Bound entangled states fit for robust experimental verification

TL;DR

This paper introduces a new method for certifying bound entangled states in experiments without full state tomography, enhancing reliability and statistical significance of verification.

Contribution

It proposes an alternative certification method that bypasses full state reconstruction and provides a statistically rigorous way to verify bound entanglement in laboratory settings.

Findings

Bound entangled states can be certified with high statistical significance.

The method applies to 3x3 and 4x4 quantum systems.

Experimental verification of bound entanglement is feasible with the proposed approach.

Abstract

Preparing and certifying bound entangled states in the laboratory is an intrinsically hard task, due to both the fact that they typically form narrow regions in the state space, and that a certificate requires a tomographic reconstruction of the density matrix. Indeed, the previous experiments that have reported the preparation of a bound entangled state relied on such tomographic reconstruction techniques. However, the reliability of these results crucially depends on the extra assumption of an unbiased reconstruction. We propose an alternative method for certifying the bound entangled character of a quantum state that leads to a rigorous claim within a desired statistical significance, while bypassing a full reconstruction of the state. The method is comprised by a search for bound entangled states that are robust for experimental verification, and a hypothesis test tailored for the detection of bound entanglement that is naturally equipped with a measure of statistical significance. We apply our method to families of states of $3\times 3$ and $4\times 4$ systems, and find that the experimental certification of bound entangled states is well within reach.