Entanglement certification and quantification in spatial-bin photonic qutrits

Abstract

Higher dimensional quantum systems are an important avenue for new explorations in quantum computing as well as quantum communications. One of the ubiquitous resources in quantum technologies is entanglement. However, so far, entanglement has been certified in higher dimensional systems through suitable bounds on known entanglement measures. In this work, we have, for the first time, quantified the amount of entanglement in bi-partite pure qutrit states by analytically relating statistical correlation measures and known measures of entanglement, and have determined the amount of entanglement in our experimentally generated spatially correlated bi-partite qutrit system. We obtain the value of Negativity in our bi-partite qutrit to be 0.85 ± 0.03 and the Entanglement of Formation (EOF) to be 1.23 ± 0.01. In terms of quantifying the deviation from the maximally entangled state, the Negativity value demonstrates ∼ 15% deviation while the EOF value demonstrates ∼ 24% deviation. This serves as the first experimental evidence of such non-equivalence of entanglement measures for higher dimensional systems.

Quantum-Assisted Graph Clustering and Quadratic Unconstrained D-ary Optimisation

“…3: Node-node interactions and corresponding interaction energies look like (coupling strength has been considered to be unity) the matrix in Figure 4. One can think of using a matrix with the cube roots of unity placed along the diagonal of the 3 × 3 matrix [14]:…”