What Are the Key Controversies in Quantum Measurement Theory?

[Fra]

Doesn't the original point of the discussion boil down to if an observer can hold (and process) a copy of the quantum state of itself? And isn't the answer to that simply "no"?

If you mean what I think, then I insist the answer is yes.

For me the starting point is that the observers internal structure somehow encodes the information state.

But the quantum state is relative. Two observers can never encode the same state - or they would be same; so there is always disagreement between observers. But then I see that simply as the cause for existence of an interaction. So this is an exploit, not a problem.

In what sense do you mean "no"? (perhaps more probably though, I am misunderstanding in what sense you mean copy of what)

/Fredrik

 

[llynne]

Is it true that if we ignore the system we allow it to function in a certain way but if we try to observe any of the individual elements the observation ITSELF causes a difference? Or is it just that some METHODS of observing quantum events necessarily affect the element or event?

 

[dextercioby]

Is it true that if we ignore the system we allow it to function in a certain way but if we try to observe any of the individual elements the observation ITSELF causes a difference? Or is it just that some METHODS of observing quantum events necessarily affect the element or event?

I think that the evolution of a quantum system (time-evolution of its state in a Hilbert space/rigged Hilbert space) should be independent of the measurements taking place on it, so that's why I reject von Neumann's projection postulate and remove it from an axiomatical basis of QM, because it logically conflicts with the postulation of Schroedinger's equation as the description of how state vectors evolve in time.

 

[Fra]

I think that the evolution of a quantum system (time-evolution of its state in a Hilbert space/rigged Hilbert space) should be independent of the measurements taking place on it, so that's why I reject von Neumann's projection postulate and remove it from an axiomatical basis of QM, because it logically conflicts with the postulation of Schroedinger's equation as the description of how state vectors evolve in time.

What's wrong with simply postulating?

1. UNITARY evolution as an EXPECTED evolution, in consequence of the current state of information.
2. And the measurement obvisouly updates this state; and thus resets the evolution.

By consistency though, then one observer O1, observing another observer O2 interacting with S2, will EXPECT unitary evolution of O2+S2, and given the equilibrium condition, then there must exists a way in which the "collapsing process" LOOKS LIKE a unitary process from a different perspective.

This merely means the collapse is of course not objective. In fact the sequence of "collapses" throughout and interaction, could then be described as an unitary evolution by a differen obserer. But then of course, this new observer has his OWN set of collapses.

I don't see the problem? Except of course the subconscious heritage of always trying to find a realist picture. I think that desire is the main problem, not the collapse itself.

/Fredrik

 

[Hurkyl]

To be honest, I'm somewhat discouraged to continue participating -- the first thing I read in your FAQ amounts to promoting ignorance of MWI (even in favor of having an informed opinion) and mocking those who would seriously consider it. Coupled with the familiar irrational argument against irrational numbers, I expect a rather low signal-to-noise ratio from continued discussion.


Let's start with something possibly very simple. I consider a CNOT gate (wikipedia link) a measuring device. It measures the qubit on its control line, and records the result of measurement by adding it to the target line.

It has properties one would like from a measuring device, and particularly good ones; e.g. it completely and clearly distinguishes between the states its measuring, and once separated from the qubit it measures, its interaction with the qubit to be measured is unitary, and it transitions into a statistical mixture of the two output states with the right weights.

It is also nice because, not only is it small enough to do easily do computations on paper to analyze it, but it's small enough that we can experiment in real life with the things we can do in principle but are usually infeasible in a practical sense, such as isolating it from its environment, and having fine enough control to reverse things that would normally be thermodynamically irreversible.

The only thing I find lacking is that the output is not (directly) human readable. But I don't think that makes it any less of a measuring device. (I had another reason, but I can't remember)

What is your opinions on CNOT gates as measuring devices?

 

[Fredrik]

What is your opinions on CNOT gates as measuring devices?

It's not a measurement if the result isn't recorded in some part of the environment that for all practical purposes can be described classically.

 

[StevieTNZ]

Do the solutions to the Schroedinger equation change AFTER a measurement has taken place?
I say this because in the book 'Entanglement' the author says that potentialities still exist even if there is actuality. I think a good way to put it is the solution to the equation still exists (i.e. superposition of states), but we are only aware of one of those states [no collapse is postulated]. For can we not find a solution to the Schroedinger equation for anytime in the future, where at that point we can see a definite state?

 

[Fredrik]

Do the solutions to the Schroedinger equation change AFTER a measurement has taken place?

