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Probing measurement problem of quantum theory with an operational approach

Shubhayan Sarkar, Debashis Saha

Published Jul 18, 2021• 0 citations
OpenAlex

Abstract

Exploiting the tension between the two dynamics of quantum theory (QT) or the so-called problem of QT within a modified version of Wigner's Friend thought experiment, we point out that two different descriptions of Friend's lab by two different observers, Wigner and his Student, applying the same textbook QT can lead to inconsistency in observed probabilities. To avoid such inconsistent predictions of QT, we hypothesize two distinct solutions inspired by the perspectives of Wigner and Student, which we term as Absoluteness of measurement (AoM), and Non-absoluteness of measurement (NoM). To test the validity of these two perceptions in an operational approach, we construct an extended Wigner's Friend scenario and probe two sets of empirical probabilities inferred from these two perceptions without assuming the details of the experiment. We show that the set of probabilities obtainable for NoM is strictly larger than the set obtainable for AoM. We then further extend our scenario for two spatially separated Friends and propose an operational task with a suitable figure of merit to single out quantum correlations achievable with NoM but cannot be achieved using AoM. Notably, the optimal value of the figure of merit in QT with AoM is the same as in classical theory. We also analyze whether different interpretations of QT are compatible with these two perceptions and provide consistent predictions or not. Finally, we point out that the recent no-go theorems of QT provided by Frauchiger-Renner [Nat. Commun. 9, 3711 (2018)], by Brukner [Entropy 20, 350 (2018)], and by K.W. Bong et al., [Nat. Phys. 16, 1199 (2020)] are particular instances of the violation of AoM.

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Exploiting the tension between the two dynamics of quantum theory (QT) in the Wigner's Friend thought experiment, we point out that the standard QT leads to inconsistency in observed probabilities of measurement outcomes between two superobservers: Wigner and his Student. To avoid such inconsistent predictions of QT, we hypothesize two distinct perspectives. The first one is ``absoluteness of measurement (AoM),'' that is, any measurement process is an absolute event irrespective of other observers and yields a single outcome. The other is ``nonabsoluteness of measurement (NoM)'' as the negation of AoM. We introduce an operational approach, first with one friend and then with two spatially separated friends, to test the validity of these two perceptions in quantum theory without assuming the details of the experiment. First, we show that the set of probabilities obtainable for NoM is strictly larger than the set obtainable for AoM. We provide the simplest scenario so far, involving a single quantum preparation and one unitary operation by a superobserver that can demonstrate correlations incompatible with AoM. Remarkably, in the scenario with spatially separated observers, we present a strict hierarchy among the sets of probabilities observed in the following three theories: classical or local realist, quantum theory with AoM, and quantum theory with NoM.

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Recent arguments, involving entangled systems shared by sets of Wigner's friend arrangements, allegedly show that the assumption that the experiments performed by the friends yield definite outcomes, is incompatible with quantum predictions. From this, it is concluded that the results of measurements cannot be thought of as being actual or objective. Here, I show that these arguments depend upon a mistaken assumption, regarding the ("mixed") correlations between the results of the friends and those of "the Wigners", which leads to invalid predictions. It is not, then, that the assumption of definite outcomes leads to trouble, but that the results derived with such an assumption are contrasted with faulty predictions. Next, I explore the more famous no-go theorems by Frauchiger and Renner and by Brukner, on which these recent arguments are motivated. Regarding the first, I show that, although it is cast in a different form, it also rests on the mistaken assumption regarding "mixed" correlations--rendering it invalid. Regarding Brukner's theorem, I point out that it depends on the quite unattractive assumption of locality, a fact that fully diminishes its force. Throughout, I illustrate my claims with explicit calculations within pilot-wave theory.

