What is meant here by "quantum mechanics–free subsystem"?

[nomadreid]

TL;DR

The reference is to the Abstract only (as I don't have full access) of the paper https://science.sciencemag.org/content/372/6542/625.

I only have the Abstract to https://science.sciencemag.org/content/372/6542/625, and an attempt to clarify it by referring to a popular science article https://scitechdaily.com/breaking-heisenberg-evading-the-uncertainty-principle-in-quantum-physics/ only made it worse.

The former indicates a set-up that at first sounds classical but is then (in the last two sentences) claimed to be quantum, so I do not understand the phrase "quantum mechanics-free" in the abstract.

The latter article (in the online magazine) is a bit off-putting in its (sensationalist, click-baiting) claim of "breaking", "getting around", or doing what is forbidden by, the Heisenberg Uncertainty Principle, which I know more as a mathematical result starting with two Hermitian operators, so this sounds a bit like "violating the Pythagorean Theorem in Euclidean Geometry". But perhaps I am overlooking some caveat that this article poses.

I would be grateful for clarification.

 

[f95toli]

The paper where the term is introduced is in an open-access journal (PRX)

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.2.031016

 

[nomadreid]

Super! Thanks, f95toli. I have downloaded the article and will now (hopefully) be able to make sense of it.

 

[atyy]

The paper mentioned in the OP is available free on the arXiv.

https://arxiv.org/abs/2009.12902
Quantum-mechanics free subsystem with mechanical oscillators
Laure Mercier de Lépinay, Caspar F. Ockeloen-Korppi, Matthew J. Woolley, Mika A. Sillanpää

 

[vanhees71]

Already the first sentence in the abstract is wrong. Is it worth using (wasting?) time reading it?

 

[atyy]

It seems to be a generalization of the EPR notion of simultaneous "measurement" of non-commuting observables (see Fig 2 of the Tsang and Caves paper linked in post #2).

If probe and particle are initially not entangled, then the position and momentum of the particle cannot be simultaneously (accurately) measured.

However, if the probe and system are initially entangled, EPR showed that in some sense, one can know both the position and momentum of the particle simultaneously. Of course this is fully quantum, but it is a quantum mechanical way of "getting around" the case in which the probe and particle are initially unentangled. So by terrible terminology, they decided to name it "quantum mechanics free". Probably about what we should expect from people who use words like "Quantum Bayesianism"

https://www.drchinese.com/David/EPR_Bell_Aspect.htm links to EPR, which says "two physical quantities, with noncommuting operators, can have simultaneous reality"

 

[vanhees71]

In the EPR example only compatible observables are measured (relative momentum and center-of-mass position).

You can also always measure all observables at any accuracy you are able to achieve. The Heisenberg uncertainty relation only says that you cannot prepare a quantum system such that two incompatible observables always take determined values.

Note that here the "always" is important, because there are exceptions. E.g., the three angular-momentum components wrt. a Cartesian basis are incompatible (i.e., the corresponding self-adjoint operators do not commute) but you can prepare a particle in a state of $J=0$, in which all three angular-momentum components $J_k$ take simultaneously the determined values 0.

 

[atyy]

So EPR is involved, but not as I guessed in post #6.

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.2.031016:
"Measurements of Q=q+q′ produce equal backaction onto p and p′, which cancels coherently in the dynamical variable, Π=p−p′, that is coupled to Q"

And the name quantum mechanics free is justified because
"Mathematically, Eq. (3) guarantees the classicality of a QMFS by virtue of the spectral theorem, which allows one to map the commuting Heisenberg-picture operators to processes in a classical probability space"

 

[f95toli]

Already the first sentence in the abstract is wrong. Is it worth using (wasting?) time reading it?

I believe it makes more sense if you read the whole introduction. I think(?) the argument they are making is that you can't actually use squeezing if you want to continuously measure X( or P) with arbitrary precision for an oscillator since the disturbance of P will dynamically ultimately lead to a disturbance in X.
That is, the two quadrature are linked in a way which sets fundamental limits on continuous position (or momentum) measurements.
That is, I believe the keyword here is continuous.

 

[atyy]

I believe it makes more sense if you read the whole introduction. I think(?) the argument they are making is that you can't actually use squeezing if you want to continuously measure X( or P) with arbitrary precision for an oscillator since the disturbance of P will dynamically ultimately lead to a disturbance in X.
That is, the two quadrature are linked in a way which sets fundamental limits on continuous position (or momentum) measurements.
That is, I believe the keyword here is continuous.

I think the first sentence in the abstract is wrong (probably too tersely summarized from the text), since their own introduction contradicts it. They say (in the arXiv version) "In a backaction evading (BAE) measurement strategy, a probe couples to only one quadrature of the oscillator’s motion, say X. The backaction associated with this measurement disturbs the P quadrature, but the disturbance is not fed back to the measured X quadrature.Therefore, the X quadrature can be measured without any fundamental limit, at the expense of lost information on the P quadrature [2–6]." There X and P are non-commuting.

I think the paper goes on to how one can talk about cases in which variables in quadrature are commuting, and so can be simultaneously continuously measured

 

[atyy]

http://nanoscale.blogspot.com/2021/05/catching-up.html
Brief mention of the OP paper by Doug Natelson in his blog