Geometry along Evolution of Mixed Quantum States

Abstract

The metric underlying the mixed state geometric phase in unitary and nonunitary evolution [Phys. Rev. Lett. {\bf 85}, 2845 (2000); Phys. Rev. Lett. {\bf 93}, 080405 (2004)] is delineated. An explicit form for the line element is derived and shown to be related to an averaged energy dispersion in the case of unitary evolution. The line element is measurable in interferometry involving nearby internal states. Explicit geodesics are found in the single qubit case. It is shown how the Bures line element can be obtained by extending our approach to arbitrary decompositions of density operators. The proposed metric is applied to a generic magnetic system in a thermal state.

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References in corpus (5)

• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• An experimental observation of geometric phases for mixed states using NMR interferometry
• Measurement of geometric phase for mixed states using single photon interferometry
• Observation of nonadditive mixed state phases with polarized neutrons

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• Complexity of Pure and Mixed Qubit Geodesic Paths on Curved Manifolds
• Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
• Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states
• Geometric Phase in Quantum Synchronization
• Quantum Geometric Tensor for Mixed States Based on the Covariant Derivative