A sufficient condition for nonclassical two-mode states in terms of three probabilities, (n2+1)p(n1−1, n2+1)2n1p(n1, n2)+(n1+1)p(n1+1, n2−1)2n2p(n1, n2)<1, is established as a new type II criterion. This criterion is applied to the two-mode coherent state, the two-mode squeezed vacuum state, and the pair coherent state to show how easily it can be used. It is also applied to the photon-added two-mode thermal state and the mixing of two two-photon states by a symmetric beam splitter to show that the type II criterion is superior to its type I counterpart in at least these two examples.
© 1998 Optical Society of America
Ching Tsung Lee, "Simple criterion for nonclassical two-mode states," J. Opt. Soc. Am. B 15, 1187-1191 (1998)