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Published on: May 30, 2014
Pre- and post-selection paradoxes and contextuality in quantum mechanics
M S Leifer1, Robert W Spekkens
1Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada.
Physical Review Letters
|December 31, 2005
Summary
Paradoxical quantum measurement effects do not disprove noncontextual hidden variable theories. However, specific conditions reveal that these paradoxical outcomes can prove the impossibility of such theories.
Area of Science:
- Quantum mechanics
- Foundations of physics
- Quantum information
Background:
- Pre- and post-selected quantum systems exhibit paradoxical intermediate measurement outcomes.
- Previous interpretations suggested these paradoxes did not rule out noncontextual hidden variable theories due to measurement disturbance.
Purpose of the Study:
- To investigate the relationship between paradoxical quantum effects and noncontextual hidden variable theories.
- To identify conditions under which paradoxical effects can prove the impossibility of noncontextual hidden variable theories.
Main Methods:
- Analysis of paradoxical effects in pre- and post-selected quantum systems.
- Reinterpreting intermediate measurements as alternative measurements at a single time.
- Focusing on cases where pre- and post-selected probabilities are 0 or 1 and states are nonorthogonal.
Main Results:
- Demonstrated that measurement disturbance does not universally preclude noncontextual hidden variable theories.
- Established a direct link between specific paradoxical effects and the impossibility of noncontextual hidden variable theories.
- Showed that for every paradoxical effect with specific probability and nonorthogonality conditions, a proof of impossibility exists.
Conclusions:
- Paradoxical quantum phenomena, under certain conditions, provide rigorous proofs against noncontextual hidden variable theories.
- The framework of considering all measurements at a single time is key to these proofs.
- This work refines our understanding of quantum foundations and the limits of classical explanations.
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