Just another straightforward textbook-based critique of the
thought-provoking ref. [37] (``Faster than Hermitian Quantum
Mechanics", arXiv:quant-ph/0609032), the message of which has
already been shown misleading in ref. [46] (arXiv:0706.3844) or,
slightly later, by Geyer, Heiss and Scholtz in Can. J. Phys. 86
(2008) 1195-1201, arXiv:0710.5593. And just another confirmation
that within the framework of the textbook quantum mechanics of
stable systems it is clearly impossible to achieve faster than
unitary evolution using PT-symmetric or other non-Hermitian
Hamiltonians.

Still, all this does not mean that the case of the ``Faster than
Hermitian Quantum Mechanics" is lost. On a purely experimental
level, a PT-symmetric setup has very recently been proposed within
the realm of optics. Makris et al, Phys. Rev. Lett. 100, 103904
(2008), Musslimani et al, Phys. Rev. Lett. 100, 030402 (2008),
El-Ganainy et al, Opt. Lett. 32, 20637 (2007) combined an even
optical index with an odd gain/loss profile and revealed the
existence of phenomena like double refraction, non-reciprocity,
power oscillations and band merging. In a topical dedicated
international conference in India (in January 2009, cf.
http://gemma.ujf.cas.cz/%7Eznojil/conf/index8(y09).html),
the first observation of the typically nonhermitian
exceptional-point related passive phase transition has also been
announced by the same authors. In parallel, Frydryszak et al.
(Phys. Rev. A 77, 014103 (2008)) considered a spin-1 system in a
magnetic field in similar context.

Apparently, an ultimate reconciliation of the theory with
experiment has been achieved by Guenther and Samsonov who
clarified that many manifestly nonhermitian PT-symmetric
Hamiltonians can be interpreted as representing a subsystem of a
standard quantum system. This has been published in Phys. Rev.
Lett. 101, 230404 (2008), arXiv:0807.3643 (and, partially, also in
Phys. Rev. A 78, 042115 (2008), arXiv:0709.0483) and reported in
another international conference in Spain (in July 2008, cf.
http://gemma.ujf.cas.cz/%7Eznojil/conf/index07(y08).html).
This opened a way towards another direct experimental
implementation of the theory describing an ultra-fast
brachistochrone regime of an entangled two-spin system. Still,
even the latter synthesis evoked certain critical comments (cf.
arXiv:0709.1756) arguing, e.g., that the the underlying quantum
theory suffers from a dynamical inconsistency and that the whole
argument is by no means sufficient for abandoning the standard
theory of measurement and/or for its various ad hoc
generalizations.



MR2442889 Giri, Pulak Ranjan,  Lower bound of minimal time
evolution in quantum mechanics. Internat. J. Theoret. Phys. 47
(2008), no. 7, 2095--2100. 81Qxx