Symmetric inseparability and entanglement of charge coherence in number conserving mixed states

We explore sufficient conditions for inseparability in mixed states with a globally conserved charge, such as a particle number. We argue that even separable states may contain entanglement in fixed charge sectors, as long as the state can not be separated into charge conserving components. Asa witness of symmetric inseparability we study the number entanglement (NE), ∆Sm, defined as the entropy change due to a subsystem’s charge measurement. Whenever ∆Sm > 0, there exist inseparable charge sectors, having finite (logarithmic) negativity, even when the full state is either separable or has vanishing negativity. We demonstrate that the NE is not only a witness of symmetric inseparability, but also an entanglement monotone. Finally, we study the scaling of ∆Sm in thermal1D systems combining high temperature expansion and conformal field theory.