**Non-classical states in extended phase space**

**Abstract:**

A family of coherent states, localized in ordinary phase space that minimize the uncertainty principle is often considered
as classical states. One may ask a question that to what extent a quantum state is non-classical [1, 2] in a sense that its
properties differs from that of coherent states? To answer this question we define a parameter for a given quantum
distribution function in extended phase space that legitimately reflects its degree of non-classicality. As an example, the
non-classicality which may be interpreted as a signature of quantum interference, is demonstrated for the Schrodinger cat
state using the corresponding quantum distribution function in different extended phase space representations [3, 4].

[2]. A. Kenfack and K. ZycZkowski, arXiv: quant-ph/0406015 v1, 2004

[3]. Y. Sobouti and S. Nasiri, Int. J. Mod. Phys. B, 7 (1993) 3255-3272

[4]. S. Nasiri, Y. Sobouti and F. Taati, “Phase space quantum mechanics-direct” J. Math. Phys. 47, 092106, 2006.

Joint work with *Sadollah Nasiri* (Zanjan University and Institute for Advanced Studies in Basic Sciences, Zanjan, Iran),
*Siamak Khademi* and *Samira Bahrami* (Zanjan University, Iran)