The state of a quantum system, consisting of two distinct subsystems,
is called separable if it can be prepared by two distant experimenters
who receive instructions from a common source, via classical communic
ation channels. A necessary condition is derived and is shown to be mo
re sensitive than Bell's inequality for detecting quantum inseparabili
ty. Moreover, collective tests of Bell's inequality (namely, tests tha
t involve several composite systems simultaneously) may sometimes lead
to a violation of Bell's inequality, even if the latter is satisfied
when each composite system is tested separately.