High-dimensional multipartite quantum transformations

A 2019 study, published in 2020, proposes experimentally meaningful architectures for general $n$-photon, $d$-dimensional transformations, using ancillary states, nondemolition measurements, and high-dimensional interferometers. It presents examples but does not prove universal implementability.

Known results

• The 2019 work gives blueprints for controlled-$\hat{X}$, controlled-controlled-$\hat{X}$, controlled-phase, and more general transformations, including $\hat{T}\ket{c_{1},c_{2}}=\ket{(c_{1}+c_{2})\%d,(2c_{1}+c_{2})\%d}$.
• It reports that some proposed components appear feasible with current technology, while others require further investigation.

2026 heralded photon gate

A 2026 report describes a heralded high-dimensional photon–photon gate, but the retrieved material does not establish that it handles arbitrary $n$ and $d$ or solves the general problem.

Current status (as of March 2026): Partial experimental progress is established, but universal control of arbitrary $n$-photon, $d$-dimensional states remains open.