Gaussian Field Invariants Reveal Quantum State Separability via Intensity Moments

Research demonstrates a direct link between universal invariants of multi-beam Gaussian fields and measurable intensity moments. This connection reformulates the Peres-Horodecki separability criterion, enabling experimental determination of quantum state separability via photon-number measurements on noisy symmetric three-beam states and characterisation of their properties.

The characterisation of multi-beam quantum states presents a significant challenge in quantum optics, particularly when assessing entanglement – a key resource for quantum technologies. Researchers are continually seeking methods to efficiently determine the properties of these states using practical measurements. A new approach, detailed in the article ‘Efficient Characterization of N-Beam Gaussian Fields Through Photon-Number Measurements: Quantum Universal Invariants’, establishes a direct link between fundamental quantum properties – termed ‘universal invariants’ – and readily measurable intensity fluctuations. This allows for the identification of Gaussian states and, crucially, provides a pathway to experimentally determine their separability – a measure of entanglement. The work is the result of a collaboration between Nazarii Sudak and Artur Barasiński from the Institute of Theoretical Physics, University of Wroclaw, and Jan Peřina Jr. and Antonín Černoch from the Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS.

Direct Measurement of Quantum State Invariants via Intensity Moments

A new method directly links universal invariants of multi-beam Gaussian fields to experimentally measurable quantities – their intensity moments. This offers a streamlined approach to characterising quantum states, bypassing the need for full state tomography – a process that requires exhaustive measurement of a quantum system.

Researchers demonstrated that the purity and correlations within these fields can be uniquely determined by analysing the statistical distribution of light intensities. This is achieved by relating fundamental, theoretical invariants to readily accessible experimental data. The work establishes a direct correspondence between these invariants and measurable intensity moments, providing a practical tool for quantifying quantum properties.

The team reformulated the Peres-Horodecki separability criterion – a key test for entanglement – in terms of these invariants, and consequently, in terms of experimental intensity moments. This allows for a direct assessment of whether a multi-beam state is entangled, a crucial property for many quantum technologies.

Experimental validation involved characterising noisy, symmetric three-beam Gaussian states using photon-number-resolved measurements. This allowed the researchers to determine the invariants of these states, demonstrating the feasibility of the technique for complex multi-beam systems.

The implications for quantum information processing and quantum imaging are considerable. The method provides a means to assess entanglement and characterise quantum states with reduced experimental overhead. This streamlined verification and optimisation of quantum states will facilitate the development of novel quantum technologies and deepen our understanding of multi-particle quantum systems.

Researchers employed statistical techniques, including those detailed in the work of Vardi & Lee, to extract the most probable values of the invariants from the measured intensity moments, accounting for experimental noise and uncertainties. The focus on Gaussian states – a common type of squeezed state where momentum and position uncertainties are linked – is significant. These states are particularly amenable to analytical treatment, simplifying the mathematical framework and facilitating the development of the proposed method.

This work builds upon existing knowledge of positive partial transposition (PPT) criteria – a method for identifying separable quantum states – refining and extending these concepts to multi-beam systems. It addresses a major challenge in quantum technology: maintaining fragile quantum properties in the presence of environmental disturbances.