  In the case of systems composed of identical particles, a typical instance in
quantum statistical mechanics, the standard approach to separability and
entanglement ought to be reformulated and rephrased in terms of correlations
between operators from subalgebras localized in spatially disjoint regions.
While this algebraic approach is straightforward for bosons, in the case of
fermions it is subtler since one has to distinguish between micro-causality,
that is the anti-commutativity of the basic creation and annihilation
operators, and algebraic independence that is the commutativity of local
observables. We argue that a consistent algebraic formulation of separability
and entanglement should be compatible with micro-causality rather than with
algebraic independence.
