Can a Quantum Observer Perceive Superpositions Inaccessible to Humans?

[cube137]

Zurek mentions in http://arxiv.org/pdf/quant-ph/9805065v1.pdf :

"It is amusing to speculate that a truly quantum observer (i.e., an observer processing quantum information in a quantum
computer-like fashion) might be able to perceive superpositions of branches which are inaccessible to us, beings limited in our information processing strategies to the record states “censored” by einselection."

Isn't it that the density matrix makes it impossible to have superpositions. This begs the question. Is the density matrix created by humans just to make classical output? In order to turn improper mixture to proper? This means somewhere out there other improper mixture branches or even pure state combination of system plus environment is still in superposition? Hence a quantum observer can still theoretically perceive the superpositions?

 

[Strilanc]

I don't think a "truly quantum" agent's experience would differ much from someone with access to a quantum computer. Their decisions and reasoning and measurements would still be driven by the Born Rule, so really all they gain is the ability to perform quantum information processing on inputs. That does make quantum state tomography a bit easier, but it's a bit "flowery" to think of it as allowing them to "directly perceive superposition". Any "perceiving" is going to require making partial copies, and that's tantamount to measurement.

 

[cube137]

So is the superposition of dead cat + alive cat or half dead cat + 1.5 alive cat still exist? Can we say we filter them using the density matrix? The density matrix just a tool to coincide with our determining the cat is either alive or dead but that doesn't mean the superposition were destroyed?

 

[Strilanc]

So is the superposition of dead cat + alive cat or half dead cat + 1.5 alive cat still exist? Can we say we filter them using the density matrix? The density matrix just a tool to coincide with our determining the cat is either alive or dead but that doesn't mean the superposition were destroyed?

Density matrices are just what you get when you marginalize over superpositions. It's interesting that you end up with ##n^2## parameters instead of ##n##, but ultimately it's just a consequence of not being able to condition on the whole state. A "truly quantum" observer would have the same problem, unless they went around collecting and un-mixing quite a lot of waste heat.

 

[bhobba]

So is the superposition of dead cat + alive cat or half dead cat + 1.5 alive cat still exist?

Of course it cant. A cat breaths air and interacts with its environment in other ways. Its entangled with it so can't be in a superposition of alive and dead - its impossible - utterly impossible. I will repeat it again - its simply not possible - even theoretically.

Here is the math in a simplified form - see post 22:
https://www.physicsforums.com/threads/is-the-cat-alive-dead-both-or-unknown.819497/page-2

Just to reiterate - because its entangled it is not in a pure state hence not in a superposition which only applies to pure states. The analysis above shows its in a mixed state.

Thanks
Bill

 

[atyy]

Just to reiterate - because its entangled it is not in a pure state hence not in a superposition which only applies to pure states. The analysis above shows its in a mixed state.

A density matrix is a vector in a vector space, so a mixed state can still be a superposition of vectors.

 

[cube137]

Of course it cant. A cat breaths air and interacts with its environment in other ways. Its entangled with it so can't be in a superposition of alive and dead - its impossible - utterly impossible. I will repeat it again - its simply not possible - even theoretically.

Here is the math in a simplified form - see post 22:
https://www.physicsforums.com/threads/is-the-cat-alive-dead-both-or-unknown.819497/page-2

Just to reiterate - because its entangled it is not in a pure state hence not in a superposition which only applies to pure states. The analysis above shows its in a mixed state.

Thanks
Bill

But is it not the argument of decoherence that the system is entangled with the environment and the whole thing is in pure state? When you measure a subsystem, you see it in mixed state but the entire thing (system + environment) is in superposition and pure state.

Or let's take the case of two electrons that are entangled.. they are in superposition and in pure state. You seem to be saying that when two things are entangled.. they are not in superposition.

 

[A. Neumaier]

A density matrix is a vector in a vector space, so a mixed state can still be a superposition of vectors.

This is mathematically correct but conceptually very misleading. Nobody ever in quantum mechanics talks seriously about superpositions of density matrices.

Superposition in quantum mechanics always refers to superposition of state vectors representing pure states in a distinguished basis, and the result is another pure state. One never talks about mixed states in terms of superposition.

 

[bhobba]

But is it not the argument of decoherence that the system is entangled with the environment and the whole thing is in pure state?.

