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 The inconsistency is with respect to the requirement that an agent should make use of updated information instead of outdated information.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.
Highlights
In quantum mechanics, the Wigner’s friend [1] thought experiment has been widely discussed as it tests the validity of many quantum interpretation theories
The Wigner’s friend experiment and the extended version are yet another set of examples that manifest the conceptual values of the relational formulation of quantum measurement [14], where quantum measurement is reformulated based on basic Relational quantum mechanics (RQM) principles [9,12] and one of RQM implementations [13]
To ensure consistent descriptions of a quantum system, measurement outcome obtained by a local observer must be communicated to other observers
Summary
The Wigner’s friend [1] thought experiment has been widely discussed as it tests the validity of many quantum interpretation theories. In RQM there is no absolute state for a quantum system, it is legitimate that Wigner and his friend have different accounts of the measurement process in the lab Both RQM and Bayesian quantum mechanics (QBism) [15,16] consider wave function as a mathematical tool that encodes the observer’s information of a quantum system. The Wigner’s friend experiment and the extended version are yet another set of examples that manifest the conceptual values of the relational formulation of quantum measurement [14], where quantum measurement is reformulated based on basic RQM principles [9,12] and one of RQM implementations [13] It is asserted [14] that for a given quantum system, description of its time evolution can be implicitly relative without calling out the observer, while description of a quantum operation must explicitly call out the observer. The EPR paradox and the Wigner’s friend type of paradox serve as examples to confirm the conceptual value of the relational formulation of quantum measurement
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