The Schrödinger equation only applies to systems that are isolated from their environments. No system is isolated from its environment during a measurement, because it interacts with the measuring device. If the system isn't destroyed by the interaction, it might become isolated again after the measurement (depending on the details of the interaction between the system and the measuring device), and in that case, once again have a state that changes with time as described by the Schrödinger equation.

 

[dextercioby]

The Schrödinger equation only applies to systems that are isolated from their environments. No system is isolated from its environment during a measurement, because it interacts with the measuring device. If the system isn't destroyed by the interaction, it might become isolated again after the measurement (depending on the details of the interaction between the system and the measuring device), and in that case, once again have a state that changes with time as described by the Schrödinger equation.

Can you give a compelling argument for which quantum mechanics should describe the interaction between observer and the physical system being observed ? Do you think that this Copenhagian view that you so vigorously defend is the only right one ?

 

[Hurkyl]

It's not a measurement if the result isn't recorded in some part of the environment that for all practical purposes can be described classically.

IYO, does the CNOT used in this fashion count as a measuring device, even if the particular interaction described doesn't count as a measurement?


What if my quantum computer loses coherence, so that the information in qubit on the target line "escapes" into the environment. Does it count as a measurement then?



This is the only thing you find objectionable? To put it differently, let me introduce a term "quasi-measurement" for this post only, which describes any sort of interaction that is like a measurement in all relevant aspects save one: there is no "size" restriction on the system into which the result is recorded.

(if you don't like "size", then please provide a description of your own)

So, all measurements count as quasi-measurements. Would you consider a CNOT gate used in that fashion to result in a quasi-measurement as well?

 

[strangerep]

[...] the familiar irrational argument against irrational numbers

I guess you're referring to Arnold's mention of irrational numbers?
I was about to prepare a response to that but it sounds like you've
thought it through more than I have.

Would you summarize, or (if that's too boring) point me to a relevant
previous thread?

Cheers.

 

[StevieTNZ]

The Schrödinger equation only applies to systems that are isolated from their environments. No system is isolated from its environment during a measurement, because it interacts with the measuring device. If the system isn't destroyed by the interaction, it might become isolated again after the measurement (depending on the details of the interaction between the system and the measuring device), and in that case, once again have a state that changes with time as described by the Schrödinger equation.

What equation governs systems that are among an environment?

 

[Fredrik]

Can you give a compelling argument for which quantum mechanics should describe the interaction between observer and the physical system being observed ? Do you think that this Copenhagian view that you so vigorously defend is the only right one ?

I'm not sure I understand these questions. I think the answer would depend on what exactly we mean by "observer". If the observer is the person doing the experiment, the interaction between him/her and the measuring device can be described in classical terms, and I don't think there's much more to say about that. This observer doesn't interact with the system directly. If the observer instead is the part of the environment that most of the quantum weirdness is moved into (e.g. the air surrounding the system) by quantum decoherence, then I don't think I can answer the question in detail, but maybe someone with greater knowledge of decoherence theory can.

I don't think that what I said in the text you quoted represents a particularly "Copenhagian" view, but I do think that what Meopemuk said in #15 is the only right way to think about QM. To be more precise, I think that's the right way to think about the theory, but there's still room to add an "interpretation of QM" on top of the theory.

 

[Fredrik]

What equation governs systems that are among an environment?

What happens is essentially that the state operator (i.e. density matrix) quickly becomes approximately diagonal in a basis of eigenvectors of an observable that commutes with the part of the Hamiltonian that describes the interaction between the system and its environment. I'm not very familiar with the details, so I can only suggest that you check out a book on decoherence.

 

[Fredrik]

IYO, does the CNOT used in this fashion count as a measuring device, even if the particular interaction described doesn't count as a measurement?

I prefer to use terms like "entanglement" and "correlation" when I talk about these things, and reserve "measurement" for those cases when the information is stored in a for all practical purposes classical system.

What if my quantum computer loses coherence, so that the information in qubit on the target line "escapes" into the environment. Does it count as a measurement then?

That's too difficult a question for this time of night.

So, all measurements count as quasi-measurements. Would you consider a CNOT gate used in that fashion to result in a quasi-measurement as well?

I guess, but you pretty much just invented a new word to describe what you're talking about, so the fact that I don't disapprove doesn't really tell you anything.

 

[Fra]

What equation governs systems that are among an environment?

Like Fredrik said already, unitary evolution applies to "isolated systems" which is a way of almost (but not quite) saying the same as how I prefer to put it, that unitary evolution only describes the EXPECTED evolution; when the observer is ISOLATED (because then the expectations is not updated).