The truth is what Professor Neumaier said in another thread:
There is no way to remove the decoherence for a macroscopic object. You can do it (approximately) only for very tiny objects such as electrons or buckyballs - and the cost for doing it grows drastically with the size of the object.

Even an electron has issues - it interacts with the quantum vacuum. Modelling a system as pure is done not because its actually like that - its done to have a tractable model. But its irrelevant - virtually everything we see around us is entangled - very very rarely do you observe even an approximate pure state and a cat certainly is not one.

You seem to be saying that when two things are entangled.. they are not in superposition.

That's exactly what I am saying and what my analysis showed. More complex models than the simple one I used are closer to what's actually happening eg the environment is modeled as harmonic oscillators.

Thanks
Bill

 

[cube137]

The truth is what Professor Neumaier said in another thread:
There is no way to remove the decoherence for a macroscopic object. You can do it (approximately) only for very tiny objects such as electrons or buckyballs - and the cost for doing it grows drastically with the size of the object.

Even an electron has issues - it interacts with the quantum vacuum. Modelling a system as pure is done not because its actually like that - its done to have a tractable model. But its irrelevant - virtually everything we see around us is entangled - very very rarely do you observe even an approximate pure state and a cat certainly is not one.

That's exactly what I am saying and what my analysis showed. More complex models than the simple one I used are closer to what's actually happening eg the environment is modeled as harmonic oscillators.

Thanks
Bill

So everytime there is truly random quantum fluctuations being entangled with any system. It is no longer called pure state? But can't you treat the random quantum fluctuations as part of the collapse (demanding Born rule)?

Superpositions can't be perceived in one of the outcomes. But if you can multiplex all the outcomes.. then isn't it like perceiving superpositions? This is what Zurek was talking about.

 

[bhobba]

So everytime there is truly random quantum fluctuations being entangled with any system..

I think you need to elaborate what you mean by that. As written it makes no sense.

Thanks
Bill

 

[cube137]

I think you need to elaborate what you mean by that. As written it makes no sense.

Thanks
Bill

Or for example the question why you can't model an electron interacting with the quantum vacuum as pure state?

 

[bhobba]

Or for example the question why you can't model an electron interacting with the quantum vacuum as pure state?

Why did you evade answering my question?

Electrons interacting with the vacuum are not pure,.

Thanks
Biolol

 

[cube137]

Why did you evade answering my question?

Electrons interacting with the vacuum are not pure,.

Thanks
Biolol

Why is it not pure? Can't you treat the electrons as "system" and the vacuum as "environment". I'm elaborating it.. not evading any. In decoherence, the system and environment are pure. Measuring the subsystem would make it mixed state. So why can't you consider the quantum vacuum the electron interacting as "environment"

 

[bhobba]

Why is it not pure?

Please answer my question first. Stop evading.

Thanks
Bill

 

[cube137]

Please answer my question first. Stop evading.

Thanks
Bill

backtracking.. it's this conversation:

I said: So everytime there is truly random quantum fluctuations being entangled with any system..
you said: I think you need to elaborate what you mean by that. As written it makes no sense.

Well.. An electron interacts with the vacuum in terms of polarizations and stuff (virtual particles or the lattice equivalent of it that doesn't use the picture of virtual particles). I mentioned this because you mentioned somewhere (I read all the thread about decoherence the whole day) that vacuum fluctuations are truly random. Remember you were debating with Ruth Kastner. You said vacuum fluctuations are really random. This is why I'm asking now if the reason electrons interacting with the quantum vacuum can't be considered pure state because of the truly random vacuum fluctuations you emphasized to ruth in the old thread.

 

[cube137]

I just searched for "pure state vs mixed state" in the archive. So pure state involves phase interference and the reason the electron interacting with the quantum vacuum can't be in pure state is because the phases of the electrons and vacuum fluctuations don't have phase interfereces?

But then superposition is related to pure state.
They say the system and environment are in superposition.. so I assume they are pure state. This is confusing. Again I'm not evading your question. See the message previously to this. Thanks.

 

[bhobba]

Well.. An electron interacts with the vacuum in terms of polarizations and stuff (virtual particles or the lattice equivalent of it that doesn't use the picture of virtual particles).

That doesn't really make much sense either, but I think I get your drift. Now that interaction with the vacuum means its entangled with it - that's how an electron will spontaneously emit a photon and drop to a lower energy state. If it was in a pure state that could not happen.

The simplified model in terms of the link I gave is c1*|a1>|b1> + c2*|a2>|b2> where |a1> is the electron in a high energy state, |b1> no photon, |a2> lower energy state, |b2> a photon. Note - this is a simplification - the overall system electron and photon is not really in a pure state. That means if you observe the electron or photon it's not in a pure state - its in a mixed state.

As I said - everything is pretty much entangled, although to good approximation some things can be taken as pure even though it really isn't.

Thanks
Bill

 

[bhobba]

I just searched for "pure state vs mixed state" in the archive..

It's not really a good idea to discuss superposition's unless you know the difference between a pure and a mixed state:
https://www.physicsforums.com/threads/vector-representation-of-a-quantum-state.79791

Superposition's are that any two pure states can be summed to form another pure state. Technically that applies to mixed states as well, but as explained in post 8 its not what's usually meant by superposition.

Thanks
Bill

 

[cube137]

It's not really a good idea to discuss superposition's unless you know the difference between a pure and a mixed state:
https://www.physicsforums.com/threads/vector-representation-of-a-quantum-state.79791

Superposition's are that any two pure states can be summed to form another pure state. Technically that applies to mixed states as well, but as explained in post 8 its not what's usually meant by superposition.

Thanks
Bill

In the thread https://www.physicsforums.com/threa...-states-in-laymens-terms.734987/#post-4642601 atyy mentioned this:

"In decoherence, the system consisting of environment + experiment is in a pure state and does not collapse. Here the experiment is a subsystem. Because we can only examine the experiment and not the whole system, the experiment through getting entangled with the environment will evolve from a pure state into an improper mixed state. Since the improper mixed state looks like a proper mixed state that results from collapse as long as we don't look at the whole system, decoherence is said to be apparent collapse."

You said the system (experiment) + environment can't be in pure state. But atyy mentioned it could. I actually learned it from him when I read it yesterday. So atyy was wrong (hope atyy can defend it).

 

[bhobba]

You said the system (experiment) + environment can't be in pure state.

What I said was:

Modelling a system as pure is done not because its actually like that - its done to have a tractable modell

Its not hard. Think about it.

Thanks
Bill

 

[cube137]

What I said was:Its not hard. Think about it.

Thanks
Bill

I'm reviewing a book called Quantum: A Guide to the Perplexed. It's written that:

"Does Decoherence solve the measurement problem?
Some would say no, it does not help us solve the second part, namely how, upon measurement, one outcome from a number of alternatives - all of which are possible results - is plucked out. Decoherence tells us why we never see a cat that is both alive and dead at the same time, but it doesn't tell us how one or the other is selected"

I've familiar with the problems of outcomes. I'd like to ask this simple question. Supposed you were walking in the street and there was no simple outcome.. meaning no particular position eigenstates selected.. does it mean the entire neighborhood and street would moving back and forth without any particle positions in all the particles although position preferred basis selected or would you see nothing? I just want to imagine how it would behave. Remember I'm writing a book on cartoon guide to decoherence for the masses. So need impressive example.

 

[bhobba]

Supposed you were walking in the street and there was no simple outcome.. meaning no particular position eigenstates selected..

If you are walking down the street then everything is decohered into the position basis. For the why you have to consult technical tomes - but it has to do with most interactions having radial symmetry.

As for the measurement problem it most assuredly does not solve that - but that is way off the query you asked. It requires a thread of its own.

You seem to be caught up with what it would be like to be a pure state thinking it would become unreal or something like that. What me and others have been trying to get across is pure states are rather difficult to come by even for things like electrons, but utterly impossible for macro objects like cats.

Thanks
Bill

 

[cube137]

If you are walking down the street then everything is decohered into the position basis. For the why you have to consult technical tomes - but it has to do with most interactions having radial symmetry.

I know everything is decohered into the position basis. But note a basis is a set of different position eigenstates. So without any single outcome chosen (just for sake of discussions). What would you see in the street? Again this is just for sake of discussions so as to understand it more thoroughly. thanks.

As for the measurement problem it most assuredly does not solve that - but that is way off the query you asked. It requires a thread of its own.

You seem to be caught up with what it would be like to be a pure state thinking it would become unreal or something like that. What me and others have been trying to get across is pure states are rather difficult to come by even for things like electrons, but utterly impossible for macro objects like cats.

