High-dimensional entanglement certification: bounding relative entropy of entanglement in $2d+1$ experiment-friendly measurements

TL;DR

This paper introduces a scalable method for certifying high-dimensional entanglement using minimal measurements, specifically bounding the relative entropy of entanglement with only one complex measurement, facilitating experimental implementation.

Contribution

The authors develop a novel entanglement certification technique that requires only a single complex measurement and scales linearly with the subsystem dimension, advancing practical high-dimensional entanglement verification.

Findings

Provides a lower bound on the relative entropy of entanglement for maximally correlated states.

The measurement complexity scales with the square-root of the system dimension.

Applicable to noisy states, with discussion on experimental measurement realization.

Abstract

Entanglement -- the coherent correlations between parties in a joint quantum system -- is well-understood and quantifiable in the two-dimensional, two-party case. Higher (>2)-dimensional entangled systems hold promise in extending the capabilities of various quantum information applications. Despite the utility of such systems, methods for quantifying high-dimensional entanglement are more limited and experimentally challenging. We review entanglement certification approaches and the large number of -- often difficult -- measurements required to apply them. We present a novel certification method whose measurement requirements scale linearly with subsystem dimension (scaling with the square-root of the system dimension) and which requires only a single complex measurement. The certification method places a lower-bound on the relative entropy of entanglement of any maximally correlated state thereby certifying system entanglement. A lower bound is also shown for any maximally correlated state in the presence of noise -- the expected experimental case. We discuss experimental realization of all required measurements.