So obviously if the system is not isolated, and we do not monitor/observer the environment (IF we do, we simply consider a BIGGER system of original system+environment; which answer we already answered) then of course the actual evolution is imply unpredictable! There IS no equation that can model this, because thequalifying info is missing. But we can STILL say that the expected evolution is the unitary one (wether this matches is another question).

So what this then predicts is the observers actions, not the systems actions. But this is how any LEARNING of inference works like! The black box is always uncertain and unpredictable and all you can decide/control is what your next question/experiment is.

So I think the right answer is that, all you EVER get, is an expectation of the evolution; which determines the observes action. But this MATCHES the actual evolution only if BOTH the observer and the system is isolated.

/Fredrik

 

[Fra]

I'm always uncertain what is discussed here. Some people discuss formalisation of current QM. Some discuss some existential philosophical issues. Some (like me) discuss seeking a new framework (which means this should goto the BTSM section) - so I apologize it I'm drifting the topic.

It's not a measurement if the result isn't recorded in some part of the environment that for all practical purposes can be described classically.

Interesting statement.

I can appreciate that this is somehow the perspective in which current QM is confirmed. Which means that there has to exists a suffciently complex controlled environment, that then is effectively classical in which the entire quantum theory and hilbert space is encoded.

BUT, I think such view of what a measurement is, is limiting, and is likely to be inadequate for solvine open issues like unification and QG.

I think a realistic analysis suggest that the above is cleary an idealisation, that is FAPP true in the normal laboratory physics domain, but which badly breaks down if one consider cosmological models, or models where the context where the THEORY itself is encoded, is inside the system and where it's impossible to record/store/hold all information. Alternatively one can see it as an open system. Which is why I think what we need to understand "observer" and "observe the observer" is to find a new framwork that is a learning model. Because a deductive theory for a not closed system, that is correct can not reasonably be encoded in the subsystem of the system under observation. It has to evolve, and it means it needs to be an adaptive inference model; not something basic in static hilberspaces.

The picture of static hilber space is IMHO, only sensible in the approximation mentioned - where we have a sufficiently complex "superobserver" encoding the theory to the extent that the recordings and statistics is essentially classical. This is what takes place in laboratory experiments.

But we still have no unification! Why?

In the picture I suggest (learning/inference view) there is a unification suggested between what rationa choices a superobserver makes and the ACTION of the system. As we konw, the action of the SYSTEM (ie. matter, and fields etc) usually we just PULL from classical models (then quantize etc), obviously this is deeply unsatisfactory, ugly and incoherent etc. We do it because it's the only way we know, and it partially works. BUT the inference views conjectures that the ACTION of matter (lets call it the "naked action) must take the same inference form as does the "rational choice" action of the superobserver - and THIS we can understand from decision theory, and it's essentially entropic to it's nature. The rational decision is made by counting evidence and weighting them. Then, what is needed ontop of that is to "renormalize" this naked choice to the scale of observation of the superobserver.

To work this picure out as a possible route to unification, my personal conviction is we need to also rework the quantum theoty as to take the form of generel inference, applicable also to open systems. In this way the entire fixed hilbert space thing, can not be the right starting point as I see it, as it assumes that the Structure of observer is somehow not changing so much that it deforms the theory indireclt by "scaling" the plattform on which the theory is encoded. So it also must incorporate a new view of RG.

The new QM, is entangled with the problem of theory scaling, and generation of mass (as determining the statistical mass of a theory (ie how MUCH data there is supporting it giving it confidence)).

Of course this is just my personal opinon, that determines my investments but this is in the light of which I think that the work of trying to formalize a structure that is likely to be inadequate seems somewhat misdirected used of resources.

/Fredrik

 

[A. Neumaier]

To be honest, I'm somewhat discouraged to continue participating -- the first thing I read in your FAQ amounts to promoting ignorance of MWI (even in favor of having an informed opinion) and mocking those who would seriously consider it.

You happened to pick one of the oldest entries in the FAQ (dating from 2002), addressing a popular, superficial account of Everett's views, and responding on the same level. My discussion skills improved a lot in the mean time.

I edited the FAQ a bit to address your concerns. A concise analysis (without any noise) of Everett's original paper is now given in a separate entry in the FAQ, called ''Circularity in Everett's measurement theory''
http://arnold-neumaier.at/physfaq/physics-faq.html#everett
(just before the many worlds entry). The main conclusion is that Everett's analysis simply derives the projection postulate by having assumed it, without any discussion, in disguise. Thus his ''interpretation'' explains nothing.

