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Topological phase for entangled two-qubit states.

Pérola Milman1, Rémy Mosseri

  • 1Laboratoire Kastler Brossel, Département de Physique de l'Ecole Normale Supérieure, 24 rue Lhomond, F-75231 Paris Cedex 05, France. Perola.Milman@lkb.ens.fr

Physical Review Letters
|July 15, 2003
PubMed
Summary

Entangled quantum states reveal the topology of the SO(3) rotation group. Cyclic evolutions of these states demonstrate a pi phase shift, confirming group path families.

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Area of Science:

  • Quantum physics
  • Quantum information processing
  • Topology

Background:

  • Entangled states are fundamental in quantum physics and quantum information.
  • The SO(3) rotation group has a complex topology with two distinct path families.

Purpose of the Study:

  • To use entangled two-qubit states to characterize the topology of the SO(3) rotation group.
  • To demonstrate the connection between cyclic evolutions of entangled states and the group's topological properties.

Main Methods:

  • Utilizing entangled two-qubit states.
  • Analyzing cyclic evolutions of these entangled states.
  • Proposing a quantum optics interference experiment.

Main Results:

  • Establishing a one-to-one correspondence between SO(3) path families and cyclic evolutions.
  • Observing a pi phase difference in these evolutions.
  • Demonstrating a topological phase shift.

Conclusions:

  • Entangled states provide a robust method for characterizing SO(3) group topology.
  • The observed pi phase shift is a direct consequence of the group's topological structure.
  • Quantum optics experiments can effectively verify these topological phenomena.

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