On the Optimization and Self-Tensoring Construction of Nonlinear Entanglement Witnesses

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please find attached

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this work, the authors studied the framework of nonlinear entanglement witnesses. In particular, the authors concerned how to obtain nonlinear entanglement witnessed for more efficient detection of entangled states, as stated in Problem 3.1 on page 3.  

Summary of their results: 

The authors provided a counterintuitive result with Example 3.1 with a nonlinear entanglement witness. Then the authors addressed how the optimization can be achieved in constructing nonlinear entanglement witnesses for more efficient entanglement detection in Theorem 3.1. The authors finally arrived at a conjecture that identical linear entanglement witnesses cannot be used to detect entanglement if they are applied nonlinearly. 

While the presented results are interesting, they lack clear explanations or implications for achieving more efficient entanglement detection. Therefore I would suggest the authors to address this comment before I wish to recommend it for publication in the journal. Is it possible to provide geometric explanations of their results, which will strengthen their results to get useful insights for optimal entanglement witnesses?

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The current version contains amendaments to my overall recommendtions and criticisms, which properly reported in the authors response letter.

Reviewer 2 Report

Comments and Suggestions for Authors

In the revised version, the authors response to my concerns are satisfactory. Thus, I am happy to recommend it for publication in the journal.