A witness to quantify high-dimensional entanglement

TL;DR

This paper introduces the P-concurrence, a new measure for quantifying and witnessing high-dimensional entanglement efficiently without full state tomography, enabling faster quantum state characterization.

Contribution

The authors propose the P-concurrence, a novel entanglement measure and dimension witness that simplifies and accelerates high-dimensional entanglement quantification.

Findings

P-concurrence effectively quantifies high-dimensional entanglement.

Requires significantly fewer measurements than full quantum state tomography.

Enables faster and more efficient quantum state characterization.

Abstract

Exploiting photonic high-dimensional entanglement allows one to expand the bandwidth of quantum communication and information processing protocols through increased photon information capacity. However, the characterization of entanglement in higher dimensions is experimentally challenging because the number of measurements required scales unfavourably with dimension. While bounds can be used to certify high-dimensional entanglement, they do not quantify the degree to which quantum states are entangled. Here, we propose a quantitative measure that is both an entanglement measure and a dimension witness, which we coin the P-concurrence. We derive this measure by requiring entanglement to extend to qubit subspaces that constitute the high-dimensional state. The computation of the P-concurrence is not contingent on reconstructing the full density matrix, and requires less measurements compared to standard quantum state tomography by orders of magnitude. This allows for faster and more efficient characterization of high-dimensional quantum states.