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Abstract
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 stateupdate rule (or "collapse") at the instant a measurement takes place. The notorious Wigner's 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 stateupdate 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 PageWootters mechanism (PWM) as a timeless description of Wigner's friendlike scenarios. We show that the standard rules to assign twotime conditional probabilities within the PWM need to be modified to deal with the Wigner's friend gedankenexperiment. We identify three main definitions of such modified rules to assign twotime conditional probabilities, all of which reduce to standard quantum theory for nonWigner's friend scenarios. However, when applied to the Wigner's friend setup each rule assigns different conditional probabilities, potentially resolving the probabilityassignment 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 welldefined, which single out those cases where Wigner's measurement does not disturb the Friend's 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.
Original language  English 

Pages (fromto)  524 
Number of pages  17 
Journal  Quantum 
Volume  5 
DOIs  
Publication status  Published  16 Aug 2021 
Austrian Fields of Science 2012
 103025 Quantum mechanics

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