Thanks
Bill

 

[bhobba]

I know everything is decohered into the position basis. But note a basis is a set of different position eigenstates. So without any single outcome chosen (just for sake of discussions). What would you see in the street?

That's the problem of outcomes. Its a consequence of the principles of QM you get an outcome in the basis selected from decoherence. Why is the central mystery of QM and is the modern version of the measurement problem..

Thanks
Bill

 

[cube137]

That's the problem of outcomes. Its a consequence of the principles of QM you get an outcome in the basis selected from decoherence. Why is the central mystery of QM and is the modern version of the measurement problem..

Thanks
Bill

Is a pure state always has outcome? or is there any example of pure state without any outcome.. what? if there is pure state without outcome.. then when it interacts with the environment.. all it's phases gets lost.. and there is outcome.. is there any experiments of transition from one without outcome slowly to one with outcome? But then if all pure state has outcome.. then this transition from state without outcome to one with outcome experiment can't be done.

 

[bhobba]

then this transition from state without outcome to one with outcome experiment can't be done.

You are getting confused. I suspect you are worrying about the so called Von Neumann regress. That needs a thread of its own. Start one if you are interested.

Thanks
Bill

 

[cube137]

You are getting confused. I suspect you are worrying about the so called Von Neumann regress. That needs a thread of its own. Start one if you are interested.

Thanks
Bill

No. I mean.. mixed state has outcome.. so I'm simply asking if pure state has outcome too or not?

 

[bhobba]

No. I mean.. mixed state has outcome.. so I'm simply asking if pure state has outcome too or not?

Pure states have no preferred basis singled out. Even mixed states don't, but with decoherene a basis is singled out for the mixed states from decoherence.

You need to study a proper text on it. At the 'lay' level I suggest:
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20

It's tough going since it uses math, but really there is no other way.

Thanks
Bill

 

[naima]

Isn't it that the density matrix makes it impossible to have superpositions. This begs the question. Is the density matrix created by humans just to make classical output?

You have a wrong notion of density matrices. they allow superposition. But the matrix of a sum is not the sum of the matrices. you can discover their inner law in Manko. http://arxiv.org/abs/quant-ph/0207033

 

[Nugatory]

I'd like to ask this simple question. Supposed you were walking in the street and there was no simple outcome.. meaning no particular position eigenstates selected.. does it mean the entire neighborhood and street would moving back and forth without any particle positions in all the particles although position preferred basis selected or would you see nothing?

That question has no satisfactory answer because for you to see something implies that light is interacting with your eyes. Either one set of rod and cone cells in your retina is triggered to form one image, or a different set is triggered to form another image; either way we see a definite outcome and not a superposition. Similar arguments apply to other senses (your eardrum ends up in a definite state after interacting with the air molecules that carry sound, for example) but this argument in no way privileges human sensory apparatus. A piece of photographic film will also capture one image or the other, and the process is not interestingly different from the process by which your retina captures one image or the other.

Do not be misled by our ability to see and photograph an interference pattern in the double-slit experiment. Each individual particle makes its own unsuperimposed position-basis dot on the screen so we aren't seeing any superposition. We're seeing the statistical result of a large number of experiments (one per dot) in which we've allowed a superposition to collapse before we observe it.

I just want to imagine how it would behave. Remember I'm writing a book on cartoon guide to decoherence for the masses. So need impressive example.

My advice is to get hold of Bruce Lindley's book "Where does the weirdness go?", read through it, and then try recasting it as a cartoon guide.

 

[cube137]

If you are walking down the street then everything is decohered into the position basis. For the why you have to consult technical tomes - but it has to do with most interactions having radial symmetry.

As for the measurement problem it most assuredly does not solve that - but that is way off the query you asked. It requires a thread of its own.

You seem to be caught up with what it would be like to be a pure state thinking it would become unreal or something like that. What me and others have been trying to get across is pure states are rather difficult to come by even for things like electrons, but utterly impossible for macro objects like cats.

Thanks
Bill

Can you give some examples of pure states. Can the electron passing thru both slits and interfering count as one (before the detector cause decoherence or collapse)? Here the electron can interfere with it. So it's not entirely wrong to call or think it would "become unreal or something like that" as you put it. How can pure state be real when a particle can interfere with itself. So after emission and before detector. We can say the electron become unreal indeed.

