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Open Quantum Systems Decoherence Quantum Simulation

The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes

arXiv
Authors: Uwe Guenther, Boris F. Samsonov

Year

2007

Paper ID

49182

Status

Preprint

Abstract Read

~2 min

Abstract Words

84

Citations

N/A

Abstract

The PT-symmetric (PTS) quantum brachistochrone problem is reanalyzed as quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as subsystem of a larger Hermitian system, we find non-unitary operator equivalence classes (conjugacy classes) as natural ingredient which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian brachistochrones is demonstrated.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2007 reference point for readers tracking recent quantum research.
  • The PT-symmetric (PTS) quantum brachistochrone problem is reanalyzed as quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0709.0483 [2] arXiv https://arxiv.org/abs/0709.0483 [3] Publisher https://arxiv.org/abs/0709.0483

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