Super quantum theory? Scientists show that quantum superposition is equivalent to quantum entanglement

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The Fundamental Questions Institute (FQXi) is a grant-making organization designed to "promote, support and disseminate inquiry into fundamental questions of physics and cosmology". FQXi-funded research has uncovered a new link between two strange quantum phenomena—superposition and entanglement—that will have implications for ultra-secure cryptography

Microphysics encompasses two well-known concepts. The first is that it's impossible to know exactly what a particle's measurements will be until you observe it; instead, the particle exists in a "superposition" of many mutually exclusive states. As a result, a particle can appear in two or more places at the same time, and scientists can only calculate the probability of finding it in a certain location while observing. The second involves "entanglement," a connection that binds two objects together no matter how far apart they are physically.

uantum theory describes superposition and entanglement mathematically. But many physicists believe that the ultimate theory of reality may lie outside quantum theory. Recently, a team of physicists and mathematicians has discovered a new connection between the properties of "entanglement" and "superposition". All Equivalent Concepts"[1] was published in Physical Review Letters and was selected as Editors' Suggestion.

The authors show that given any two general probability theories (GPTs), the following are equivalent: (i) If both theories are non-classical, then their state spaces are not simplex (simplex); (ii) each theory satisfies that the strong incompatibility is equivalent to the existence of a "superposition state"; (iii) if the combination of the two theories exhibits an entangled state or a measure of entanglement, then They are entangled. Intuitively, in the post-quantum GPT setting, a superposition state refers to an ensemble of two binary states that can be clearly distinguished if the ensemble of states is manifested before the measurement takes place, but not the other way around. This concept is important because the authors show that, as in quantum theory, superpositions of strongly incompatible forms are sufficient to implement the key distribution protocol proposed by Bennett-Brassard in 1984.

FQXi members, Ludovico Lami, physicist, University of Ulm, Germany, Guillaume Aubrun, Claude Bernard University Lyon 1, France, Carlos Palazuelos, Complutense University, Spain, Germany Martin Plávala of Siegen University co-authored the study. "We're very excited about discovering this new connection that goes beyond quantum theory, as this connection will hold even for more exotic theories that haven't been discovered," Lami said. "It's also important because it's independent of the mathematical form of quantum theory. Doctrine, using only concepts with direct operational explanations."

The discovery also has practical implications for quantum cryptography. Quantum entanglement plays a key role in the design of quantum computers: quantum computers, combined with existing security protocols, use quantum rules to provide ultra-secure communications over channels that are theoretically immune to hacking. But if future quantum theory eventually needs to be replaced by another, more fundamental theory, will we find that these rules don't really work, or that these cryptographic protocols aren't as secure as promised?

 To discover this, you need to analyze superposition and entanglement from some general (or even unclear) theory, without using the mathematics of quantum theory. How can this be done? Lami and colleagues tackle this conundrum by studying "general probability theory," rather than quantum theory. The research was partially funded by FQXi to investigate the characteristics and limitations of intelligence in generalized probability theory, allowing them to study how information is processed in abstract classical, quantum and "superquantum" systems.

The research shows that two physical theories exhibit entanglement when combined if and only if they both exhibit local superposition. This means that entanglement and superposition are equivalent in any physical theory, not just quantum theory. They also calculated that in systems where this equivalence holds, whether quantum or superquantum, the laws of the theory can be used to make super-secure encryption. Among other things, the research team showed that the popular quantum encryption protocol, known as "BB84," will always work, even if one day it turns out that quantum theory isn't quite right and needs to be replaced with a more fundamental one.

"It is somewhat reassuring to know that cryptography is indeed a feature of all non-classical theories, not just a quantum loop, since many of us believe that the ultimate theory of nature will likely be non-classical," "Even if one day we find out that quantum theory is incorrect, we still know that key distribution works in principle," Lami said.

Reference link:

[1]https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.160402

[2]https://scitechdaily.com/new-connection-discovered-between-two-weird-quantum-phenomena-superposition-and-entanglement/