aiqbench analysis
This is a theoretical quantum foundations preprint, not yet peer-reviewed. It argues that the GHZ nonlocality game can be won using only real-valued amplitudes in a "misty state" formalism, at the cost of doubling each party's resources. For quantum computing readers, the useful takeaway is the general point that complex numbers can be encoded with an extra qubit, but nonlocality proofs need that tag distributed across the parties rather than shared.
The GHZ Game in Black and White
arXiv:2610.14411v1 Announce Type: new Abstract: We show that it is possible for three people to win the GHZ game with just the standard real valued misty state formalism, but each party will need to have two balls instead of one. That is, there will be six balls involved, rather than three. In fact, as a general rule, instead of using complex numbers in a quantum computer you can always add a qubit to "tag" complex numbers. But for proofs of non-locality, like the GHZ game, we cannot have a single universal tagging qubit, because all three parties would need access to it and therefore they could potentially transfer information via it. That's where we need to replace the one ball with three that each only need to be accessed locally.
Abstract:We show that it is possible for three people to win the GHZ game with just the standard real valued misty state formalism, but each party will need to have two balls instead of one. That is, there will be six balls involved, rather than three. In fact, as a general rule, instead of using complex numbers in a quantum computer you can always add a qubit to "tag" complex numbers. But for proofs of non-locality, like the GHZ game, we cannot have a single universal tagging qubit, because all three parties would need access to it and therefore they could potentially transfer information via it. That's where we need to replace the one ball with three that each only need to be accessed locally.
arXiv:2610.14411 [quant-ph]
(or arXiv:2610.14411v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.14411 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 216 words
