To this end, a resource theory is required.
Perspectives and debates aside, it is clear that to better understand non-locality/non-classicality we must find good ways to quantify it. Critically, these causal principles can also hold quantum mechanically upon generalizing our idea of what a common cause is. Conceptually, this new len’s on Bell’s theorem replaces the often hazy and much debated concepts of local causality and realism with mathematically well defined concepts given by Reichenbach’s principle (correlations have to be explained causally) and the principle of no fine-tuning (observed statistical independences are a reflection of the underlying causal structure). From the causal perspective, Bell’s theorem can be seen as a particular case of a causal inference problem, a realization that has sparked a number of generalizations to causal scenarios of growing size and complexity. Ironically, the nascent mathematical theory of causality was only first developed (mostly by the computer science and artificial intelligence community) 30 years after Bell’s seminal result. In hindsight, it is clear that Bell’s theorem is a statement about the incompatibility of quantum theory with classical notions of causality. In practice, applications ranging from randomness certification to self-testing (the ability to identify quantum states and measurements from observed correlations alone) and distributed computing have been firmly founded on that which is now known as the device-independent framework, where tasks are accomplished without the need of a precise characterization of the physical devices. The non-classicality exposed by Bell’s theorem has become a guiding principle for efforts to recover quantum theory from information-theoretical principles, which one might hope will provide a more palatable explanation as compared to the standard textbook postulates. Irrespectively of personal choices of which assumption to abandon, realism or locality, the guidance provided by Bell inequalities has proven valuable over the years both in foundational and applied sides. In fact, those violations have synonymous with Bell’s theorem, the phenomenon generally known as Bell non-locality (a nomenclature that the authors defy in favour of a more neutral choice of non-classicality).
Quantum correlations obtained by measurements of distant shares of an entangled state can be incompatible with the conjunction of those notions, something that can be witnessed experimentally by the violation of a Bell inequality. Or locality, the idea that two distant (space-like separated) events should not have any direct causal influence one over the other. Traditionally, Bell’s theorem has been understood as the need to give up at least one of our two most ingrained concepts about the world: Realism, stating that the properties of a physical system are well-defined independently of our act of measuring them. That is precisely what the paper “Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes” by Wolfe et. When viewed from a new perspective, however, apparent simplicity can give rise to a rich mathematical structure and a plethora of interesting novel phenomena and potential applications.
Often, however, I’m the one shocked by the attitude of those listening, who misinterpret the elementary mathematics required to prove Bell’s theorem as a reflection of its unimportance. This is the least I would expect from those suddenly learning that seemingly metaphysical concepts like realism or even “free-will” can, to some extent, be tested in the laboratory. When presenting Bell’s theorem to audiences seeing it for the first time, be they students or (surprisingly) physicists from areas with little regard to the quantum foundations, I often anticipate a reaction of shock.
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