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 bounds on the location of this boundary using analytical and numerical methods; our tightest bound scales as $N\ensuremath{\sim}T$, giving a lower bound requiring at least $N\ensuremath{\sim}22\phantom{\rule{0.2em}{0ex}}000$ 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.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 bounds on the location of this boundary using analytical and numerical methods; our tightest bound scales as $N\ensuremath{\sim}T$, giving a lower bound requiring at least $N\ensuremath{\sim}22\phantom{\rule{0.2em}{0ex}}000$ 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.

arXiv:quant-ph/0409170Physical Review AMar 24, 200511 citations

N

and its temperature

T

. We provide bounds on the location of this boundary using analytical and numerical methods; our tightest bound scales as $N\ensuremath{\sim}T$, giving a lower bound requiring at least $N\ensuremath{\sim}22\phantom{\rule{0.2em}{0ex}}000$ 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.