 

[bhobba]

Can you give some examples of pure states.

The truth is what Professor Neumaier said in another thread:
There is no way to remove the decoherence for a macroscopic object. You can do it (approximately) only for very tiny objects such as electrons or buckyballs - and the cost for doing it grows drastically with the size of the object.

You have seen a number of cases in this thread where states are modeled as pure, as well as the elections and buckyballs mentioned above where it is often a good approximation.

Can the electron passing thru both slits and interfering count as one (before the detector cause decoherence or collapse)?

In this case electrons are treated as pure to good approximation as is rather clear from the literature.

While it is common in the literature to say electrons pass through both slits in fact QM is silent on what's happening when objects are not observed. That's the territory of interpretations - in this case Feynman's sum over histories. Here is much better way of looking at the double slit:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

How can pure state be real when a particle can interfere with itself. So after emission and before detector. We can say the electron become unreal indeed.

We deal with science here not new age philosophical mumbo jumbo such as things becoming unreal. Philosophers can't even agree on what real is. In science we take a very common sense view of reality and think of science as describing it. Personally I believe reality is what science describes - but that's just me, and here, by forum rules, is not the place to discuss philosophy. When not observed QM is silent on what's going on. But interpretations have all sorts of takes from very real such as BM to I basically give up like Ignorance Ensemble.

Thanks
Bill

 

[cube137]

You have seen a number of cases in this thread where states are modeled as pure, as well as the elections and buckyballs mentioned above where it is often a good approximation.
In this case electrons are treated as pure to good approximation as is rather clear from the literature.

Thanks
Bill

Bill. I've been doing some researching. According to physicist JesseM, it may be possible to prepare pure state for the cat.. he said in an old thread:

"In principle it should be possible to prepare the contents of the box in a pure state, which I think just means you would perform a measurement that would give you the maximum possible information about the particles in the box allowed by quantum physics (like a precise measurement of a complete set of commuting observables), allowing you to construct a state vector for the system."

Bill.. In pure state, you have interferences in the phases.. if a cat would be prepare in pure state.. there may still be a very tiny portion of all the zillions and zillions of particles where there may be interferences.

I think he meant that as long as there is a tiny interference (non-zero).. it can be called pure state? perhaps in your view, pure state should be complete interferences? Is your view or his the mainstream belief? How do you interpret his statements?

 

[bhobba]

Bill. I've been doing some researching. According to physicist JesseM, it may be possible to prepare pure state for the cat.. he said in an old thread:

He is wrong - if he is saying that - which is doubtful. I have explained why - its basic QM that you can't.

which I think just means you would perform a measurement that would give you the maximum possible information about the particles in the box allowed by quantum physics (like a precise measurement of a complete set of commuting observables), allowing you to construct a state vector for the system."

That is not what a pure state is. Its independent of the measurement you can perform on it. You are likely not giving the proper context which is what's known as a state preparation procedure. You can't do that with a cat since it breaths air, but state preparation procedures are outside this tread and needs one of its own.

Instead of twisting this way and that trying to justify an incorrect notion you came to this forum with, learn the theory from the sources that have been mentioned in this thread. That way you will be in a better position to see when even physicists get things wrong if he got it wrong - which I doubt.

For completeness I will tell you exactly what a pure state is. A state in QM is by definition a positive operator of unit trace. States of the form |a><a| are called pure. States of the form Σ pi |ai><ai| are called mixed. Its easy to show any state must be mixed or pure. For pure states the |a> in |a><a| can be mapped to a vector space which is how they are usually presented in beginner and intermediate texts - but more advanced texts tell the whole story. Its an example of something you have to unlearn as you progress which unfortunately happens on occasion in physics and sometimes leads to confusion. This is a famous example, the idea of virtual particles as particles is another. They lead to thread after thread here because people for some reason don't want to unlearn what they have been told elsewhere. Its a very frustrating human quirk.

Once you understand the above you can see what that guy wrote is off target but more likely you are taking it out of context.

Why are states positive operators of unit trace? There is a very beautiful theorem called Gleason's theorem:
https://en.wikipedia.org/wiki/Gleason's_theorem

Why can't a cat be in a pure state. He breaths air and is entangled with the air because the cat interacts with the air. The link I gave previously explains what that implies ie its no longer is a separate state, but acts like a mixed state.

Thanks
Bill