Dear William,

I would like to help, the question is in my domain of investigations, but this is an article, not a question. One has to read a long story for finding what in fact you ask.

What you ask?

Also, look at this:

"Is detector setting dependence (as opposed to apparatus parameter or measurement setting dependence) as used by Horward Wiseman (among others), a code word for a dependence between contexts, or on the kind of outcome dependence (or correlation dependence)  between two entangled systems,  on how you set the detector in the channel; either"

What is the difference between "detector setting" and "measurement setting"? And what is "code word"?  And what is "dependence between contexts"? Context of WHAT? In which "channel" you set the  detector, what is this "channel"?

Please do not invent new words, try to use the standard terminology. And I advise you, instead of a long ellaboration, it is better to expose simply the problem that you encountered.

I appologize for asking you: the term "context of a measurement" is clear to you? If you want, I can explain it. Maybe it would simplify all your question.

With kind regards,

Sofia

Dear Sofia,

I apologize for this convoluted 'disquisition. Essentially I am trying to get at the distinction; between

(1)different contexts, differentiated by distinct observables/particles (m,u,t),  being measured alongside the 'measured observable of interest, "y: '; where (m,u,t) may t be observables entangled with y, but which are measured along different componenents of spin in each context

(2)

different contexts, differentiated by distinct observables/particles (m,u,t),  being measured alongside the 'measured observable of interest, "y: '; where (m,u,t) are be not observables entangled with y, but which (that is m,u t,) are measured along different componenents of spin in each context.

Where in (1) and (2) the prepared state and component measured in y is the same,

but where in (2), even the entities entangled with y, are the prepared and measured the same way ( I presume this is independent state contextuality- where the tensor product state remains the same) there is  its some totally distint observable, not entangled with y that is measured along a distinct component

and (3)

where the distinct contexts, are almost indiscernible completely, in that no measurement setting (component of spin of any particle) is distinct, but where the detector of one of the particles (perhaps y) is placed in the spin up beam, versus the spin down beam.

That is, the angle, in which a spin up particle travels along or will be detected, if that is the particle). So by detector dependence I presume it is not meant that it is dependent on, 'which component is measured', (which is a dependence on the kind of measurement, pre-measurement)

That is, whether the detector is set to register 'yes' for 'spin up' versus yes, for 'spin down' , along the Same component of the very same particle; where this may be construed as depending on where you position the detector (the device that clicks if a particle if pass through a detector along the spin up path, thus registering that a spin up result obtains)

So I am not talking about the settings of the gerlach device, which determines the component measured of a particle, or some related particle,  but merely the registration devices for the outcome results, which are positioned between the the gerlach device and the screen which; and which register which outcome occurs in virtue of the particle passing through them.THat is in virtue,  of their placing (in some sense) along the direction in which a spin up (or spin down )particle would travel, if that is the outcome result

Dear William,

Your English is not so good and this is a problem. Let me make clear a couple of things, I believe that it may be of help.

Context of an experiment. Assume three observables, A, B, C, and the respective operators Ȃ, B̂, Ĉ. Assume that the operator Ȃ commutes with the operator B̂, and also with the operator Ĉ, however, B̂ doesn't commute with Ĉ.

If the observable A is measured together with the observable B (or C), then B (or C) is said to be the context in which is measured A. Assume an experiment in which these three observables are measured. The contextuality principle says that if A is measured together with B, the value obtained for A may differ from the value obtained (for A) if A were measured together with C.

The measurement process and configuration. If we want to measure some observable, e.g. spin of a particle, there are three main components in the configuration: the source in which the particles are produced, the Stern-Gerlach apparatus, and the macroscopic recorder/detector.

The source produces the particles according to some wave-function, ψ0. Inside the Stern-Gerlach apparatus the wave-function evolves according to the construction of the apparatus, i.e. the direction of the magnetic field, its strength, width, etc. In general, one obtains at the exit of the apparatus one or more beams, depending on ψ0. What exits the apparatus is therefore a wave-function ψ, which reflects how ψ0 evolved. Let's assume that ψ consists of three branches.

Now, ψ impinges on a macroscopic detector. In each trial and trial of the experiment, the detector will report a detection on only one of the three branches. This phenomenon is known as "collapse" of the wave-function. To the difference from the evolution of the wave-function inside the Stern-Gerlach apparatus, which we can controll by defining the parameters: direction of field, etc, in the detector we cannot controll which of the branches of ψ would produce a recording.

I hope that it helps!

I presume we control though where we place the detectors; whether to have a detector along the first branch, the second, the third, any two of them, or all three. I know there is some phenomena call polarization path contextuality as well as detector dependency, and piron also mentioned or at least allude to the notion that perhaps the ontic correlate of this ortho-question, 'is it spin up' versus is it 'spin down' may correspond to where one places the detector (or which question one asks or puts to nature). Of course I don't know how one could falsify or verify these kind of single case counterfactual statements; that had we place the detector in the other path, if we received yes originally (when the detector is in spin up channel), we still would have gotten yes' had the detector been in the spin down channel , corrresponding to the opposite result. Pykacz, Shimony, Giles mention some phenomena like this; Stachel and some others in the quantum logic kind of traditional have some articles about this kind of thing as well

here are some related notions; although I mention piron talking about compatible complements; such that each question has an opposite question (a compatible ortho-complement question, which corresponds to the orthocomplement of the original proposition), but such that both questions cannot be asked at once; although one can nonetheless place the detector in both channels at once