  The role of mixed state entanglement in liquid-state nuclear magnetic
resonance (NMR) quantum computation is not yet well-understood. In particular,
despite the success of quantum information processing with NMR, recent work has
shown that quantum states used in most of those experiments were not entangled.
This is because these states, derived by unitary transforms from the thermal
equilibrium state, were too close to the maximally mixed state. We are thus
motivated to determine whether a given NMR state is entanglable - that is, does
there exist a unitary transform that entangles the state? The boundary between
entanglable and nonentanglable thermal states is a function of the spin system
size $N$ and its temperature $T$. We provide new bounds on the location of this
boundary using analytical and numerical methods; our tightest bound scales as
$N \sim T$, giving a lower bound requiring at least $N \sim 22,000$ proton
spins to realize an entanglable thermal state at typical laboratory NMR
magnetic fields. These bounds are tighter than known bounds on the
entanglability of effective pure states.
