Bounds on the entanglability of thermal states in liquid-state nuclear magnetic resonance

Abstract

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.

REVTeX4, 15 pages, 4 figures (one large figure: 414 K)

References in corpus (3)

• Preparing high purity initial states for nuclear magnetic resonance quantum computing
• Implementing Grover's Quantum Search on a Para-Hydrogen based Pure State NMR Quantum Computer
• Implementation of NMR quantum computation with para-hydrogen derived high purity quantum states

Cited by in corpus (10)

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• Cones of ball-ball separable elements
• Experimentally identifying the entanglement class of pure tripartite states
• Single-experiment-detectable multipartite entanglement witness for ensemble quantum computing
• Sharing Polarization within Quantum Subspaces
• Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift