When will Two Agents Agree on a Quantum Measurement Outcome? Intersubjective Agreement in QBism.

Area of Science:

• Quantum mechanics
• Foundations of physics
• Quantum information theory

Background:

• The QBist approach to quantum mechanics posits that quantum measurement outcomes and probabilities are personal to the agent.
• QBism suggests no inherent requirement for mutual consistency between different agents' quantum state assignments or measurement outcomes.
• Khrennikov claimed Ozawa's intersubjectivity theorem invalidates QBism's personalist measurement theory.

Purpose of the Study:

• To refute Khrennikov's claim that Ozawa's intersubjectivity theorem invalidates QBism.
• To clarify the conditions under which intersubjective agreement can be achieved within the QBist framework.

Main Methods:

• Analysis of Khrennikov's claim by distinguishing Ozawa's mathematical theorem from Khrennikov's additional assumptions.
• Following Stacey's work to demonstrate the incompatibility lies with Khrennikov's assumptions, not Ozawa's theorem itself.
• General discussion on achieving intersubjective agreement in QBism.

Main Results:

• Khrennikov's claim is refuted by showing QBism's incompatibility stems from an unstated assumption, not Ozawa's theorem.
• QBism does not necessitate agreement between agents' measurement outcomes.
• Conditions can be created for QBist agents to expect agreement with another agent's reported outcomes.

Conclusions:

• Ozawa's theorem's assumptions provide a concrete example of conditions that facilitate intersubjective agreement in QBism.
• QBism remains a viable interpretation of quantum mechanics, with intersubjective agreement being a condition that can be sought, not a necessity.
• The study clarifies the relationship between personal quantum measurements and the potential for shared understanding.