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Exploiting the tension between the two dynamics of quantum theory (QT) or the so-called problem of QT within a modified version of Wigner's Friend thought experiment, we point out that two different descriptions of Friend's lab by two different observers, Wigner and his Student, applying the same textbook QT can lead to inconsistency in observed probabilities. To avoid such inconsistent predictions of QT, we hypothesize two distinct solutions inspired by the perspectives of Wigner and Student, which we term as Absoluteness of measurement (AoM), and Non-absoluteness of measurement (NoM). To test the validity of these two perceptions in an operational approach, we construct an extended Wigner's Friend scenario and probe two sets of empirical probabilities inferred from these two perceptions without assuming the details of the experiment. We show that the set of probabilities obtainable for NoM is strictly larger than the set obtainable for AoM. We then further extend our scenario for two spatially separated Friends and propose an operational task with a suitable figure of merit to single out quantum correlations achievable with NoM but cannot be achieved using AoM. Notably, the optimal value of the figure of merit in QT with AoM is the same as in classical theory. We also analyze whether different interpretations of QT are compatible with these two perceptions and provide consistent predictions or not. Finally, we point out that the recent no-go theorems of QT provided by Frauchiger-Renner [Nat. Commun. 9, 3711 (2018)], by Brukner [Entropy 20, 350 (2018)], and by K.W. Bong et al., [Nat. Phys. 16, 1199 (2020)] are particular instances of the violation of AoM.
Exploiting the tension between the two dynamics of quantum theory (QT) in the Wigner's Friend thought experiment, we point out that the standard QT leads to inconsistency in observed probabilities of measurement outcomes between two superobservers: Wigner and his Student. To avoid such inconsistent predictions of QT, we hypothesize two distinct perspectives. The first one is ``absoluteness of measurement (AoM),'' that is, any measurement process is an absolute event irrespective of other observers and yields a single outcome. The other is ``nonabsoluteness of measurement (NoM)'' as the negation of AoM. We introduce an operational approach, first with one friend and then with two spatially separated friends, to test the validity of these two perceptions in quantum theory without assuming the details of the experiment. First, we show that the set of probabilities obtainable for NoM is strictly larger than the set obtainable for AoM. We provide the simplest scenario so far, involving a single quantum preparation and one unitary operation by a superobserver that can demonstrate correlations incompatible with AoM. Remarkably, in the scenario with spatially separated observers, we present a strict hierarchy among the sets of probabilities observed in the following three theories: classical or local realist, quantum theory with AoM, and quantum theory with NoM.
Recent extended formulations of the Wigner's friend thought experiment throw the measurement problem of quantum mechanics into sharper relief. Here I respond to an invitation by Renner to provide a consistent and concrete set of rules for quantum mechanics which can avoid the apparent paradox formulated by Frauchiger and Renner [Nat. Comm. 9, 3711 (2018)]. I propose a slight addition to standard textbook quantum mechanics, in the form of two rules, which avoids the paradox. The first specifies when a given quantum dynamics can be interpreted as a measurement. Potentially any dynamics can, but doing so depends on the context of other performed operations. The second requires that a joint context be used to determine whether several different dynamical evolutions can all be interpreted as measurement. The paradox is then avoided because not every participant in the Frauchiger-Renner thought experiment regards the stated dynamical descriptions of the experiment as measurements.
Abstract The Wigner’s friend type of thought experiments manifest the conceptual challenge on how different observers can have consistent descriptions of a quantum measurement event. In this paper, we analyze the extended version of Wigner’s friend thought experiment (Frauchiger and Renner in Nat Commun 3711:9, 2018) in detail and show that the reasoning process from each agent that leads to the no-go theorem is inconsistent. The inconsistency is with respect to the requirement that an agent should make use of updated information instead of outdated information. We then apply the relational formulation of quantum measurement to resolve the inconsistent descriptions from different agents. In relational formulation of quantum mechanics, a measurement is described relative to an observer. Synchronization of measurement result is a necessary requirement to achieve consistent descriptions of a quantum system from different observers. Thought experiments, including EPR, Wigner’s Friend and it extended version, confirm the necessity of relational formulation of quantum measurement when applying quantum mechanics to composite system with entangled but space-like separated subsystems.
Does quantum theory apply at all scales, including that of observers? New light on this fundamental question has recently been shed through a resurgence of interest in the long-standing Wigner’s friend paradox. This is a thought experiment addressing the quantum measurement problem—the difficulty of reconciling the (unitary, deterministic) evolution of isolated systems and the (non-unitary, probabilistic) state update after a measurement. Here, by building on a scenario with two separated but entangled friends introduced by Brukner, we prove that if quantum evolution is controllable on the scale of an observer, then one of ‘No-Superdeterminism’, ‘Locality’ or ‘Absoluteness of Observed Events’—that every observed event exists absolutely, not relatively—must be false. We show that although the violation of Bell-type inequalities in such scenarios is not in general sufficient to demonstrate the contradiction between those three assumptions, new inequalities can be derived, in a theory-independent manner, that are violated by quantum correlations. This is demonstrated in a proof-of-principle experiment where a photon’s path is deemed an observer. We discuss how this new theorem places strictly stronger constraints on physical reality than Bell’s theorem. For a scenario of two separated but entangled observers, inequalities are derived from three fundamental assumptions. An experiment shows that these inequalities can be violated if quantum evolution is controllable on the scale of an observer.
The notorious quantum measurement problem brings out the difficulty to reconcile two quantum postulates: the unitary evolution of closed quantum systems and the wave-function collapse after a measurement. This problematics is particularly highlighted in the Wigner's friend thought experiment, where the mismatch between unitary evolution and measurement collapse leads to conflicting quantum descriptions for different observers. A recent no-go theorem has established that the (quantum) statistics arising from an extended Wigner's friend scenario is incompatible when one try to hold together three innocuous assumptions, namely no-superdeterminism, parameter independence and absoluteness of observed events. Building on this extended scenario, we introduce two novel measures of non-absoluteness of events. The first is based on the EPR2 decomposition, and the second involves the relaxation of the absoluteness hypothesis assumed in the aforementioned no-go theorem. To prove that quantum correlations can be maximally non-absolute according to both quantifiers, we show that chained Bell inequalities (and relaxations thereof) are also valid constraints for Wigner's experiment.
Recent arguments, involving entangled systems shared by sets of Wigner's friend arrangements, allegedly show that the assumption that the experiments performed by the friends yield definite outcomes, is incompatible with quantum predictions. From this, it is concluded that the results of measurements cannot be thought of as being actual or objective. Here, I show that these arguments depend upon a mistaken assumption, regarding the ("mixed") correlations between the results of the friends and those of "the Wigners", which leads to invalid predictions. It is not, then, that the assumption of definite outcomes leads to trouble, but that the results derived with such an assumption are contrasted with faulty predictions. Next, I explore the more famous no-go theorems by Frauchiger and Renner and by Brukner, on which these recent arguments are motivated. Regarding the first, I show that, although it is cast in a different form, it also rests on the mistaken assumption regarding "mixed" correlations--rendering it invalid. Regarding Brukner's theorem, I point out that it depends on the quite unattractive assumption of locality, a fact that fully diminishes its force. Throughout, I illustrate my claims with explicit calculations within pilot-wave theory.