On Bell's theorem, quantum communication, and entanglement detection

TL;DR

This paper explores the foundational assumptions of Bell's theorem, links it to communication complexity, and introduces a new, more powerful criterion for detecting entanglement in quantum states.

Contribution

It presents a stronger version of Bell's theorem incorporating rotational symmetry and introduces a novel entanglement criterion surpassing traditional entanglement witnesses.

Findings

Stronger Bell's theorem with rotational symmetry

Experimental links between Bell's theorem and communication complexity

New entanglement detection method more powerful than existing witnesses

Abstract

(A) Bell's theorem rests on a conjunction of three assumptions: realism, locality and ``free will''. A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational symmetry of physical laws, a stronger version of the theorem emerges. (B) A link between Bell's theorem and communication complexity problems will be presented. This also includes experimental realizations, which surprisingly do not involve entanglement. (C) A new sufficient and necessary criterion for entanglement of general (mixed) states is be presented. It is derived using the same geometric starting point as the inclusion of the symmetry in (A). The set of entanglement identifiers (EI's) emerging via this method contains entanglement witnesses (EW's), but they form only a subset of all EI's. Thus the method is more powerful than the one based on EW's.