  Entanglement is a resource central to quantum information (QI). In
particular, entanglement shared between two distant parties allows them to do
certain tasks that would otherwise be impossible. In this context, we study the
effect on the available entanglement of physical restrictions on the local
operations that can be performed by the two parties. We enforce these physical
restrictions by generalized superselection rules (SSRs), which we define to be
associated with a given group of physical transformations. Specifically the
generalized SSR is that the local operations must be covariant with respect to
that group. Then we operationally define the entanglement constrained by a SSR,
and show that it may be far below that expected on the basis of a naive (or
``fluffy bunny'') calculation. We consider two examples. The first is a
particle number SSR. Using this we show that for a two-mode BEC (with Alice
owning mode $A$ and Bob mode $B$), the useful entanglement shared by Alice and
Bob is identically zero. The second, a SSR associated with the symmetric group,
is applicable to ensemble QI processing such as in liquid-NMR. We prove that
even for an ensemble comprising many pairs of qubits, with each pair described
by a pure Bell state, the entanglement per pair constrained by this SSR goes to
zero for a large ensemble.
