system
Given the following post, respond as if you're commenting on Reddit:
human
Can the Standard Quantum Limit for the repeated measurement of a free mass be broken in theory?

Maybe I am cheating here, given that my not knowing the answer may come from my incomplete literature review. But I am getting confused by the claims of the contractive states breaking the limit, and yet a reinterpretation of definitions of precision and resolution seems to validate that *repetitive* measurements can *never be broken* due to the Heisenberg Uncertainty Relation between the Standard Deviations of the positions of the free mass at the first and the second measurements, which equals to the SQL. But the review paper I read itself said, after pointing the the HUP=SQL, that the SQL is not a fundamental limit. How?

Does the Uncertainty relation mean that the SQL can never be broken? Shouldn't it? Does it mean no one's working on breaking it? All the above paragraph was from papers from before 2000s, so what's the consensus now?
gpt
It's hard to answer without more context or without knowing the papers you're actually reading, but maybe it's *squeezing*?

The Heisenberg inequality is typically the product of the variances of two conjugated variables or quadratures, e.g. ΔX²ΔY²≥ħ²/4. Naively, one would assume that ΔX²≥ħ/2 and ΔY²≥ħ/2 in this case. 

However, it's possible that one of the variance is smaller than that *naive* limit, as long as the other is greater, e.g.  ΔX²=ħ/4 and ΔY²=ħ. In this case, we say that X is *squeezed* (because ΔX²<ħ/2); i.e. that it *appears* to beat the quantum limit. In reality, no real limit is violated because ΔX²ΔY²≥ħ²/4 holds.