Coupled with the familiar irrational argument against irrational numbers

I don't understand what you refer to. The MWI article doesn't (and didn't) mention irrational numbers.

What is your opinions on CNOT gates as measuring devices?

I'll address this separately.

 

[A. Neumaier]

I'm always uncertain what is discussed here. Some people discuss formalisation of current QM. Some discuss some existential philosophical issues. Some (like me) discuss seeking a new framework (which means this should goto the BTSM section) - so I apologize it I'm drifting the topic.

I believe that discussion about changing the framework for QM does not belong into this forum but to ''beyond the standard model'' (or to ''independent research'').

 

[A. Neumaier]

Let's start with something possibly very simple. I consider a CNOT gate (wikipedia link) a measuring device. It measures the qubit on its control line, and records the result of measurement by adding it to the target line.

[...] the output is not (directly) human readable. But I don't think that makes it any less of a measuring device. [...]

What is your opinions on CNOT gates as measuring devices?

According to the common usage in the discussion of quantum foundations, a measurement device produces a (fairly) permanent recording.

Thus a CNOT gate is not a measuring device but a reversible filter. It is represented by a unitary transformation like other reversible filters such as a beam splitter that have two input and two output ports. It changes a prepared state (control,target) into another prepared state (control',target') without performing a measurement.

On the other hand, perfect (projective) measurement devices are represented by irreversible filters orthogonal projectors that are not unitary.

 

[A. Neumaier]

What equation governs systems that are among an environment?

Systems in interaction with an environment are either modeled by the Schroedinger equation for the combination system+environment, or by a so-called Lindblad equation, http://en.wikipedia.org/wiki/Lindblad_equation, which eliminates the environment in favor of a (slightly approximate) non-unitary evolution.

For example, realistic quantum optics account for dissipation to the environment
(e.g., energy losses due to imperfections of the experimental set-up) by using Lindblad equations.

 

[A. Neumaier]

Do the solutions to the Schroedinger equation change AFTER a measurement has taken place?
I say this because in the book 'Entanglement' the author says that potentialities still exist even if there is actuality. I think a good way to put it is the solution to the equation still exists (i.e. superposition of states), but we are only aware of one of those states [no collapse is postulated]. For can we not find a solution to the Schroedinger equation for anytime in the future, where at that point we can see a definite state?

It is difficult to interpret your question.

A system is at all times in a well-defined state (pure or mixed). ''potential'' are only measurement results - namely before an actual measurement is done.

The Schroedinger equation applies only when the system is fully isolated (and hence unobserved).

 

[A. Neumaier]

What if my quantum computer loses coherence, so that the information in qubit on the target line "escapes" into the environment. Does it count as a measurement then?

In order to qualify as a quantum measurement of a system X, the experimental setup must contain a detector describable by nonzero operators M_1,...,M_n (n>1) satisfying
\sum_i M_i^*M_i = 1,
leading to n distinguishable measurement results, such that the measurement transforms a pure state psi of X into the state
\psi'=M_i \psi/||M_i \psi_i||
when result number i is observed and the system X still exists after the measurement.
(Measurements where the state can disappear must be described in a bigger state space describing the system X together with an empty system - called in this context a vacuum state.)

Corresponding to the detector is a POVM http://en.wikipedia.org/wiki/POVM with the operators F_i=M_i^*M_i (in the notation of this reference).

As long as nothing is observed, there is no measurement result, and hence no measurement took place. Observation here means a macroscopic irreversible change, no matter whether in a detector, a piece of equipment recording a result, or in a human brain.

 

[Hurkyl]

I guess, but you pretty much just invented a new word to describe what you're talking about, so the fact that I don't disapprove doesn't really tell you anything.

I was trying to be specific in how what I'm talking about differs from what you're talking about. The gist I get is that the only real difference between the CNOT gate and what you're willing to call a measuring device is that the measuring device is too unwieldy to have complete control over or to analyze in complete detail. (both meant jointly with the system being measured)

That difference is something I find rather unimportant -- and it also means that quasi-measurements are good models for real measurements, because we can analyze the quasi-measurement in complete detail, and then work out what would happen if we weren't in control of some aspect of it.

 

[Fredrik]

The difference is extremely important, because measurements can test the accuracy of QM, and possibly falsify it. Quasi-measurements can't (unless they're part of a sequence of events that ends with an actual measurement).

 

[Hurkyl]

Thus a CNOT gate is not a measuring device but a reversible filter. It is represented by a unitary transformation

...

On the other hand, perfect (projective) measurement devices are represented by irreversible filters orthogonal projectors that are not unitary.

