Experimental investigation of the information entropic Bell inequality

Abstract

Inequalities of information entropic play a fundamental role in information theory and have been employed effectively in finding bounds on optimal rates of various information-processing tasks. In this paper, we perform the first experimental demonstration of the information-theoretic spin-1/2 inequality using the high-fidelity entangled state. Furthermore, we study the evolution of information difference of entropy when photons passing through different noisy channels and give the experimental rules of the information difference degradation. Our work provides an new essential tool for quantum information processing and measurement, and offers new insights into the dynamics of quantum correlation in open systems.

Experimentally Demonstrate the Spin-1 Information Entropic Inequality Based on Simulated Photonic Qutrit States

“…The experimental data of nine combinations of measurement basis, , , and , were collected, as shown in Figure 2 . Through the above operation, we could obtain the entangled state with a fidelity of 97.8 ± 0.2%, which could prove that the entangled system had good properties [ 20 , 21 ].…”

“…The experimental results and experimental errors of information difference when the θ was rotated from 0 to θ /5, θ /5 to 2 θ /5, 2 θ /5 to 3 θ /5, 3 θ /5 to 4 θ /5, and 4 θ /5 to θ are shown in Figure 3 . It can be seen that within the error range, the measurement results of these five parts were very close, and the error was likely caused by the modulation of the measurement equipment angle [ 20 ].…”

“…However, in order to prove the inequality and study its application experimentally, especially the higher-dimensional inequality, the quality requirement of the entangled system is very strict [ 17 , 18 , 19 ]. To our knowledge, experimental reports on quantum entanglement entropy are very few [ 18 , 19 , 20 , 21 ].…”

Monogamy relations of entropic non-contextual inequalities and their experimental realization

“…Subsequently, the work was extended to include non-contextual scenarios [33,34] as well, and the inequalities are generally termed as entropic non-contextuality (ENC) inequalities. Since their inception, these inequalities have been studied extensively and have also been realized experimentally [35][36][37][38][39]. Experimental implementations of state dependent [38] as well as state independent [39] ENC inequalities have been performed on optical systems.…”

Indistinguishability of causal relations from limited marginals

“…The entropic approach to the marginal problem and causal discovery has received growing attention [45][46][47][48][49][50][51][52][53][54][55][56], but still suffers from two main drawbacks. The first stands from a computational complexity issue.…”