Quantification of Entanglement and Coherence with Purity Detection

TL;DR

This paper introduces experimentally feasible methods to quantify entanglement and coherence in quantum systems using purity measurements, providing bounds that are analytically derived and validated through optical experiments, thus aiding large-scale quantum information verification.

Contribution

It presents universal, analytically computable bounds for entanglement and coherence based on purity, validated by optical experiments, simplifying quantum state quantification.

Findings

Bounds for coherent information and coherence are experimentally validated.

Purity detection methods effectively estimate quantum properties.

The approach simplifies large-scale quantum state verification.

Abstract

Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies, such as quantum computation, quantum communication and quantum metrology. Yet, their quantification, rather than mere detection, generally requires reconstructing the spectrum of quantum states, i.e., experimentally challenging measurement sets that increase exponentially with the system size. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence that are universally valid, analytically computable, and experimentally friendly. Specifically, our main theoretical results are lower and upper bounds to the coherent information and the relative entropy of coherence in terms of local and global purities of quantum states. To validate our proposal, we experimentally implement two purity detection methods in an optical system: shadow estimation with random measurements and collective measurements on pairs of state copies. The experiment shows that both the coherent information and the relative entropy of coherence of pure and mixed unknown quantum states can be bounded by purity functions. Our research offers an efficient means of verifying large-scale quantum information processing.