High-Dimensional Pixel Entanglement: Efficient Generation and Certification

Abstract

Photons offer the potential to carry large amounts of information in their spectral, spatial, and polarisation degrees of freedom. While state-of-the-art classical communication systems routinely aim to maximize this information-carrying capacity via wavelength and spatial-mode division multiplexing, quantum systems based on multi-mode entanglement usually suffer from low state quality, long measurement times, and limited encoding capacity. At the same time, entanglement certification methods often rely on assumptions that compromise security. Here we show the certification of photonic high-dimensional entanglement in the transverse position-momentum degree-of-freedom with a record quality, measurement speed, and entanglement dimensionality, without making any assumptions about the state or channels. Using a tailored macro-pixel basis, precise spatial-mode measurements, and a modified entanglement witness, we demonstrate state fidelities of up to 94.4% in a 19-dimensional state-space, entanglement in up to 55 local dimensions, and an entanglement-of-formation of up to 4 ebits. Furthermore, our measurement times show an improvement of more than two orders of magnitude over previous state-of-the-art demonstrations. Our results pave the way for noise-robust quantum networks that saturate the information-carrying capacity of single photons.

Measuring dimensionality and purity of high-dimensional entangled states

“…Consider a pair of photons entangled in their polarisation, energy–time, momentum or in the spatial basis 24 , the so-called structured light 25 , the former useful to access high dimensions, with up to 100 × 100 dimensions already demonstrated 26 . In this work, we will consider two examples: the OAM basis 27 , 28 and the pixel (position) basis 29 . Due to the great potential of the former, particularly for quantum information processing and communications 30 – 44 , we first illustrate and demonstrate our method for OAM entangled states.…”

“…Here, Q is the average quantum contrast. Our experiment used a gating time of 25 ns for the coincidences with averaging over 10 s. Reducing the gating time, increasing the averaging time and taking care with the experimental conditions would significantly enhance the purities 29 , even for the low noise conditions.…”

Entanglement Detection with Imprecise Measurements

“…Naturally, high-dimensional entanglement has been the focus of many optics experiments [32,33]. Realisations have been reported for instance in transverse spatial modes [34][35][36][37], in path [38,39], in time-bins [40,41] and in frequency modes [42][43][44]. Beyond optics, higher-dimensional entanglement has been developed in e.g.…”

“…Notably, when the state is expected to feature relatively little noise, then small choices for m and n are sufficient to detect high Schmidt numbers. To exemplify this, we have examined the data reported in [37] from measuring two global product MUBs on a state of local dimension d = 19. A direct use of our criterion for m = 2 MUBs implies an entanglement fidelity of at least 92.7% and a Schmidt number of at least 18.…”

“…The other criterion is based on equiangular measurements (EAMs), among which the most well-known example is the symmetric informationally complete measurement (SIC-POVM) [52,53]. Both these classes of measurements are broadly relevant in quantum information science and they are frequently studied in both theory [54,55] and experiment [19,37,[56][57][58][59][60][61].…”