Indian Institute of Technology Kanpur: Researchers Unlock Radial Schmidt Mode Detection for Quantum Information Science

Radhika Prasad and colleagues at Indian Institute of Technology Kanpur and Paderborn University now measure the radial Schmidt spectrum of entangled photons, unlocking potential advances in quantum information science. They demonstrate a new technique for extracting high-dimensional radial Schmidt modes, previously a key obstacle in utilising radial entanglement. Their work theoretically proves that azimuthal averaging of spontaneously parametrically down-converted photons results in a radial Schmidt-decomposed form, and experimentally achieves measurement of up to 50 radial Schmidt modes with approximately 98% fidelity. This breakthrough provides a vital capability for harnessing the advantages of high-dimensional entanglement and expands the set of tools for quantum technologies.

High-fidelity detection unlocks access to previously unexplored radial entanglement of photons

The researchers at Indian Institute of Technology Kanpur have measured up to 50 radial Schmidt modes with 98% fidelity, a substantial improvement over previous detectors. Limited to four or eight modes with poor efficiency or performance, earlier devices could not achieve this level of precision. This breakthrough crosses a critical threshold, enabling access to high-dimensional radial entanglement previously impossible due to a lack of suitable detection techniques. The significance of this improvement lies in the ability to encode more information per photon, a crucial factor in increasing the capacity and security of quantum communication protocols. Prior limitations stemmed from the difficulty in efficiently separating and identifying the numerous spatial modes that constitute high-dimensional entanglement.

Azimuthal averaging of spontaneously parametrically down-converted photons yields a radial Schmidt-decomposed form, simplifying the process of extracting these modes. Spontaneous parametric down-conversion (SPDC) is a nonlinear optical process where a pump photon is split into two entangled photons, known as the signal and idler. The spatial properties of these photons are inherently linked, and their entanglement can be described using Schmidt decomposition, which expresses the state as a sum of orthogonal basis states. The researchers demonstrate that by performing an azimuthal average, effectively integrating over all angles around the beam axis, the complex spatial entanglement simplifies into a purely radial form. Successful measurements were achieved under varying experimental conditions, indicating the robustness of the technique. Data analysis revealed that azimuthal averaging of the spontaneous parametric down-conversion two-photon state yields a radial Schmidt-decomposed form under typical experimental situations. This approach allows for the extraction of radial Schmidt modes and their spectrum by characterising the density matrix in the radial basis of one of the photons. The density matrix provides a complete description of the quantum state, enabling precise quantification of the entanglement.

A radial Schmidt spectrum of up to 50 radial Schmidt modes was reported for the first time, with approximately 98% fidelity. This new technique characterizes the radial Schmidt spectrum, opening avenues for quantum information science applications. The radial Schmidt spectrum represents the distribution of entanglement across the different radial modes. A higher number of significantly populated modes indicates stronger and more versatile entanglement. Current radial-mode sorters can sort only a limited set of pre-specified modes or modes based on whether l + p is odd or even, and further work is needed to address these limitations and explore the full potential of radial-mode entanglement. These existing sorters often rely on physical apertures or diffractive optical elements, restricting their ability to access the full range of radial modes. The ability to fully characterize the radial Schmidt spectrum allows for a more complete understanding and control of the entangled state.

Scaling radial mode entanglement presents ongoing technical hurdles

This advance unlocks exciting possibilities for high-dimensional quantum communication, but a key limitation remains. Scaling this technique to even greater numbers of radial modes presents a significant challenge. Existing methods for manipulating and detecting these modes become increasingly complex and inefficient as dimensionality increases, potentially negating the benefits of higher-dimensional entanglement. This is particularly relevant when compared to established polarisation-based quantum key distribution, which benefits from mature, readily available technology. The difficulty arises from the need to resolve and distinguish increasingly similar spatial modes, requiring higher-resolution optics and more sophisticated detection schemes. Furthermore, maintaining the fidelity of entanglement across a many number of modes is a significant technical hurdle.

Despite the acknowledged difficulties in scaling to very high numbers of radial modes, this demonstration of radial Schmidt mode measurement represents a step forward. A method to theoretically describe and experimentally measure these modes was previously lacking, and the technique overcomes this longstanding obstacle in utilising them for quantum technologies. This advancement expands the set of tools for quantum communication, offering an alternative to polarisation-based systems and potentially enabling more secure and higher-capacity networks. Polarisation-based systems, while well-established, are susceptible to certain types of eavesdropping attacks. Higher-dimensional entanglement, such as that based on radial modes, offers increased security due to the larger Hilbert space, making it more difficult for an eavesdropper to intercept the quantum signal without being detected.

The team’s demonstration establishes a vital capability previously absent from quantum photonics. Theoretical proof confirms azimuthal averaging simplifies the state of down-converted photons, and experimental verification supports this with up to 50 radial modes at 98% fidelity. Consequently, scientists have overcome a longstanding limitation in accessing high-dimensional radial entanglement. This advance expands the possibilities for manipulating spatial entanglement, a property linked to the shape of light, and opens questions regarding the scalability of this technique to even greater dimensions for complex quantum protocols. The ability to control the spatial shape of photons allows for the encoding of information in a manner that is robust to environmental noise and offers increased bandwidth. Future research will likely focus on developing more efficient and scalable methods for generating, manipulating, and detecting radial Schmidt modes, paving the way for practical applications in quantum communication, quantum computing, and quantum imaging.

Researchers successfully measured up to 50 radial Schmidt modes of entangled photons with 98% fidelity, overcoming a significant technical hurdle in quantum photonics. This achievement is important because it provides a method for accessing and characterising high-dimensional radial entanglement, previously lacking in the field. The technique simplifies the state of down-converted photons through azimuthal averaging, enabling the extraction of radial Schmidt modes and their spectrum. This expands the toolkit for quantum communication, offering a potential alternative to polarisation-based systems and increasing the possibilities for manipulating spatial entanglement.