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A major contributions of Wigner’s work was the introduction of group theory to study both the dynamics and the classification of states in quantum mechanics. The use of rotational symmetry to study the properties of angular momentum eigenstates is particularly associated with him. Following along a similar path, it is shown here that advances in the study of entangled and correlated two-photon states allow the rapid detection of rotational symmetries in complex macroscopic objects, and that knowledge of this symmetry structure can allow identification, and in some circumstances reconstruction, of the object.The potential for efficient identification of objects carrying elements of high-order symmetry using correlated orbital angular momentum (OAM) states is demonstrated. The enhanced information capacity of this approach allows the recognition of specific spatial symmetry signatures present in objects with the use of fewer resources than in a conventional pixel-by-pixel imaging, representing the first demonstration of compressive sensing using OAM states. This approach demonstrates the capability to quickly evaluate multiple Fourier coefficients directly linked with the symmetry features of the object. The results suggest further application in small-scale biological contexts where symmetry and small numbers of noninvasive measurements are important

Efficient Identification of Objects Carrying Elements of High-Order Symmetry By Using Correlated Orbital Angular Momentum (OAM) States