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arXiv:quant-ph/0604124 · Foundations of Physics Letters

What's Wrong with this Rebuttal?

Aloysius F. Kracklauer

Published Nov 1, 2006• 3 citations
arXivHTMLPDF
DOI
10.1007/s10702-006-1016-3

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Rebuttal - Why SuperGrok's Objection to the MUB Proof is Wrong C.M. Pompetzki (AKA Captain Ahab AKA Shrek)

Christopher Pompetzki

The ObjectionSuperGrok claims the following is a “critical logical flaw”:“The claim that |fˆrs(j)| = √d for all j ̸= 0 is justified by ‘unbiasedness to Fourier basis (implied by the MUB structure)’. This is the core flaw. Unbiasedness to the Fourier basis is not implied by general MUB structure. The Fourier basis (the DFT matrix) is unbiased to the computational basis, but in an arbitrary MUB set, the Fourier basis may not be part of the set, and the other bases are not required to be unbiased to it.”This objection reflects a fundamental misunderstanding of the Fourier-analytic structure of mutual unbiasedness. Final VerdictSuperGrok’s “critical logical flaw” is not a flaw. It is a misreading of the proof.The bi-unimodularity lemma stands. The CRT factorization stands. The Z₂ obstruction stands.M (6) = 3."Wir müssen wissen. Wir werden wissen."- David Hilbert of Deutschland, the greatest mathematician of all time

•Dec 30, 2025•0 citations
The paper is a Chapter of a book. In it an exhaustive review of the proposals to send faster than light signals resorting to quantum nonlocality and the reduction process is presented, together with a critical analysis and rebuttal of all proposals. The most interesting part of the Chapter is the one in which the problem of quantum cloning is discussed. Actually, a proposal of superluminal signaling based on an hypothetical cloning machine has been presented by N. Herbert. The proposal does not work just because of the assumption that one can clone nonorthogonal states. The fact that such a machine is incompatible with quantum theory (i.e., the so-called No-Cloning Theorem) has been proved, for the first time, by the author of the present chapter in his referee's report to Herbert's paper. In the final part of the paper some recent (different but similarly not correct) proposals are analyzed and the reasons for which they are basically wrong are presented.
The ObjectionSuperGrok claims the following is a “critical logical flaw”:“The claim that |fˆrs(j)| = √d for all j ̸= 0 is justified by ‘unbiasedness to Fourier basis (implied by the MUB structure)’. This is the core flaw. Unbiasedness to the Fourier basis is not implied by general MUB structure. The Fourier basis (the DFT matrix) is unbiased to the computational basis, but in an arbitrary MUB set, the Fourier basis may not be part of the set, and the other bases are not required to be unbiased to it.”This objection reflects a fundamental misunderstanding of the Fourier-analytic structure of mutual unbiasedness. Final VerdictSuperGrok’s “critical logical flaw” is not a flaw. It is a misreading of the proof.The bi-unimodularity lemma stands. The CRT factorization stands. The Z₂ obstruction stands.M (6) = 3."Wir müssen wissen. Wir werden wissen."- David Hilbert of Deutschland, the greatest mathematician of all time