A seldom recognized fundamental difficulty undermines the concept of
individual ``state'' in the present formulations of quantum statistical
mechanics (and in its quantum information theory interpretation as well). The
difficulty is an unavoidable consequence of an almost forgotten corollary
proved by E. Schroedinger in 1936 and perused by J.L. Park, Am. J. Phys., Vol.
36, 211 (1968). To resolve it, we must either reject as unsound the concept of
state, or else undertake a serious reformulation of quantum theory and the role
of statistics. We restate the difficulty and discuss a possible resolution
proposed in 1976 by G.N. Hatsopoulos and E.P. Gyftopoulos, Found. Phys., Vol.
6, 15, 127, 439, 561 (1976).Comment: RevTeX4, 7 pages, corrected a paragraph and added an example at page
3, to appear in Mod. Phys. Lett.
