Certification of a Nonprojective Qudit Measurement using Multiport Beamsplitters

Abstract: Generalised quantum measurements go beyond the textbook concept of a projection onto an orthonormal basis in Hilbert space. They are not only of fundamental relevance but have also an important role in quantum information tasks. However, it is highly demanding to certify that a generalised measurement is indeed required to explain the results of a quantum experiment in which only the degrees of freedom are assumed to be known. Here, we use state-of-the-art multicore optical fiber technology to build multiport beamsplitters and faithfully implement a seven-outcome generalised measurement in a four-dimensional Hilbert space with a fidelity of $99.7\%$. We apply it to perform an elementary quantum communication task and demonstrate a success rate that cannot be simulated in any conceivable quantum protocol based on standard projective measurements on quantum messages of the same dimension. Our approach, which is compatible with modern photonic platforms, showcases an avenue for faithful and high-quality implementation of genuinely nonprojective quantum measurements beyond qubit systems.