Symmetric inseparability and number entanglement in charge 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. As a witness of symmetric inseparability we study the number entanglement (NE), $ΔS_m$, defined as the entropy change due to a subsystem's charge measurement. Whenever $ΔS_m > 0$, 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 $ΔS_m$ in thermal 1D systems combining high temperature expansion and conformal field theory.

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