Entanglement verification with finite data

TL;DR

This paper introduces a universal statistical method using likelihood ratio tests to reliably quantify evidence for entanglement in quantum experiments with finite data, applicable to any measurement type.

Contribution

It presents a novel, universally applicable statistical approach for entanglement verification based on likelihood ratios, suitable for any measurement scheme.

Findings

Effective in simulated experiments with two qubits

Applicable to both witness measurement and tomography

Provides quantifiable evidence for entanglement

Abstract

Suppose an experimentalist wishes to verify that his apparatus produces entangled quantum states. A finite amount of data cannot conclusively demonstrate entanglement, so drawing conclusions from real-world data requires statistical reasoning. We propose a reliable method to quantify the weight of evidence for (or against) entanglement, based on a likelihood ratio test. Our method is universal in that it can be applied to any sort of measurements. We demonstrate the method by applying it to two simulated experiments on two qubits. The first measures a single entanglement witness, while the second performs a tomographically complete measurement.