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arXiv:2208.13746

A Questionable Fundamental Basis for Quantum Computing Advantage

Stuart Mirell, Daniel Mirell

Published Jun 4, 2022• 0 citations
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Abstract

The widely accepted basis for quantum computing advantage is derived from the entanglement and superposition properties of the probabilistic interpretation of the underlying quantum mechanical formalism which in turn is widely accepted based upon results of Bell experiments. That advantage is questioned here in view of a locally real interpretation that is not negated by Bell experiments and under which entanglement and superposition are excluded.

DOI
10.48550/arxiv.2208.13746

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The widely accepted basis for quantum computing advantage is derived from the entanglement and superposition properties of the probabilistic interpretation of the underlying quantum mechanical formalism which in turn is widely accepted based upon results of Bell experiments. That advantage is questioned here in view of a locally real interpretation that is not negated by Bell experiments and under which entanglement and superposition are excluded.
Abstract The recent claim of Google to have brought forth a breakthrough in quantum computing represents a major impetus to further analyze the foundations for any claims of superiority regarding quantum algorithms. This note attempts to present a conceptual step in this direction. I start with a critical analysis of what is commonly referred to as entanglement and quantum nonlocality and whether or not these concepts may be the basis of quantum superiority. Bell-type experiments are then interpreted as statistical tests of Bohr’s principle of complementarity (PCOM), which is, thus, given a foothold within the area of quantum informatics and computation. PCOM implies (by its connection to probability) that probabilistic algorithms may proceed without the knowledge of joint probability distributions (jpds). The computation of jpds is exponentially time consuming. Consequently, classical probabilistic algorithms, involving the computation of jpds for n random variables, can be outperformed by quantum algorithms (for large values of n). Quantum probability theory (QPT) modifies the classical formula for the total probability (FTP). Inference based on the quantum version of FTP leads to a constructive interference that increases the probability of some events and reduces that of others. The physical realization of this probabilistic advantage is based on the discreteness of quantum phenomena (as opposed to the continuity of classical phenomena).
Locally real states of electromagnetic radiation derived from the underlying quantum mechanical formalism are shown to provide an alternative basis for definite polarized states of the widely accepted probabilistic interpretation. The locally real states traverse common loop configurations without invoking non-local superposition. Correlated photon pairs represented by the locally real states are consistent with the underlying quantum mechanical formalism independent of Bell's inequality and without invoking entanglement. Replacement of interdependent non-local probabilistic states with the locally real states yields independence of those states. A novel loop configuration provides differential testability of the representation of the locally real states relative to the probabilistic interpretation with the prediction of a unique polarization state.
A locally real representation of quantum mechanics deduced from the underlying quantum formalism is presented here. The representation is based upon Mirell's local hidden variable theory, an LHVT, [doi: 10.1103/PhysRevA.65.032102] that provides correlations in agreement with reported Bell experiments. Conversely, the non-local phenomenon of entanglement is necessarily invoked by the Copenhagen Interpretation of that formalism for those reported experiments by maintaining that the formalism is complete. Although a broad class of LHVT's has been disproven by Bell's inequality, Mirell's LHVT is identifiable as a special exempted case by its inherent inclusion of the property of enhancement. Clauser and Horne [doi: 10.1103/PhysRevD.10526] showed that LHVT's with the property of enhancement are not testable by Bell's inequality. In order to address that lack of testability, the representation presented here substantially expands on Mirell's earlier LHVT by self-consistently demonstrating locally real photon state transits of common loop configurations, transits that necessarily invoke non-local superposition under the Copenhagen Interpretation of the quantum formalism. We then analyze those locally real transits and deduce methods to re-engineer the loop configurations to achieve selected output state distributions and show that these re-engineered configurations are predicted by the present representation to yield novel distributions of locally real states. Conversely, the Copenhagen Interpretation predicts corresponding output distributions for these re-engineered configurations that are unremarkable. Those mutually disparate output distributions provide the experimentally testable basis for definitively falsifying either the present locally real representation or the completeness of the original quantum formalism as postulated under the Copenhagen Interpretation.
It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. This paper presents a stronger Bell argument which even forbids certain non-local theories. Among these excluded non-local theories are those whose only non-local connection is a probabilistic (or functional) dependence between the space-like separated measurement outcomes of EPR/B experiments (a subset of outcome dependent theories). In this way, the new argument shows that the result of the received Bell argument, which requires just any kind of non-locality, is inappropriately weak. Positively, the remaining non-local theories, which can violate Bell inequalities (among them quantum theory), are characterized by the fact that at least one of the measurement outcomes in some sense probabilistically depends both on its local as well as on its distant measurement setting (probabilistic Bell contextuality). Whether an additional dependence between the outcomes holds, is irrelevant for the question whether a certain theory can violate Bell inequalities. This new concept of quantum non-locality is considerably tighter and more informative than the one following from the usual Bell argument. We prove that (given usual background assumptions) the result of the stronger Bell argument presented here is the strongest possible consequence from the violation of Bell inequalities on a qualitative probabilistic level.