Entanglement is a property which generally has been associated with quantum systems. However, recently various groups have been looking at the possibility of entanglement in classical systems. In particular there is a close connection between partial coherence and entanglement [1,2]. If entanglement in classical systems exists [3] then we need to understand what it means physically and how one can develop quantitative measures of such entanglement. We specifically consider optical beams with topological singularities and show that such classical beams share many features of two mode entanglement in quantum optics. We quantify the classical entanglement by deriving an inequality similar to the Bell inequality and present experimental results to demonstrate its violation for beams with topological singularities. Our results are also applicable to electron beams with vortices [5].

[1] G. S. Agarwal, J. Banerji, Opt. Lett. 27, 800 (2002).

[2] K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, B. E. A. Saleh, Nat. Photon. 7, 72 (2013).

[3] P. Chowdhury, A. S. Majumdar, G. S. Agarwal, Phys. Rev. A 88, 013830 (2013).

[4] B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, L. L. Sánchez-Soto, G. S. Agarwal, to be published.

[5] B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, J. Unguris, Science 331, 192 (2011).