Revivals of Bell nonlocality require Schrödinger and Heisenberg non-Markovianity

Abstract

Bell nonlocality is a key resource in quantum information, demonstrating the nonclassicality of quantum theory. Noise, however, {is in general detrimental to} nonlocality, and can cause the loss of the ability to violate any Bell inequality. Memory effects, on the other hand, can restore {this} quantumness and, as recently shown, they can be {differently characterized} in the Schrödinger and in the Heisenberg picture. Here, we show that if memory effects allow for revivals in time of nonlocality, then the dynamics must be non-Markovian in both pictures. We showcase our findings through a device-independent quantum key distribution task, for which Bell nonlocality is necessary.

4 pages, 1 figure. Companion paper: "Schrödinger and Heisenberg non-Markovianity in quantum information tasks"