Encoding and measuring information in high-dimensional quantum states

Jacq Romero

Zhenghong Li, Shun Li, M. Al-Amri

A theoretical framework utilizing sequential non-demolition measurements to extract information from high-dimensional quantum systems is proposed. In our scheme, an unsuccessful measurement does not cause collapse of the system state but allows it to revert to its pre-measurement state for subsequent measurements. Compared with conventional schemes, our approach enables flexible switching of the bases used for encoding and transmitting signals, making it particularly suitable for high-dimensional quantum-secure communication protocols based on mutually unbiased bases (MUBs). Moreover, our scheme does not strictly require orthogonality of the signal states, which relaxes the precision requirements for the information encoding processes while supporting more flexible signal state selection strategies. Our work opens a new pathway for the practical design of high-dimensional quantum communication systems.

Miller Eaton

Dawei Lyu, Qianke Wang, Jun Liu +1 more

ABSTRACT Quantum state tomography plays a fundamental role in quantum information science. Spatial modes of photons offer a promising encoding platform for high‐dimensional quantum states, yet efficient reconstruction of such states remains challenging. Recent advances in diffractive neural networks (DNNs) have introduced powerful capabilities for spatial mode manipulation, offering new opportunities for realizing efficient projective measurements. Here, we propose and experimentally demonstrate an efficient high‐dimensional state reconstruction method, enabled by parallel measurement of the full Bloch vectors for high‐dimensional states encoded in spatial modes of photons. By employing a DNN, our method maps mutually unbiased basis states to spatially separated Gaussian spots, thereby performing parallel projective measurements with a single measurement setting. We successfully reconstruct spatial‐mode‐encoded states in dimensions two through four, achieving state fidelities up to 99% and measurement process fidelities up to 97%. The method is further extended to spin‐orbit non‐separable states and mixed states, demonstrating its capability for reconstructing different classes of states within the selected spatial‐mode encoding space. Our method significantly improves the efficiency of tomography for spatial‐mode‐encoded high‐dimensional states and provides a versatile tool for the rapid characterization of high‐dimensional quantum systems.

Simon White, Emanuele Polino, Farzad Ghafari +6 more

Quantum states encoded in the time-bin degree of freedom of photons represent a fundamental resource for quantum information protocols. Traditional methods for generating and measuring time-bin-encoded quantum states face severe challenges due to optical instabilities, complex setups, and timing resolution requirements. To circumvent these issues, we leverage an approach based on Hong-Ou-Mandel interference and we propose and demonstrate a robust and scalable protocol to generate and measure arbitrary high-dimensional time-bin quantum states. We experimentally implement the protocol in a photonic setup reaching high-fidelity quantum state tomographies of two- and three-dimensional quantum states encoded in time bins with short temporal separation. We also certify intrasystem polarization-time entanglement of single photons through a nonclassicality test. The demonstrated approach enables access to high-dimensional states and tasks that are practically inaccessible with standard schemes, thereby advancing fundamental quantum information science and opening applications in quantum communication.

V. Ravishankar