Activation of the Violation of Svetlichny Inequality for a Broad Class of States

Abstract

The fact that several copies of a local quantum state — when processed together — can generate a nonlocal correlation, i.e. the superactivation of quantum nonlocality, is a well-known feature of quantum mechanics. Most of research results focused strongly on the bipartite scenario. In this paper we show that the activation of violation of Svetlichny inequality, reported for the first time in our previous paper, is not an exceptional phenomenon but holds for a broad class of quantum states as well for pure as for mixed, noisy ones.

Noise resistance of activation of the violation of the Svetlichny inequality

“…Taking the above considerations into account in our previous paper [7,8], we have shown that the violation of the Svetlichny inequality can be activated for a class of GHZ states. We considered GHZ states because for these states the maximum value of the Svetlichny operator for a single copy of the state was determined analytically in [1].…”

“…The analytical formula for S (1) max (ρ GHZ ) as a function of parameters was found in [1]. In our previous papers [7,8], we have shown that there exist such GHZ states for which S (1) max (ρ GHZ ) < 4 while S (2) max (ρ ⊗2 GHZ ) > 4. Moreover, due to the very simple form of white noise, we were able to find S (1) max (ρ wnGHZ ) where…”

“…We considered GHZ states because for these states the maximum value of the Svetlichny operator for a single copy of the state was determined analytically in [1]. Moreover, due to the very simple form of the white noise, we were able to show that noisy GHZ states of the form (1 − p)ρ GHZ + pI can also be activated for nonzero values of p [8]. We could not analyze different types of noise because of the difficulties described above.…”