A Limit on Non-Locality Distillation

TL;DR

This paper proves that non-local correlations of the CHSH type cannot be significantly distilled using classical methods, revealing fundamental limits and implying an infinite hierarchy of bounds in non-locality.

Contribution

It establishes a fundamental limit on the distillability of non-local correlations, extending previous bounds and showing the existence of infinitely many such bounds.

Findings

CHSH-type non-locality has limited distillability by classical methods

There are fundamental bounds, including Bell and Tsirelson bounds, that cannot be surpassed

Certain entangled states cannot be distilled without communication

Abstract

Non-local correlations are not only a fascinating feature of quantum theory, but an interesting resource for information processing, for instance in communication-complexity theory or cryptography. An important question in this context is whether the resource can be distilled: Given a large amount of weak non-local correlations, is there a method to obtain strong non-locality using local operations and shared randomness? We partly answer this question by no: CHSH-type non-locality, the only possible non-locality of binary systems, which is not super-strong, but achievable by measurements on certain quantum states, has at best very limited distillability by any non-interactive classical method. This strongly extends and generalizes what was previously known, namely that there are two limits that cannot be overstepped: The Bell and Tsirelson bounds. Moreover, our results imply that there must be an infinite number of such bounds. A noticeable feature of our proof of this purely classical statement is that it is quantum mechanical in the sense that (both novel and known) facts from quantum theory are used in a crucial way to obtain the claimed results. One of these results, of independent interest, is that certain mixed entangled states cannot be distilled without communication. Weaker statements, namely limited distillability, have been known for Werner states.