Elitzur-Dolev Quantum Liar Paradox

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Discussion Overview

The discussion revolves around the Elitzur-Dolev Quantum Liar Paradox, exploring the implications of quantum measurements and entanglement in a specific experimental setup involving excited atoms and a detector. Participants seek to clarify the logic behind the paradox and its relation to Bell's inequality, while also sharing references and interpretations of the underlying quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion over the vague description of the experiment and seeks clarification on the logic behind the test.
  • Another participant requests references to facilitate a more informed discussion.
  • A participant describes a quantum circuit involving parity measurements that create entanglement between two qubits, noting that performing a measurement can force the system into a specific state.
  • One participant shares a reference to a document that discusses the Quantum Liar Paradox, highlighting the role of superposition and the interaction of particles with photons.
  • Questions are raised about whether quantum mechanics allows photons to traverse both boxes in the experimental setup, and the implications of entangled particles having a 50% chance of being in a "blocking" box.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are multiple interpretations of the paradox and the implications of the quantum measurements involved. Uncertainties and questions remain regarding the nature of the interactions and the paradox itself.

Contextual Notes

Participants express limitations in understanding the experimental setup and its implications, indicating a dependence on specific definitions and unresolved aspects of the quantum mechanics involved.

Quantum of Solace
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I've seen Elitzur's brief presentations on this. Two excited atoms pointed at a detector. The detector goes off, it isn't known which particle fired the photon, so you interrogate one, it gives a definite answer but violates bell's inequality? I'm sorry but I'm lost at such a vague description and this was the best I could find. What is the logic behind this test? I appreciate any references you could offer.
 
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Quantum of Solace said:
I've seen Elitzur's brief presentations on this...
Do you have a reference? Without that, it's going to be hard for anyone to comment sensibly.
 
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A quick google search found, well, this very thread. But also these slides:

Screenshot from 2016-07-28 11:53:04.png


Basically it's describing this quantum circuit, where a parity measurement creates entanglement between two qubits that start off separable:

Screenshot from 2016-07-28 11:56:41.png


This is an example of "performing a measurement forces the system into the state indicated by the measurement outcome, even if that state is entangled and you feel like that's weird".

This particular setup works on inputs that are in X-axis states (e.g. On+Off), but not Z-axis states (e.g. just On). Doing an X-axis or Y-axis parity measurement in addition to the Z-axis parity measurement would fix that, but kinda breaks the analogy with the simple physical system. With both parity measurements it's a full fledged Bell basis measurement, which must force the system into one of the Bell basis states (and tell you which one). All of those basis states are fully entangled, so the output is entangled.
 
It took a while, but I finally found the reference:

http://a-c-elitzur.co.il/uploads/articlesdocs/MultipleIFM.pdf

Section 10, Page 13 "The Quantum Liar Paradox"

Still trying to understand this properly, but it seems to me until the Z measurement (which box?) is performed, each particle Z exists in the blocking(or non blocking) box only as part of a superposed state, and is thus not forced to interact with the photon, leaving it to interfere with itself.

If two entangled particles have a 50% chance of being in the "blocking" box, (mutually exclusive), does that mean one of them MUST interact with a traversing photon? or does quantum mechanics allow a possibility for photons to traverse both boxes? If so, then I'm not sure I get why this is supposed to be a paradox.
 

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