Tomographic characterisation of correlations in a photonic tripartite state

TL;DR

This paper experimentally characterizes correlations in a photonic tripartite state derived from a four-qubit hyper-entangled Dicke resource, verifying entanglement sharing and monogamy relations with minimal measurements.

Contribution

It demonstrates a full tomographic analysis of reduced states from a four-qubit Dicke resource, verifying the Koashi-Winter relation efficiently using symmetry-based measurement reduction.

Findings

Fidelities with expected states >87%

Verified Koashi-Winter relation for monogamy of correlations

Achieved full characterization with only 5 measurement settings

Abstract

Starting from a four-partite photonic hyper-entangled Dicke resource, we report the full tomographic characterization of three-, two-, and one-qubit states obtained by projecting out part of the computational register. The reduced states thus obtained correspond to fidelities with the expected states larger than 87%, therefore certifying the faithfulness of the entanglement-sharing structure within the original four-qubit resource. The high quality of the reduced three-qubit state allows for the experimental verification of the Koashi-Winter relation for the monogamy of correlations within a tripartite state. We show that, by exploiting the symmetries of the three-qubit state obtained upon projection over the four-qubit Dicke resource, such relation can be experimentally fully characterized using only 5 measurement settings. We highlight the limitations of such approach and sketch an experimentally-oriented way to overcome them.