A principle of equivalence “beyond the quantum” for

image: A new link between entanglement and superposition in any physical theory has been discovered, confirming that secret key distribution in current quantum cryptographic protocols will work, even if the quantum theory is incorrect and needs to be replaced by a more fundamental theory, “beyond the quantum”. ‘ the theory.
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Credit: Louis Lami.

Microdomain physics involves two famous and bizarre concepts: the first is that before observation, it is impossible to know with certainty the result of a measurement on a particle; rather, the particle exists in a “superposition” encompassing several mutually exclusive states. So a particle can be in two or more places at the same time, and you can only calculate the probability of finding it in a certain place when you look. The second involves “entanglement,” the frightening bond that can unite two objects, no matter how far apart they are. Superposition and entanglement are mathematically described by quantum theory. But many physicists believe the ultimate theory of reality may lie beyond quantum theory. Now a team of physicists and mathematicians has discovered a new link between these two strange properties that doesn’t assume quantum theory is correct. Their study appears in Physical examination letters and was selected as an Editors’ Suggestion by the journal.

“We were really excited to find this new connection that goes beyond quantum theory, because the connection will hold even for more exotic theories that are yet to be discovered,” says physics think tank member Ludovico Lami, the fundamental questions. Institute, FQXi, and physicist at the University of Ulm, Germany. “This is also important because it is independent of the mathematical formalism of quantum theory and only uses notions with immediate operational interpretation,” he adds. Lami co-authored the study with Guillaume Aubrun from the University Claude Bernard Lyon 1, France, Carlos Palazuelos, from the Complutense University of Madrid, Spain, and Martin Plávala, from the University of Siegen, Germany .

While quantum theory has proven to be a supreme success since its development a century ago, physicists have struggled to unify it with gravity to create an all-encompassing “theory of everything.” This suggests that quantum theory may not be the last word to describe reality, inspiring physicists to search for a more fundamental framework. But any such ultimate theory must always incorporate superposition, entanglement and the probabilistic nature of reality, since these characteristics have been repeatedly confirmed by laboratory tests. The interpretation of these experiments does not depend on the correctness of quantum theory, notes Lami.

Quantum cryptography

There are also practical implications. Quantum entanglement plays a key role in the design of quantum computers – machines that could outperform standard computers in certain tasks – and in quantum cryptographic protocols, which are already in use and exploit quantum rules to provide ultra-secure communication through channels that, in theory, are immune to hacking. But if quantum theory were to eventually be replaced by another more fundamental theory in the future, would we find that those rules weren’t really valid or that those cryptographic protocols aren’t secure as promised?

The problem is that to find out, you have to analyze superposition and entanglement in terms of a general – and still unknown – theory without using the mathematics of quantum theory. How can you do this? Lami and his colleagues solved this puzzle by studying “general probabilistic theories” rather than quantum theory. The research was funded in part by a grant Lami and others received from the Foundational Questions Institute, FQXi, to study the characteristics and limits of intelligence in generalized probabilistic theories, allowing them to examine how the Information is processed in classical abstract, quantum and ‘beyond quantum’ systems. “This FQXi fellowship gave me the opportunity to think more closely about some universal features of information processing in theories beyond quantum mechanics, mathematically modeled by general probabilistic theories,” says Lami. “And the cryptographic primitive example we’re looking at, secret key distribution, is one of the simplest tasks where this formalism can be applied.”

In the new article, published in Physical examination letters, the team showed that two physical theories exhibit entanglement when combined, if and only if they both exhibit local superpositions. This means that entanglement and superposition are equivalent in any physical theory, not just in quantum theory. They also calculated that in systems where this equivalence holds, whether quantum or beyond quantum, the laws of the theory can be exploited for ultra-secure encryption. In particular, the team showed that a certain popular quantum cryptographic protocol, known as “BB84”, will still work, even if one day it is discovered that the quantum theory is not entirely correct and must be replaced by a more fundamental theory.

“It’s kind of reassuring to know that cryptography really is a feature of all non-classical theories, and not just some quantum oddity, because many of us think that the ultimate theory of nature is likely to be non-classical,” Lami says. “Even if one day we find quantum theory to be incorrect, we will still know that secret key distribution can in principle work.”

This work was partially supported by FQXi’s Intelligence in the Physical World program.

LRP article: Entanglement and superposition are equivalent concepts in any physical theory.


The Institute for Fundamental Questions, FQXi, catalyses, supports and disseminates research on fundamental questions in science, particularly new frontiers in physics and innovative ideas that are integral to a deeper understanding of reality, but little likely to be supported by conventional funding sources. Visit fqxi.org for more information.

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