  It has been known for some years that entanglement entropy obtained from
partial trace does not provide the correct entanglement measure when applied to
systems of identical particles. Several criteria have been proposed that have
the drawback of being different according to whether one is dealing with
fermions, bosons or distinguishable particles. In this Letter, we give a
precise and mathematically natural answer to this problem. Our approach is
based on the use of the more general idea of restriction of states to
subalgebras. It leads to a novel approach to entanglement, suitable to be used
in general quantum systems and specially in systems of identical particles.
This settles some recent controversy regarding entanglement for identical
particles. The prospects for applications of our criteria are wide-ranging,
from spin chains in condensed matter to entropy of black holes.
