these puzzles associated with quantum measurements. It is the aim of the present essay to discuss them in the context of Relational Quantum Mechanics. In fact, it is shown here how this interpretative framework dissolves the QMP. More precisely, two variants of this issue are considered: on the one hand, I focus on the "the problem of outcomes" contained in Maudlin (1995) - in which the projection postulate is not mentioned - on the other hand, I take into account Rovelli's reformulation of this problem proposed in Rovelli (2022), where the tension between the Schrödinger equation and the stochastic nature of the collapse rule is explicitly considered. Moreover, the relational explanation to the Wigner's friend paradox is reviewed, taking also into account some interesting objections contra Rovelli's theory contained in Laudisa (2019). I contend that answering these critical remarks leads to an improvement of our understanding of RQM. Finally, a possible objection against the relational solution to the QMP is presented and addressed.
Sensitive observables of quantum mechanics
International Journal of Theoretical Physics, 1973
We prove that there are quantum mechanical observables which are sensitive to the type of state-vector (first type or second type) describing two correlated physical systems, in the sense that the expectation value of these 'sensitive observables' is measurably different in the two cases. The proof centers around Bell's inequality since we show that in quantum mechanics for all state-vectors of the second type (and only for them) sensitive observables exist in the absence of super-selection rules. Experimental verification of the existence of sensitive observables rules out local hidden variables.
Bell measurements and observables
Physics Letters A, 2000
A general matrix approach to study entangled states is presented, based on operator completeness relations. Bases of unitary operators are considered, with focus on irreducible representations of groups. Bell measurements for teleportation are considered, and robustness of teleportation to various kinds of non idealities is shown.
Generalized Observables, Bell’s Inequalities
2016
The extended semantic realism (ESR) model proposes a new theoretical perspective which embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) into a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide in this review an overall view on the present status of our research on this topic. We attain in a new, shortened way a mathematical representation of the generalized observables introduced by the ESR model and a generalization of the projection postulate of elementary QM. Basing on these results we prove that the Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, a modified BCHSH inequality and quantum predictions hold together in the ESR model because they refer to different parts of the picture of the physical world supplied by the model. Then we show that a new mathematical representation of mixtures must be introduced in the ESR model which does not coincide with the standard representation in QM and avoids some deep problems that arise from the representation of mixtures provided by QM. Finally we get a nontrivial generalization of the Lüders postulate, which is justified in a special case by introducing a reasonable physical assumption on the evolution of the compound system made up of the measured system and the measuring apparatus. Keywords quantum mechanics • quantum theory of measurement • Bell inequalities