Reply on Comments on "Observation of a Fast Evolution in a Parity-time-symmetric System"(Aixiv.1106.1550)

TL;DR

This paper clarifies a previous discussion on the efficiency costs in PT-symmetric systems, emphasizing that the apparent contradiction was due to measurement probabilistic effects, and updates the original work accordingly.

Contribution

The authors resolve a comment on their previous work by clarifying the role of measurement probability in PT-symmetric evolution and update their results to reflect this.

Findings

No disagreement between the comment and original work.

Efficiency cost involves probabilistic measurement of auxiliary qubit.

Updated spectra illustrate the probabilistic nature of the evolution.

Abstract

Masillo [1] commented on our manuscript [2] "Observation of a Fast Evolution in a Parity-time-symmetric System", pointing out a contradiction of our work with Ref.[3]. In this reply, we pointed out there is no disagreement between Masillo's comment and our work in Ref. [2]. The efficiency cost pointed out in Ref.\cite{masillo} exists, namely to obtain the PT-symmetric hamiltonian evolution, one has to make a measurement on the auxiliary qubit and the auxiliary qubit is at state $|0\ket$ only probabilistically. This is reflected in the amplitude of the spectrum in the NMR quantum simulation. As a result, we made a small modification in a new version of the Ref. [2], and Fig. 2 of Ref.[2] has been replaced by spectra of two different $\alpha$'s in order to illustrate this fact.