8:27 AM
@JarekDuda Congratulations for asking an interesting question on physics.se, and for finding an informed person able and willing to discuss details of quantum computing. Craig Gidney engages with his real name, has understood your question, tried to give an honest answer from his own perspective, and he provided evidence that he has thought about that kind of questions before. Even if you should turn out to be right in this specific disagreement, he will still be a valuable discussion partner...

9:17 AM
From your discussion, it is clear that Craig Gidney thinks in terms of density matrices, at least why it comes to thinking about subsystems. For for him, what the measurement of (y,z) and then throwing away z does is to partition the system into the subsystems for y and z, and then measure y. This partitioning operation for him is different (namely weaker) than measuring z.
However, in his other writings, it also becomes clear that he is uncertain about whether he can assume that his readers understand density matrices. So he ends up trying to explain some fact which is clear to him (because he thinks about density matrices) to somebody else in a language which feels rigid or dogmatic. That rigidity or dogmatism is designed to give correct answers compatible with the density matrix formalism, but it is more limited and ...
That ... is hard to explain: The density matrix formalism talks "clearly" about what happens for a "statistical ensemble of experiments" and doesn't care too much about what happens in a single experiment. The normal QM language into which it gets translated seems to talk about single experiments (or single events in a single experiment), even if it is rarely clarified whether it is really applicable in that sense. The current tendency is to assume that it really is applicable in that sense.
There are experiments trying to demonstrate this, but I have seen people like Dieter Zeh point out ... why those experiments don't really demonstrate what they try to demonstrate. But that is not important here. The point is just that density matrices allow to see certain facts (especially when it comes to subsystems) quite clearly, but that those facts often get translated back (and then become harder to understand) because one never knows whether the reader understands density matrices.

10:02 AM
Thinking in terms of density matrices is actually easy. While no measurement or partitioning into subsystems occurs, one just takes an eigenvalue decomposition of the density matrix, and track those eigenvectors like one would track a normal wavefunction state. And one just doesn't worry about the fact that those wavefunctions are not "real", but just the optimal coherent description of the available statistical information.
And when a measurement of partitioning into subsystems occurs, one computes the reduced density matrices, which one can then track again in later computations by doing the eigenvalue decomposition again. And one has the additional advantage that on can take any other decomposition into coherent systems as well, even so they won't be as optimal (i.e. they will need more terms for the same accuracy) as the eigenvalue decomposition.
So the real contribution of the density matrix formalism is just to free oneself from the "reality of the wavefunction" in favour of "any wavefunction which provides reasonable economy of description".

3 hours later…
12:58 PM
Not measuring z: just performing some unitary operations, the ensemble is $\sum_y |y, f(y)>$, there is just the original ensemble of all 2^n possibilities for y - performing QFT on such ensemble, the period is 1, what gives no information about the factor.
To get nontrivial ensemble on input, which period leads to a factor, we need to fix z - what is done by measuring it

3 hours later…
4:23 PM
am long interested in the “probability fluid” or “probability density” formulation of QM. it is found in a few scattered refs. need to try to compile some survey. have not seen one. there is some treatment in this book.
> It is though there s a current of “probability fluid” that flows thru space. at any fixed time, the density of this fluid is largest where the particle is most likely to be found. this analogy is the basis of an extremely useful concept— the probability current density— which affords us new insights into quantum motion. p214
it looks like gidney may be working in the google martinis lab...?
Craig Gidney, Santa Barbara, California, United States
3.9k 1 12 26

1 hour later…
5:35 PM
re morrison, p216 caveat
> WARNING thou must not take probability fluid too seriously. probability fluid does not exist in real space; “probability flow” is colorful language designed to create in your mind a picture, an analog of the evolution of a quantum system.
reminds me of copenhagen interpretation and...
"Here be dragons" means dangerous or unexplored territories, in imitation of a medieval practice of putting illustrations of dragons, sea monsters and other mythological creatures on uncharted areas of maps. == History == Although several early maps, such as the Theatrum Orbis Terrarum, have illustrations of mythological creatures for decoration, the phrase itself is an anachronism. There are just two known historical uses of this phrase in the Latin form "HC SVNT DRACONES" (i.e. hic sunt dracones, 'here are dragons'). One is on the Hunt–Lenox Globe[1] (c. 1503–07), on which the term appeared...
!!! o_O finding all kinds of amazing refs with some google searches! some recent! just didnt have the magic words until now! cant wait to share/ write em up!

2 hours later…
8:02 PM
@JarekDuda @ThomasKlimpel Thomas did a reasonable job of describing how I think about these systems. Although I think of my approach as "beforehand instead of in-the-moment" thinking, as opposed to "density matrices".

Consider a markov process (a simple state machine with probabilistic transitions). The in-the-moment experience of running a markov process is different from the before-hand experience of describing expected states. In-the-moment, nothing never settles down. You're forever bouncing from state to state. Before-hand, the description *does* settle down. Every markov process appr

3 hours later…
11:15 PM
@CraigGidney hi craig. thx for dropping by, its awesome. do you know daniel sank? have chatted with him quite a bit. saw your recent google paper. was wondering how long youve worked there? what a great spot nowadays! youve been busy this year... wondering, do you have a home pg at google? arxiv.org/find/quant-ph/1/au:+Gidney_C/0/1/0/all/0/1 ... was wondering what you think about interpretations of QM? do you think the density formulation allows any alternative interpretation? etc