Detecting high-dimensional entanglement with simple measurements

As quantum technologies scale to higher dimensions, the standard methods for certifying entanglement—specifically the Schmidt number—become increasingly difficult to implement. Conventional approaches require complex, high-depth optical circuits to perform measurements in mutually unbiased bases (MUBs). This paper addresses the need for a more scalable, lower-complexity approach to certifying high-dimensional entanglement in photonic systems.

The researchers propose a Schmidt number witness method that decomposes high-dimensional observables into strings of simple, two-dimensional Pauli observables. By grouping these into parallel, low-depth operations, they significantly reduce the required circuit depth. They experimentally validate this technique using photonic spatial mode entanglement, employing multi-plane light conversion (MPLC) technology to perform the necessary transformations. They test this approach on systems with local dimensions of 4, 8, and 16.

The study demonstrates that simple, low-depth circuits are sufficient to certify high-dimensional entanglement. For an 8-dimensional system, they successfully certified the maximal Schmidt number using circuits with a depth of only one. For a 16-dimensional system, they achieved certification of a 13-dimensional Schmidt number using circuits with a depth of 1.5. This represents a substantial reduction in experimental overhead compared to state-of-the-art methods, which typically require much deeper circuits to achieve similar results.

This work provides a practical pathway for scaling quantum information protocols. By lowering the requirements for entanglement certification, the method mitigates issues related to optical losses, alignment complexity, and the manufacturing of large-scale photonic circuits. It demonstrates that complex entanglement properties can be verified with modular, parallelized measurements, which is essential for the future development of high-capacity quantum communication and computing networks.