Entanglement Detection Beyond Local Bound with Coarse Calibrated measurements

TL;DR

This paper develops a systematic method to strengthen Bell inequalities for qubit systems using coarse calibrated measurements, enhancing entanglement detection beyond local bounds.

Contribution

It introduces a new approach to improve Bell inequality bounds with limited device calibration, applicable to multipartite entanglement detection.

Findings

Derived trade-offs between bounds for separable and general states.

Strengthened Bell inequalities for detecting diverse entanglement structures.

Demonstrated entanglement detection using partial device characterization.

Abstract

Bell's test, initially devised to distinguish quantum theory from local hidden variable models through {violations of local bounds}, is also a common tool for detecting entanglement. For this purpose, one can assume the quantum description of devices and use available information to strengthen the bound for separable states, which may go beyond the local bound, enabling more efficient entanglement detection. Here we present a systematic approach for strengthening Bell inequalities for qubit systems, using Mermin-Klyshko-Bell inequalities as examples, by considering measurement devices that are coarsely calibrated only by their ability to generate nonlocal correlations without requiring precise quantum characterization. In the case of bipartite and tripartite systems, we derive trade-offs between upper bounds for separable states and general states in terms of structure functions to optimize the entanglement detection. We then strengthen $n$-partite Bell inequalities for the detection of states exhibiting a diversity of entanglement structures such as genuine multipartite entanglement. For general Bell scenarios with some measurements characterized, we demonstrate that entanglement can also be detected with some local correlations by exploiting the Navascu\'{e}s-Pironio-Ac\'{i}n hierarchy of tests.