 The quantum state of a system may be either pure or mixed (see related entry  quantum mechanics).  In ordinary quantum mechanics a pure state is represented by a vector in the system’s Hilbert space. On one common understanding, any  entangled quantum systems  violate state separability in so far as a vector representing the state of the system they compose does not factorize into a product of vectors, one in the Hilbert space of each individual subsystem, that could be taken to represent their pure states. On the other hand, in such a case each subsystem may be uniquely assigned what is called a mixed state represented in its Hilbert space not by a vector but by a more general object—a so-called von Neumann density operator. But then state separability fails for a different reason: the subsystem mixed states do not uniquely determine the compound system’s state. A failure of state separability may not occasion much surprise if states are thought of merely in their role of specifying a system’s chances of exhibiting various possible properties on measurement. But it becomes more puzzling if one believes that a system’s quantum state also has a role in specifying some or all of its categorical properties. For that role may connect a failure of state separability to metaphysical holism and nonseparability.