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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

Permalink: https://www.hzdr.de/publications/Publ-16549
Publ.-Id: 16549