Dynamics-Based Entanglement Witnesses for Non-Gaussian States of Harmonic Oscillators

TL;DR

This paper presents a novel entanglement witness for continuous variable systems based on dynamics, capable of detecting non-Gaussian entangled states without false positives, using minimal measurements and the Tsirelson test.

Contribution

It introduces a new dynamic-based entanglement witness that detects non-Gaussian entanglement in harmonic oscillators without prior state knowledge.

Findings

Detects non-Gaussian entangled states missed by other criteria

Requires only sign measurements of one coordinate at multiple times

Does not produce false positives from classical theories

Abstract

We introduce a family of entanglement witnesses for continuous variable systems, which rely on the sole assumption that their dynamics is that of coupled harmonic oscillators at the time of the test. Entanglement is inferred from the Tsirelson nonclassicality test on one of the normal modes, without any knowledge about the state of the other mode. In each round, the protocol requires measuring only the sign of one coordinate (e.g., position) at one among several times. This dynamic-based entanglement witness is more akin to a Bell inequality than to an uncertainty relation: in particular, it does not admit false positives from classical theory. Our criterion detects non-Gaussian states, some of which are missed by other criteria.