Talk:Incompatibility of quantum measurements

Excellent work!

Thank you for your excellent work! I enjoy it so much!

The article provides a concise and clear explanation of a fundamental concept in quantum mechanics. It outlines how certain measurements cannot be performed simultaneously with arbitrary precision due to the Heisenberg uncertainty principle. The article effectively introduces the mathematical framework and physical implications of incompatible measurements, making it accessible to readers with a basic understanding of quantum mechanics. Additionally, the references and links to related topics are helpful for those seeking a deeper understanding of the subject. Overall, the article is well-structured and informative. AzzurroLan (talk) 13:00, 12 July 2024 (UTC)[reply]

Good work!

A good work! This article provides a detailed overview of the concept, focusing on the inability to measure certain sets of quantum observables simultaneously with arbitrary precision. This incompatibility arises due to the intrinsic properties of quantum mechanics, specifically the non-commutativity of some operators. JohnWYu (talk) 13:21, 12 July 2024 (UTC)[reply]

Very good!

I really enjoyed your article. I've just correct a typo on one paragraph title: "...quantum information proessing" to "..information processing". One last thing: I saw that POVMs are in the 'see also' section, even if they are cited in the body of the article. Should a link to the POVM Wikipedia article be put directly the first time you introduce it in the body? Anyway, very good work, I deeply enjoyed it! 77Davide77 (talk) 13:26, 12 July 2024 (UTC)[reply]

Thank you so much for your review, and I am quite glad that you enjoy it. Concerning the POVM in the 'see also' section, I agree with you that it should be removed provided that there is a already link in the 'Definition' section. Many thanks for your kind remainder. Have a nice day! Daath3 (talk) 14:15, 12 July 2024 (UTC)[reply]

Great work

Very interesting topic, you have done a great work! Some little observations:

1) Maybe in the first line of Section "Numerical critria" there are too many "finite". Maybe it is possible to avoid the repetitions, but I didn't change anything since I was worried to modify the sense of the sentence.

2) In the subsection Incompatibility robustness the first line says Incompatibility weight of POVMs is defined by, exactly as it is written in the previous subsection Incompatibility weight.

3) Even if there is a proper reference, while reading I had the feeling you should have provided a brief definition/explanation of "quantum key distribution" and quantum "metrology". CarloSapo97 (talk) 13:55, 12 July 2024 (UTC)[reply]

Thanks a lot for your reasonable suggestions! I will improve the article according to them. Have a nice day! Daath3 (talk) 14:44, 12 July 2024 (UTC)[reply]

Observations and suggestions for improvements

The following observations and suggestions for improvements were collected, following an expert review of the article within the Science, Technology, Society and Wikipedia course at the Politecnico di Milano, in July 2024.

This article provides a complete and very accessible review on Quantum Incompatibility. The main aspects of the topic are clearly and succinctly presented. I have only some minor remarks and suggestions for further improvements:

(1) References are sometimes unnecessarily repeated and not always match with the discussed topics. This is particularly evident with the review papers 1 and 2, which are cited almost everywhere in the article. For example, ref. 1 is cited in connection with quantum cryptography, although it is completely unrelated with this topic. This is a general comment: when possible, it is better to refer to specific papers rather than citing extensive reviews.

(2) The History section needs some revision. Indeed, dividing the history of Quantum Incompatibility into 4 periods is perhaps a bit excessive. Moreover, it is somehow strange that no reference is provided to the early characterization of compatibility in terms of commutativity of self-adjoint operators (the classical approach formalized by von Neumann) and the subsequent elaboration of the notion of coexistence for POVMs (the approach developed by Ludwig, Kraus, Mittelstaedt, Lahti etc. which led to the "modern" definition of compatibility).

(3) Perhaps some words should be spent to explain the definition of compatibility in terms of classical post-processings and its equivalence with the definition in terms of marginals of a joint POVM. See e.g. ref. [1, sect. 6] below.

(4) There is some gap between the notations for continuous and discrete POVMs. The notation for binary measurements M_\pm should be made consistent with the notation for arbitrary measurements M:A\to B(H), where A is a \sigma-algebra.

(5) It should be stressed that the inequality |\alpha| + |\vec{m}| \leq 1 must be satisfied in order that the qubit measurement M_\pm constitutes a valid POVM.

(6) The standard name for a "compatiblizer" is "joint measurement" (or "joint POVM").

(7) To provide a comparison with the classical approach of von Neumann, it should be stressed that commutativity for POVMs implies compatibility.

(8) The standard name for "incompatibility noise robustness" is "incompatibility random robustness" [2, 3].

(9) There are some imprecisions in the following sentence related to incompatibility noise robustness: "This quantity is a monotone under quantum channels since (i) it vanishes on {M_{x|i}} that are compatible, (ii) it is symmetric under the exchange of POVMs, and (iii) it does not increase under the pre-processing by a quantum channel." First, monotonicity is only under pre-processing by a quantum channel. Probably here the author meant that the incompatibility noise robustness is an "incompatibility monotone" in the sense of ref. 8. However, since ref. 8 does not require monotonicity under classical post-processings, perhaps it is better to merely list the monotonicity properties of each incompatibility quantifier (under pre-processing by a quantum channel and/or under classical post-processings) rather than sticking to the definition of "incompatibility monotone" given in ref. 8. See e.g. [3, sect. 2.3].

(10) In the subsection on incompatibility weight, "pre-processing by a quantum instrument" should be replaced by "pre-processing by a quantum channel".

(11) The section on Quantifiers of incompatibility should cite also the review papers [2, 3] below.

REFERENCES:

[1] S.T. Ali, C. Carmeli, T. Heinosaari, A. Toigo, Commutative POVMs and Fuzzy Observables, Found. Phys. 39, 593-612 (2009)

[2] D. Cavalcanti, P. Skrzypczyk, Quantitative relations between measurement incompatibility, quantum steering, and nonlocality, Phys. Rev. A 93, 052112 (2016)

[3] S. Designolle, M. Farkas, J. Kaniewski, Incompatibility robustness of quantum measurements: a unified framework, New J. Phys. 21, 113053 (2019)

--Aandurro (talk) 15:24, 29 August 2024 (UTC)[reply]