Quantifying entanglement in a 68-billion dimensional quantum state space

TL;DR

This paper introduces a novel method to quantify high-dimensional entanglement in quantum systems efficiently, requiring vastly fewer measurements than traditional approaches, enabling practical analysis of extremely large quantum states.

Contribution

The authors develop an adaptive, compressed data-based entanglement quantification technique that drastically reduces measurement requirements for large quantum systems.

Findings

Certifies 7.11 ebits of entanglement with only 6,456 measurements.

Operates on a 68-billion-dimensional quantum state space.

Requires 20-million times fewer measurements than uncompressed methods.

Abstract

Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which demands an intractable number of measurements even for modestly-sized systems. Here we demonstrate a method for rigorously quantifying high-dimensional entanglement from extremely limited data. We improve an entropic, quantitative entanglement witness to operate directly on compressed experimental data acquired via an adaptive, multilevel sampling procedure. Only $6,456$ measurements are needed to certify an entanglement-of-formation of $7.11 \pm .04$ ebits shared by two spatially-entangled photons. With a Hilbert space exceeding 68 billion dimensions, we need $20$-million-times fewer measurements than the uncompressed approach and $10^{18}$-times fewer measurements than tomography. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.