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arXiv:1809.09711 · Lecture notes in computer science

Milestone Developments in Quantum Information and No-Go Theorems

Kapil K. Sharma, Vladimir P. Gerdt, Pyotr V. Gerdt

Published Jan 1, 2020• 10 citations
arXivHTMLPDF
DOI
10.1007/978-3-030-66471-8_39

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We give a comprehensive and constructive proof of the no-go theorem of a bit commitment given by Mayers, Lo, and Chau from the viewpoint of quantum information theory. It is shown that there is a trade-off relation between information acquired by Bob during the commitment phase and the ability to change a commit bit by Alice during the opening phase. It is clarified that a protocol that is unbiased to both Alice and Bob cannot be, at the same time, secure against both parties. Fundamental physical constraints that govern this no-go theorem are also discussed.
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A recent paper by two of us and co-workers \cite{CQD20}, based on an extended Wigner's friend scenario, demonstrated that certain empirical correlations predicted by quantum theory (QT) violate inequalities derived from a set of metaphysical assumptions we called "Local Friendliness" (LF). These assumptions are strictly weaker than those used for deriving Bell inequalities. Crucial to the theorem was the premise that a quantum system with reversible evolution could be an observer (colloquially, a "friend"). However, that paper was noncommittal on what would constitute an observer for the purpose of an experiment. Here, we present a new LF no-go theorem which takes seriously the idea that a system's having thoughts is a sufficient condition for it to be an observer. Our new derivation of the LF inequalities uses four metaphysical assumptions, three of which are thought-related, including one that is explicitly called "Friendliness". These four assumptions, in conjunction, allow one to derive LF inequalities for experiments involving the type of system that "Friendliness" refers to. In addition to these four metaphysical assumptions, this new no-go theorem requires two assumptions about what is technologically feasible: Human-Level Artificial Intelligence, and Universal Quantum Computing which is fast and large scale. The latter is often motivated by the belief that QT is universal, but this is not an assumption of the theorem. The intent of the new theorem is to give a clear goal for future experimentalists, and a clear motivation for trying to achieve that goal. We review various approaches to QT in light of our theorem. The popular stance that "quantum theory needs no interpretation" does not question any of our assumptions and so is ruled out. Finally, we quantitatively discuss how difficult the experiment we envisage would be, and briefly discuss milestones on the paths towards it.