Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

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PT brachistochrone and state discrimination
Günther, U.;
In recent work by Bender, Brody, Caldeira and Meister it was shown that the brachistochrone solution of PT Quantum Mechanics (PTQM) can be used to orthogonalize a set of two originally non-orthogonal quantum states. The still remaining draw-back of the proposed technique is in its use of a non-Hermitian PT-symmetric Hamiltonian to achieve the PTQM brachistochrone evolution --- a Hamiltonian which up to now for quantum systems is beyond experimental reach.

We demonstrate that the Bender-Brody-Caldeira-Meister approach can be naturally extended into a higher-dimensional Hilbert space. This allows to interpret the PTQM setup as a very special subsystem of a larger Hermitian system. Moreover we show that this extension can be connected with the standard text-book scheme of unambiguous quantum state discrimination. Technical details of the extension procedure are discussed and ways toward a time-optimal unambiguous state discrimination scheme are indicated.
Keywords: PT quantum mechanics, unambiguous state discrimination, time-optimal state discrimination, PT brachistochrone, extension scheme
  • Invited lecture (Conferences)
    PTQM 2011 symposium, 25.-28.09.2011, Heidelberg, Deutschland

Publ.-Id: 16549 - Permalink