### Abstract

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as nonpositive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. It is this feature that enables the quantum system to evolve to an entangled state. We conclude that the dynamics are a quantum element of nuclear magnetic resonance quantum-information processing. There are two limits where our quantum evolution coincides with the classical one: the short-time limit before spin-spin interaction sets in and the long-time limit when phase diffusion is incorporated.

Original language | English |
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Pages (from-to) | 032316-1-032316-10 |

Number of pages | 10 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 65 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2002 |

### Bibliographical note

Copyright 2003 by The American Physical Society. Reprinted from Physical review A.## Fingerprint Dive into the research topics of 'Quantum dynamics of two coupled qubits'. Together they form a unique fingerprint.

## Cite this

Milburn, G. J., Laflamme, R., Sanders, B. C., & Knill, E. (2002). Quantum dynamics of two coupled qubits.

*Physical Review A - Atomic, Molecular, and Optical Physics*,*65*(3), 032316-1-032316-10. https://doi.org/10.1103/PhysRevA.65.032316