### Abstract

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 language | English |
---|---|

Journal | Journal of Optics B: Quantum and Semiclassical Optics |

Volume | 7 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 1 2005 |

Externally published | Yes |

### Fingerprint

### Keywords

- 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)

### Cite this

*Journal of Optics B: Quantum and Semiclassical Optics*,

*7*(10). https://doi.org/10.1088/1464-4266/7/10/011

**Elliptical orbits in the Bloch sphere.** / Mandilara, A.; Clark, J. W.; Byrd, M. S.

Research output: Contribution to journal › Article

*Journal of Optics B: Quantum and Semiclassical Optics*, vol. 7, no. 10. https://doi.org/10.1088/1464-4266/7/10/011

}

TY - JOUR

T1 - Elliptical orbits in the Bloch sphere

AU - Mandilara, A.

AU - Clark, J. W.

AU - Byrd, M. S.

PY - 2005/10/1

Y1 - 2005/10/1

N2 - 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.

AB - 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.

KW - Bloch vector

KW - Cartan decomposition

KW - Correlation tensor

KW - Entanglement

KW - Heisenberg exchange Hamiltonian

KW - Nonlocal interactions

KW - Quantum control

KW - Quantum interfaces

KW - Two-level system

UR - http://www.scopus.com/inward/record.url?scp=25644451164&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25644451164&partnerID=8YFLogxK

U2 - 10.1088/1464-4266/7/10/011

DO - 10.1088/1464-4266/7/10/011

M3 - Article

VL - 7

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

SN - 0953-4075

IS - 10

ER -