Talk:Weak value

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The weak value of the observable becomes large when the post-selected state, ${\displaystyle |\phi _{2}\rangle }$, approaches being orthogonal to the pre-selected state, ${\displaystyle |\phi _{1}\rangle }$.

Although this sentence may make sense to those familiar with quantum measurement theory, it makes very little sense to someone without this background:

"After the measurement the measuring device is shifted by what is called the "weak value"."

How is the measurement device "shifted?" For instance, in the spin-1/2 experiment proposed by AAV, what is shifted by ${\displaystyle A_{w}}$? This should be explained, I think.

I added an example after this sentence to clarify. hope it's better this way. —Preceding unsigned comment added by Cap.fwiffo (talk • contribs) 08:42, 6 April 2009 (UTC)Reply

Lacking a better article to point the undefined internal link [two state vector formalism] with more precision, I defined it to point to [Quantum state|two state vector formalism] (ie: two state vector formalism).
Could someone understanding QM fix this, if necessary, by providing a better link or an article (perhaps a subsection) to point the original link [two state vector formalism]? . Thanks. Pmronchi (talk) 18:57, 27 April 2009 (UTC)Reply

The two state vector formalism creates a few paradoxes which can be solved by weak measurements. One such paradox is the famous Hardy's pradox, another is the three box paradox. Rather then having those as part of the main body, these should have a section devoted to paradoxes. Also the recent experimental results "solving" Hardy's paradox with photons are great examples of weak measurements but are a bit contervrersial, and in my opinion belong in the realm of scientific discussion rather then on wikipedia. Any comments on this?

On october 20 (2015) I gave the article a major overhaul. I think we should see which talk pieces are still relevant and remove the rest. Yama jlac (talk) 17:06, 30 October 2015 (UTC)Reply

On 20 October 2015 I gave the article a major overhaul. I didn’t fully complete it—I stopped at the applications section. In this new overhaul, I will focus on three main tasks:

- Improving the explanations in my earlier text

- Removing text snippets and citations that promote niche research papers rather than educate broadly

- Overhauling the second half of the article

Since the latter part includes the applications and criticisms of weak values, I’ll aim to write those sections as succinctly and neutrally as possible. This will hopefully somewhat address Stephen Parrott's comments below. Yama jlac (talk) 03:08, 25 October 2025 (UTC)Reply

Ok I have finished the draft.

The proposed draft is here: https://en.wikipedia.org/wiki/Draft:Weak_Value_v2

Comments and suggestions are most welcome! Yama jlac (talk) 01:05, 9 November 2025 (UTC)Reply

The article is out of place in two ways: 1) Use of "we" is avoided in Wikipedia. It's not needed. 2) History is mixed up with facts. Johnjbarton (talk) 04:15, 25 November 2025 (UTC)Reply

I will make edits on the proposed draft to fix those issues. Yama jlac (talk) 22:44, 27 November 2025 (UTC)Reply

After a review from Johnjbarton I have a new draft of the page. I will replace one section at a time with the edited draft from https://en.wikipedia.org/wiki/Draft:Weak_Value_v2 . Yama jlac (talk) 04:22, 9 December 2025 (UTC)Reply

Thanks, but I guess I should have been more explicit. By one section at a time I intended that you would give us a chance to respond to the additions.

To be clear, my review was that the draft version is not reviewable since we had an existing article. I also mentioned that the Criticism section was not appropriate. Johnjbarton (talk) 16:51, 9 December 2025 (UTC)Reply

The current Criticism section is inappropriate. It is a editor's summary of primary sources on a controversial subject. The section should be a summary of secondary sources that review the primary arguments. Alternatively we could consider this a History section since it include names and dates. Then we need a secondary source to establish the notability of these primary sources. Johnjbarton (talk) 16:57, 9 December 2025 (UTC)Reply

In many academic areas, review articles only appear when a field is large enough. In this case, the critics simply didn’t care enough to write a review. In light of that, I’ll remove all sections that don’t have a review article (the only section that has a review is the metrology section), except for the original criticism of the AAV paper.

