Persistency of tripartite nonlocality sharing with noise

Abstract

Recently, researchers have proven that an infinite number of Charlies and a pair of Alice and Bob can share standard tripartite nonlocality and genuinely nonsignal nonlocality by violating the Mermin and NS inequalities within tripartite systems. This discovery undoubtedly provides new perspectives and potential in quantum information science. However, it should be noted that the above-mentioned conclusion is derived on the highly idealized assumption that the quantum system is perfect and free from external disturbances. In reality, the realization of this ideal state is a challenging proposition. As a fundamental aspect of quantum mechanics, the phenomenon of quantum entanglement is susceptible to the influence of external factors, such as noise, during its practical implementation. Additionally, the process of quantum measurement can introduce potential errors, which may potentially diminish or even negate the observed quantum nonlocality. In light of the above situation, we investigate whether it is possible to share the corresponding quantum nonlocality, despite the inevitable occurrence of noise and error. This paper aims to study and discuss the persistency of nonlocality in noisy three-qubit systems. Firstly, the sufficient conditions are provided for Alice and Bob to share standard tripartite nonlocality with any number of Charlies, even when measurements are noisy and the initial three-qubit system is in a maximally entangled state with noise. This finding indicates that certain standard tripartite nonlocality can persist under non-ideal conditions as long as certain conditions are met. Moreover, this article elucidates the necessary conditions for multiple independent Charlies to share genuinely nonsignal nonlocality with a pair of Alice and Bob in a non-ideal state. This implies that despite the presence of noise and errors, this type of genuinely nonsignal nonlocality can still be securely shared among multiple parties as long as specific conditions are met. This research provides a new theoretical basis for the security and feasibility of quantum communication. The comprehensive analysis presented in this paper offers insights into the behavior of triple quantum nonlocality under noiseless conditions.