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تسجيل مستخدم جديدGeneralized probability rules from a timeless formulation of Wigners friend scenarios
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The quantum measurement problem can be regarded as the tension between the two alternative dynamics prescribed by quantum mechanics: the unitary evolution of the wave function and the state-update rule (or collapse) at the instant a measurement takes place. The notorious Wigners friend gedankenexperiment constitutes the paradoxical scenario in which different observers (one of whom is observed by the other) describe one and the same interaction differently, one --the Friend-- via state-update and the other --Wigner-- unitarily. This can lead to Wigner and his friend assigning different probabilities to the outcome of the same subsequent measurement. In this paper, we apply the Page-Wootters mechanism (PWM) as a timeless description of Wigners friend-like scenarios. We show that the standard rules to assign two-time conditional probabilities within the PWM need to be modified to deal with the Wigners friend gedankenexperiment. We identify three main definitions of such modified rules to assign two-time conditional probabilities, all of which reduce to standard quantum theory for non-Wigners friend scenarios. However, when applied to the Wigners friend setup each rule assigns different conditional probabilities, potentially resolving the probability-assignment paradox in a different manner. Moreover, one rule imposes strict limits on when a joint probability distribution for the measurement outcomes of Wigner and his Friend is well-defined, which single out those cases where Wigners measurement does not disturb the Friends memory and such a probability has an operational meaning in terms of collectible statistics. Interestingly, the same limits guarantee that said measurement outcomes fulfill the consistency condition of the consistent histories framework.
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The measurement problem is seen as an ambiguity of quantum mechanics, or, beyond that, as a contradiction within the theory: Quantum mechanics offers two conflicting descriptions of the Wigners-friend experiment. As we argue in this note there are, h
owever, obstacles from within quantum mechanics and regarding our perspective onto doing physics towards fully describing a measurement. We conclude that the ability to exhaustively describe a measurement is an assumption necessary for the common framing of the measurement problem and ensuing suggested solutions.
In a joint paper Jeff Bub and Itamar Pitowski argued that the quantum state represents `the credence function of a rational agent [...] who is updating probabilities on the basis of events that occur. In the famous thought experiment designed by Wign
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Wigners friend thought experiment is intended to reveal the inherent tension between unitary evolution and measurement collapse. On the basis of Wigners friend experiment, Brukner derives a no-go theorem for observer-independent facts. We construct a
n extended Wigners friend scenario including three laboratories, namely, Alices laboratory, Bobs laboratory and Charlies laboratory, where Alice, Bob and Charlie are standing outside the laboratories while their friends are placed inside their own laboratories. We consider quantum simulation via Q# quantum programming and also realize the primary quantum circuits using IBM quantum computers. Then, we calculate the probabilities and corresponding statistical uncertainties. It has been shown that the results of quantum simulation are clearly consistent with theoretical values, while it has a slightly higher error rates for the experimental results of quantum computers mainly because of a series of quantum gates, especially CNOT gates.
Wigners gedankenexperiment is often taken as requiring a reassessment of the notion of objective reality. In this note however we present a classical toy model in which (i) The relevant quantum mechanical predictions of Wigners thought experiment are
reproduced (ii) Every system is in a well-defined state at all times. The toy model shows how puzzles such as Wigners friends experience of being in a superposition, conflicts between different agents descriptions of the experiment, the positioning of the Heisenbergs cut and the apparent lack of objectivity of measurement outcomes can be explained within a classical model where there exists an objective state of affairs about every physical system at all times. Within the model, the debate surrounding Wigners friend thought experiment and its resolution have striking similarities with arguments concerning the nature of the second law of thermodynamics. The same conclusion however does not straightforwardly apply to more recent extensions of the gedankenexperiment featuring multiple encapsulated observers.
The Wigners friend paradox concerns one of the most puzzling problems of quantum mechanics: the consistent description of multiple nested observers. Recently, a variation of Wigners gedankenexperiment, introduced by Frauchiger and Renner, has lead to
new debates about the self-consistency of quantum mechanics. At the core of the paradox lies the description of an observer and the object it measures as a closed system obeying the Schrodinger equation. We revisit this assumption to derive a necessary condition on a quantum system to behave as an observer. We then propose a simple single-photon interferometric setup implementing Frauchiger and Renners scenario, and use the derived condition to shed a new light on the assumptions leading to their paradox. From our description, we argue that the three apparently incompatible properties used to question the consistency of quantum mechanics correspond to two logically distinct contexts: either one assumes that Wigner has full control over his friends lab, or conversely that some parts of the labs remain unaffected by Wigners subsequent measurements. The first context may be seen as the quantum erasure of the memory of Wigners friend. We further show these properties are associated with observables which do not commute, and therefore cannot take well-defined values simultaneously. Consequently, the three contradictory properties never hold simultaneously.
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