I'll change it back to something more closely resembling the old Criticism section. Yama jlac (talk) 22:18, 9 December 2025 (UTC)Reply

Reviews to exist: we cite at least 4 reviews in the article. Only one (Kohman/Ashhab/Nori) mentions criticisms (Leggett and Peres). Critics chose not to write a review. We shouldn't write one either. Johnjbarton (talk) 00:46, 10 December 2025 (UTC)Reply

The current definition section is unclear and lacks basic structure. It introduces notation before defining it, and includes unnecessary generalizations (e.g. “nth-order weak value”) and non-standard terms such as “unitary perturbation operator” and “unperturbed probability of detection.” These terms are not broadly used in the established weak-value literature and are not defined in the article, which makes the section confusing and difficult to follow for readers.

For these reasons, the section should be reverted to the improved version I provided. Yama jlac (talk) 22:27, 9 December 2025 (UTC)Reply

This content is from the Reviews of Modern Physics article of 2014, the section "What is a Weak Value?"

• Which notation is not defined?
• The n-th order is used in the source to explain where "weak" comes from.
• I agree that we don't need "unitary" and I changed the text.
• I used "unperturbed probability of detection" as my summary of the probability of detecting an event corresponding to the final state ${\displaystyle |f>}$ is given by the squared modulus of their overlap ${\displaystyle |<f|i>|^{2}}$. I agree that my phrase is too short. I'm open to other suggestions.

I disagreed with the previous version. The previous version did not give any sense of "why" this definition. We need to explain the circumstances of the definition. We should not introduce superfluous information like max and min eigenvalues. We should not have a paragraph about expectation values before we have completed a discussion of weak value unless it is central to the definition.

We should not have 4 sources if they agree, that just makes verification more difficult.

• Kohman/Ashhab/Nori have similar definition in section 2.4 (but harder to understand).
• Tamir and Cohen have similar definition in 3.1
• Svensson uses a similar definition in 5.1

So in my opinion, all of the cited sources in the previous version agree with the Dressel source and that is the definition summarized in the current version.

I'm sure that the current content can be improved and I welcome your suggestions. Johnjbarton (talk) 00:23, 10 December 2025 (UTC)Reply

Do as you wish. As it stands, the section obscures the key points and introduces extraneous ideas that don’t help readers. I have no interest in a long argument or an edit war. The new version also introduces notation before defining it and adds unnecessary generalizations. Let me flag just one of several major issues: the weak value is noteworthy precisely because it can lie outside the eigenvalue range of the operator (A). That central point is no longer explained.

You have more influence on Wikipedia, so I won’t push this further. I’ll simply note that this is, in my view, a quality-reducing edit. The current version is not a good starting point to make further edits. If you don’t want the improvements I suggested, then that section should be reverted to its previous form. I’ll leave it there.

Thank you again for your help with the other updates, I appreciate it! However, after this recent exchange, I have no plans to contribute to Wikipedia again, and I won’t be responding again. Yama jlac (talk) — Preceding unsigned comment added by Yama jlac (talk • contribs)

(I'm unsure why but the previous post has no "Reply" button.)

The previous post made the claim that:

• "the weak value is noteworthy precisely because it can lie outside the eigenvalue range of the operator (A)."

The previous version of page made this unsourced claim:

• If ${\displaystyle A_{w}}$ is larger than the largest eigenvalue of ${\displaystyle A}$, ${\displaystyle a_{\rm {max}}}$, or smaller than its smallest eigenvalue, ${\displaystyle a_{\rm {min}}}$, the weak value is said to be anomalous. Such anomalous weak values are interesting because they can be complex and fall outside the usual eigenvalue range, both features absent in standard expectation values.

This claim is cryptic. What does "interesting" mean? Since we are talking about observables, the expectation values are real: it is not even clear what fall outside the range means. Since this claim had no sources I could not fix it. But if you have sources then it could be fixed. Johnjbarton (talk) 23:42, 10 December 2025 (UTC)Reply

Ok the Dressel discusses "conditioned average associated with an observable" as an interpretation of the real part of the weak value. Conditioned averages outside the normal eigenvalue range have been linked to paradoxes... So I think the above claim relates to the real part of the weak value and the phrase "because they can be complex" should be read as "linked to paradoxes". (Dressel never uses "expectation value")

The Abbot paper introduction also discusses the relationship between the real part of the weak value and eigenvalues. It points out that the real part can be large when the post/pre states are almost orthogonal. Unfortunately this source is about a variant of the weak value and their notation is not always clear.

I think we should have a section on the "Real part" with these things covered. Johnjbarton (talk) 01:50, 11 December 2025 (UTC)Reply