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