I would like to point out that the interaction of CNOT gate is only represented by a unitary transformation if you consider the joint (control, target) system. On the (control) system, the interaction truly is the non-unitary projection that turns the state represented by the ket a|0\rangle + b|1\rangle into the state represented by the density matrix |a|^2 |0\rangle\langle 0| + |b|^2 |1\rangle\langle 1|.

 

[Hurkyl]

The difference is extremely important, because measurements can test the accuracy of QM, and possibly falsify it. Quasi-measurements can't (unless they're part of a sequence of events that ends with an actual measurement).

In some sense, your parenthetical is the whole point -- we are considering measuring devices as quantum systems to see if the laws of quantum mechanics is at least plausible in that generality.

I suppose you can break a measurement into two parts: the effect on the measured system, and the "recording" and "viewing" of the results.

I have always viewed the first part as being the part that was actually interesting, particularly because the initial development of QM had enshrined the conclusion of a no-go theorem (time evolution is unitary, projection from a pure to a mixed state is not) whose crucial hypothesis really isn't ever satisfied.

The latter, on the other hand, sounds more like an engineering problem than a foundational physics problem.



The CNOT is interesting because it has the same effect on the measured qubit as a real measurement would, barring the universe being in an "odd" state that makes the gate behave oddly.

 

[Fredrik]

The latter, on the other hand, sounds more like an engineering problem than a foundational physics problem.

It may sound that way, but engineering has nothing to do with it. I would say that this concept of measurement is the single most important detail in the foundations of physics.

 

[Hurkyl]

It may sound that way, but engineering has nothing to do with it. I would say that this concept of measurement is the single most important detail in the foundations of physics.

But being important doesn't mean it's interesting or problematic. Is there a theoretical obstacle between "I've done a quasi-measurement and the result is contained in sub-system A" and "The engineering department has built a machine that will display the information contained in sub-system A"?


Or are you thinking now about treating the observer as a quantum system too? That one is interesting and problematic. (unfortunately, IMO, I think a big part of "problematic" is a reluctance to seriously consider (approximately) classical probabilities as reality rather than an ignorance measure)

 

[ConradDJ]

I suppose you can break a measurement into two parts: the effect on the measured system, and the "recording" and "viewing" of the results.

I don’t think this statement is supported by QM itself, and there’s a lot of experimental evidence against it – for example, in the various versions of the “quantum eraser”.

To try to put this issue in context –

It seems that there are three empirical findings at the basis of QM. One is that isolated systems need to be described in a peculiar way – as “superpositions” evolving cyclically according to the wave-function. The second is that the state of a system depends on what can be known about it.

For example, when an electron is bound to a proton in a hydrogen atom, we know (without interacting) that its momentum is within a certain range, since otherwise it would no longer be bound. By Heisenberg’s principle this requires a corresponding “uncertainty” in the position of the electron, and I understand that this is the explanation for the size of a hydrogen atom.

The third finding is just an extension of the second. It is that besides the unitary evolution of “isolated” systems, something else happens that (as Fra says) physically “updates” the state of a system when new information about it becomes available, in what we call measurement.

In general, physical interaction as described by QM does not do this. It only “entangles” the two interacting systems, correlating their superposed states. If I understand correctly, your CNOT gate only entangles the input and output channels – so does not model measurement in the sense of QM. There’s a different kind of gate that does model a measurement – see for example http://arxiv.org/abs/0808.1582" .

There’s a “measurement problem” because QM tells us nothing about the difference between interaction in general and this “updating” interaction. Implicitly it says, any way of obtaining new information about a system – including indirect means that don’t involve any interaction with the system at all – constitute “measurements” that physically affect the system’s state.

Of course any actual measurement involves many different physical interactions. A main point of Von Neumann’s analysis was to show that it’s not relevant to QM which of these interactions is taken to be the “measurement” – the result is the same in any case.

To me, the problem with the various interpretations of Bohr, Heisenberg, Von Neumann and Wigner is that they’re all operating with a conceptual framework in which something is either objectively real in itself, out there in the world, or it’s something in the mind of a conscious observer. This subject/object dichotomy is completely foreign to the structure of QM.

Heisenberg was right in that QM describes the world not as a reality “in itself” but as a structure of information. As http://arxiv.org/abs/quant-ph/9609002" says, “Physics concerns the information systems have about each other.” There’s no reason to think this has anything to do with consciousness, other than the fact that we lack a well-developed analysis of how information actually gets defined and communicated in the physical world.

So I agree with Fredrik – “...this concept of measurement is the single most important detail in the foundations of physics. ”