Christian Schilling

Entanglement is a fascinating feature of the quantum world and serves as a key resource for quantum information processing. While its foundation is well-established in the context of distinguishable particles, the concept of entanglement for identical particles is still subject to misconceptions and controversial views. To settle this issue, we first clarify conclusively that identical particles do not define proper subsystems: the algebra of observables of single particles cannot be faithfully embedded into the one of the total system, resulting inevitably in a violation of the subsystem axioms. Accordingly, no notion of entanglement and more general types of correlation between identical particles exists that is genuine, i.e., valid independent of the underlying quantum state. Yet, there exist specific non-generic wave functions which allow one to label the identical particles through disjoint spatial regions or generally orbital subspaces. As a consequence of our work, the crucial idea of `electron correlation' can only be established ad hoc, without the common operational meaning, as the deviation of a given many-electron wave function from the manifold of mean-field states.