  We show how to find families of infima and suprema for the entanglement
negativity using only a few, low-order moments of the partially transposed
density matrix $\rho^{T_2}.$ These moments can be measured using the multi-copy
quantum circuits previously given by the author, which define a set of
multi-copy expectation values and thus can be used with the replica trick. As
such, these bounds are suitable for use with Quantum Monte Carlo methods, and
the lower order versions of the estimates may be experimentally accessible for
some systems. Using more moments for higher-order versions of these methods
will produce tighter estimates, unless and until statistical noise causes the
measurement of the highest order moment to fail. Should this happen, the data
from lower order moments can still be used for lower-order estimates.
