Dilution of Entanglement: Unveiling Quantum State Discrimination Advantages

TL;DR

This paper investigates how different entanglement levels in three-qubit GHZ states affect quantum state discrimination, revealing that maximal entanglement is generally needed for perfect discrimination, and proposing a method to explore this with non-maximally entangled states.

Contribution

It introduces a novel approach to analyze perfect distinguishability of orthogonal product states using non-maximally entangled GHZ states, linking entanglement structure to discrimination capabilities.

Findings

Maximally entangled states enable perfect discrimination.

Generic GHZ states offer advantages in probabilistic distinguishability.

Open problem: achieving perfect discrimination with non-maximally entangled states.

Abstract

The states in the three-qubit GHZ SLOCC class can exhibit diverse entanglement patterns, as they may have no entanglement in any reduced subsystems, or show entanglement across one, two, or all three bipartite cuts. Significant research has explored how such states can be used in entanglement-assisted discrimination tasks. In this paper, we analyze the relationship between probability of error and amount of bipartite and multiparty entanglement, examining how different levels of entanglement impact the accuracy of state discrimination. Also we have shown that the generic class of GHZ state provide some advantages in probabilistic distinguishibility. However, perfect discrimination typically requires maximally entangled states. The use of non-maximally entangled states as a resource for perfect discrimination remains an open problem in this area of research. In this manuscript, we propose a method to explore the perfect distinguishability of orthogonal product states using non-maximally entangled states, utilizing the GHZ SLOCC class structure. Moreover, these findings offer deeper insights into the relationship between entanglement classification and nonlocality, potentially shedding light on how different entanglement structures influence nonlocal behavior in quantum systems.