Quantum Tomography of Two-Qutrit Werner States

Round 1

Reviewer 1 Report

In the manuscript by Wang and He, the authors present a scheme for tomography of "three-dimensional Werner states" with Gaussian noise, which uses SIC-POVM. The motivation of this manuscript is clear. Moreover, the authors have demonstrated the validity of their method based with numerical simulation of experimental cases. The result is clear. So I recommend the publication in Photonics.

 

Minor:

- The terms "two-qubit Werner state" seem to be misleading since qubit always means a system with dimension 2. When both system have dimension 2, it is common to call it "two-qutrit Werner state".

Moreover, it is strange to say "two-qubit Werner states in three-dimensional Hilbert space".

- Due to the same reason, I recommend to change "three-dimensional Werner states" into "qutrit-qutrit Werner states" or something else they prefer. 

-In Eq. (2), domains for the two parameters should be clarified, and I_4 should be explained.

-Sec.3, "Experimental results and analysis"->"Numerical results and analysis".

Author Response

Dear reviewers,
Thank you for your comments. My reply to you is in the following pdf attachment. Please check it.

Author Response File: Author Response.pdf

Reviewer 2 Report

Quantum state tomography is one of the important topics in quantum mechanics and quantum information technology. In this paper, the authors propose a scheme of Werner state tomography under noisy environment, in which symmetric informationally complete (SIC) POVM and modified Chi-Squared estimator are applied. By simulation the performance are evaluated in fidelity, purity, concurrence and l1-norm of coherence.

 However, there are several comments the authors shall clarify.

 (1) In section 2.2, “The measurement scheme implemented in our work is based on the SIC-POVM in three-dimensional Hilbert space.” Why are the measurement operators two dimensional (the sum of operators is 2-dimension unit matrix, Line 79, Page 4 of 12)?

 (2) Please give the reason why the number of quantum states with measurement result of k is normal distributed (i.e. in Eq. (13))?

 (3) How to improve the efficiency of the estimator, i.e. Eq. (17), might be the key issue in the proposed scheme. The authors have not discussed.

 (4) In addition, how the noise is added to the quantum tomography process?

  (5) How’s the performance compared with other algorithms?

Author Response

Dear reviewer,
Thank you for your comments. My reply to you is in the following pdf attachment. Please check it.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have given appropriate responses to the comments.

 I am very happy to recommend its publication as this revised version.