Testing Information Causality for General Quantum Communication Protocols

TL;DR

This paper tests the principle of information causality in general quantum communication schemes, extending previous binary-focused results and finding that the bounds differ from the Tsirelson bound.

Contribution

It generalizes the testing of information causality to non-binary quantum communication schemes using semi-definite programming and numerical methods.

Findings

Supports the validity of information causality principle

Finds the bounds for information gain differ from Tsirelson bound

Uses semi-definite programming and brute-force methods for analysis

Abstract

Information causality was proposed as a physical principle to put upper bound on the accessible information gain in a physical bi-partite communication scheme. Intuitively, the information gain cannot be larger than the amount of classical communication to avoid violation of causality. Moreover, it was shown that this bound is consistent with the Tsirelson bound for the binary quantum systems. In this paper, we test the information causality for the more general (non-binary) quantum communication schemes. In order to apply the semi-definite programming method to find the maximal information gain, we only consider the schemes in which the information gain is monotonically related to the Bell-type functions, i.e., the generalization of CHSH functions for Bell inequalities in a binary schemes. We determine these Bell-type functions by using the signal decay theorem. Our results support the proposal of information causality. We also find the maximal information gain by numerical brute-force method for the most general 2-level and 2-setting quantum communication schemes. Our results show that boundary for the information causality bound does not agree with the one for the Tsirelson bound.