  PT-symmetric quantum theory does not require the Hermiticity property of
observables and hence allows a rich class of dynamics. Based on PT-symmetric
quantum theory, various counter-intuitive phenomena like faster evolution than
that allowed in standard quantum mechanics, single-shot discrimination of
nonorthogonal states has been reported invoking Gedanken experiments. By
exploiting open-system experimental set-up as well as by computing the
probability of distinguishing two states, we prove here that if a source
produces an entangled state shared between two parties, Alice and Bob, situated
in a far-apart location, the information about the operations performed by
Alice whose subsystem evolves according to PT-symmetric Hamiltonian can be
gathered by Bob, if the density matrix is in complex Hilbert space. Employing
quantum simulation of PT-symmetric evolution, feasible with currently available
technologies, we also propose a scheme of sharing quantum random bit-string
between two parties when one of them has access to a source generating
pseudo-random numbers. We find evidence that the task becomes more efficient
with the increase of dimension.
