Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups

Round 1

Reviewer 1 Report

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Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This is an important paper that presents a novel approach to weak continuous quantum measurements as a stochastic process in the operator algebra of quantum instruments. This is novel as previous approaches formulate the theory in terms of the states of the measured system.  The focus on simultaneous measurement of non commuting observables means this formulation is especially relevant to the quantum case. The authors could have made this case even more convincing by considering an equivalent formulation of the classical case in terms of stochastic differential processes on phase-space. However perhaps that is a good exercise for potential readers.  

In the conclusion the authors mention that a similar approach could be done for fermionic systems. Certainly there are master equations to describe open fermionic systems such as occur in mesoscopic electronics.  Treating these as continuous weak measurements has been done but it is rare. Mostly the description  uses full counting statistics for jump processes. The problem is that the measurement apparatus is very different from the quantum optics case. For example, based on an RF single electron transistor for charge detection in a quantum dot. The measurement signal itself is a current emended in an external circuit. I have no doubt that the approach of this paper could be done but I expect it will need to use Grassmann numbers. Not easy.

It is not an easy read however,  so will take some time to have an impact but I have no doubt that it will have a very considerable  impact. The level of mathematical sophistication will ensure that.  

 I recommend that the paper be accepted in its current form without any changes. 

Author Response

Author's response to report of second referee (Manuscript ID: entropy-2469255)
Christopher S. Jackson and Carlton M. Caves
August 8, 2023

No response is really required, except perhaps to thank this reviewer for a very favorable report.  

And we do know that the extension to fermions might involve highly nontrivial developments.  Nonetheless, we are relatively confident.