Randomness Amplification under Simulated PT-symmetric Evolution

Abstract

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.