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Bounds on the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance

Publication ,  Journal Article
Yu, TM; Brown, KR; Chuang, IL
Published in: Physical Review A - Atomic, Molecular, and Optical Physics
March 1, 2005

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 ∼ T, giving a lower bound requiring at least N∼22000 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. © 2005 The American Physical Society.

Duke Scholars

Published In

Physical Review A - Atomic, Molecular, and Optical Physics

DOI

EISSN

1094-1622

ISSN

1050-2947

Publication Date

March 1, 2005

Volume

71

Issue

3

Related Subject Headings

  • General Physics
  • 03 Chemical Sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Yu, T. M., Brown, K. R., & Chuang, I. L. (2005). Bounds on the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance. Physical Review A - Atomic, Molecular, and Optical Physics, 71(3). https://doi.org/10.1103/PhysRevA.71.032341
Yu, T. M., K. R. Brown, and I. L. Chuang. “Bounds on the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance.” Physical Review A - Atomic, Molecular, and Optical Physics 71, no. 3 (March 1, 2005). https://doi.org/10.1103/PhysRevA.71.032341.
Yu TM, Brown KR, Chuang IL. Bounds on the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance. Physical Review A - Atomic, Molecular, and Optical Physics. 2005 Mar 1;71(3).
Yu, T. M., et al. “Bounds on the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance.” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 71, no. 3, Mar. 2005. Scopus, doi:10.1103/PhysRevA.71.032341.
Yu TM, Brown KR, Chuang IL. Bounds on the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance. Physical Review A - Atomic, Molecular, and Optical Physics. 2005 Mar 1;71(3).

Published In

Physical Review A - Atomic, Molecular, and Optical Physics

DOI

EISSN

1094-1622

ISSN

1050-2947

Publication Date

March 1, 2005

Volume

71

Issue

3

Related Subject Headings

  • General Physics
  • 03 Chemical Sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences