Elliptical orbits in the Bloch sphere

A. Mandilara, J. W. Clark, M. S. Byrd

Research output: Contribution to journalReview articlepeer-review

6 Citations (Scopus)


As is well known, when an SU(2) operation acts on a two-level system, its Bloch vector rotates without change of magnitude. Considering a system composed of two two-level systems, it is proven that for a class of nonlocal interactions of the two subsystems including (with ) and the Heisenberg interaction, the geometric description of the motion is particularly simple: each of the two Bloch vectors follows an elliptical orbit within the Bloch sphere. The utility of this result is demonstrated in two applications, the first of which bears on quantum control via quantum interfaces. By employing nonunitary control operations, we extend the idea of controllability to a set of points which are not necessarily connected by unitary transformations. The second application shows how the orbit of the coherence vector can be used to assess the entangling power of Heisenberg exchange interaction.

Original languageEnglish
Pages (from-to)S277-S282
JournalJournal of Optics B: Quantum and Semiclassical Optics
Issue number10
Publication statusPublished - Oct 1 2005


  • Bloch vector
  • Cartan decomposition
  • Correlation tensor
  • Entanglement
  • Heisenberg exchange Hamiltonian
  • Nonlocal interactions
  • Quantum control
  • Quantum interfaces
  • Two-level system

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Physics and Astronomy (miscellaneous)

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