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Related Experiment Videos

Mixed state geometric phases, entangled systems, and local unitary transformations.

Marie Ericsson1, Arun K Pati, Erik Sjöqvist

  • 1Department of Quantum Chemistry, Uppsala University, Box 518, SE-751 20 Sweden.

Physical Review Letters
|October 4, 2003
PubMed
Summary

Uhlmann's geometric phase for mixed quantum states depends on system geometry and entangled state evolution. This contrasts with simpler phases that only consider system path geometry.

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Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Geometric phase

Background:

  • The geometric phase of a pure quantum state captures the geometry of its evolution path in projective Hilbert space.
  • Understanding geometric phases for mixed quantum states is crucial for quantum information processing.

Purpose of the Study:

  • To investigate the geometric phase for mixed quantum states undergoing unitary evolution.
  • To differentiate between system-dependent and system-independent contributions to the geometric phase.
  • To propose an experimental verification of the findings.

Main Methods:

  • General analysis of Uhlmann's geometric phase for mixed states.
  • Illustration using the qubit case.
  • Theoretical framework for purified entangled states.

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Main Results:

  • Uhlmann's geometric phase for mixed states depends on both the system's path geometry and the bilocal unitary evolution of its purified entangled state.
  • A distinction is made between phases requiring bilocal evolution (Uhlmann's) and those requiring only unilocal transformations (system-dependent).

Conclusions:

  • The geometric phase of mixed quantum states is a richer concept than previously thought, incorporating entanglement.
  • Experimental verification is proposed to distinguish between different definitions of geometric phase for mixed states.