Quantum Technology Detects Non-Gaussian Entanglement, Escaping Limitations of Covariance-Based Criteria

Detecting entanglement, a key resource in quantum technologies, presents a significant challenge when quantum states deviate from simple Gaussian forms. Abhinav Verma, Olga Solodovnikova, and Jonas S. Neergaard-Nielsen, all from the Technical University of Denmark, alongside Ulrik L. Andersen, now demonstrate a new method for identifying entanglement in these more complex, non-Gaussian systems. The team developed a criterion that reveals entanglement missed by standard techniques, which rely on Gaussian statistics, by incorporating information from higher-order statistical moments. This advancement avoids the need for complete state characterisation and allows researchers to directly assess entanglement using readily available measurement data, offering a practical pathway to harness non-Gaussian resources for quantum applications.

In Gaussian statistics, limitations arise when quantum correlations are encoded in higher moments of the field quadratures. Researchers introduce an inseparability criterion that detects non-Gaussian entanglement, escaping detection by covariance-based criteria, by incorporating higher-order quadrature cumulants. This criterion extends Gaussian theory without necessitating full state tomography and can be evaluated directly from homodyne and heterodyne data. Furthermore, it is possible to extend this approach to arbitrary superpositions of Fock states in two modes, providing an experimentally viable method for identifying non-Gaussian resources in continuous-variable platforms.

Gaussian State Separability via Second Moments

Scientists have established a new criterion to determine if a pair of quantum particles are entangled, or linked in a way that defies classical physics. This work focuses on bipartite quantum states, and the criterion relies on analyzing the second-order moments of quantum variables, which describe the spread of properties like position and momentum. By examining these moments and their correlations, researchers can identify entanglement even in complex systems. The criterion is particularly effective for Gaussian states, where higher-order moments are zero, simplifying the analysis and allowing for precise calculations. The team demonstrated that this criterion can be more sensitive to entanglement than existing methods, especially for Gaussian states, and connects to a well-known criterion, the Duan criterion, providing a consistent framework for understanding separability. Calculations for several Gaussian states, including vacuum states, squeezed vacuum states, and split squeezed vacuum states, confirm that the criterion accurately identifies both separable and entangled states, validating the method’s effectiveness.

Detecting Non-Gaussian Entanglement with Cumulants

Scientists have developed a new method to identify non-Gaussian entanglement, a specific type of quantum entanglement challenging to detect in systems where signals aren’t perfectly predictable. This work addresses a long-standing problem in quantum information science by providing a method to reliably detect entanglement even when standard techniques fail, extending existing theories to incorporate higher-order quantum properties. The core of this breakthrough lies in a new mathematical inequality that determines if two quantum particles are entangled, utilizing “cumulants” to measure the deviation from a simple Gaussian distribution and expose entanglement hidden from conventional methods. Importantly, this criterion can be directly measured using readily available experimental techniques, such as homodyne and heterodyne detection.

Experiments revealed that the inseparability criterion is robust even when signals are degraded by loss, a common challenge in quantum communication. Cumulants scale predictably under loss, allowing the criterion to remain effective even with reduced signal strength, and requires only a practical number of measurements, approximately 10 6 samples, routinely achievable in current continuous-variable optical experiments operating at MHz acquisition rates. To demonstrate the versatility of this approach, scientists applied the criterion to several quantum states, including a split photon number state and a lossy photon-subtracted squeezed vacuum state, accurately identifying entanglement in these non-Gaussian states, even with high fidelity approximations. For example, the team found that a split single photon remains entangled until the channel transmittivity drops below 0.57, extending the inseparability criterion to arbitrary superpositions of Fock states in two modes, opening new avenues for exploring complex quantum systems and advancing quantum technologies.

Higher Order Cumulants Reveal Hidden Entanglement

Scientists have developed a new method for identifying quantum entanglement in continuous-variable systems, specifically addressing a long-standing challenge in detecting it when correlations are not adequately described by standard Gaussian statistics. The team’s approach utilizes higher-order quadrature cumulants, effectively revealing entanglement hidden from traditional covariance-based criteria, demonstrating a significant improvement in sensitivity. The newly developed criterion is compatible with standard detection techniques, such as homodyne and heterodyne measurements, and provides a single, quantifiable measure of entanglement based on experimentally accessible parameters, making it scalable to more complex, multimode systems where existing methods become increasingly difficult to apply. Beyond its utility as a detection tool, this work offers a new perspective on the structure of quantum correlations in non-Gaussian states, potentially enabling further exploration of resources vital for applications like long-distance quantum communication and quantum error correction. The authors acknowledge that extending the framework to large-scale multimode cluster states represents a natural next step, and further research will investigate entanglement generated by non-Gaussian states and operations relevant to fault-tolerant photonic quantum computation, building upon this foundational achievement.