# B Perceiving Superpositions

1. Jan 21, 2016

### 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?

2. Jan 21, 2016

### 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.

3. Jan 21, 2016

### 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?

4. Jan 21, 2016

### Strilanc

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.

5. Jan 21, 2016

### Staff: Mentor

Of course it cant. A cat breaths air and interacts with its environment in other ways. Its entangled with it so cant 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:

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

6. Jan 22, 2016

### atyy

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

7. Jan 22, 2016

### cube137

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.

8. Jan 22, 2016

### A. Neumaier

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.

9. Jan 22, 2016

### Staff: Mentor

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 modelled as harmonic oscillators.

Thanks
Bill

Last edited: Jan 22, 2016
10. Jan 22, 2016

### cube137

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 cant 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.

11. Jan 22, 2016

### Staff: Mentor

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

Thanks
Bill

12. Jan 22, 2016

### cube137

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

13. Jan 22, 2016

### Staff: Mentor

Electrons interacting with the vacuum are not pure,.

Thanks
Biolol

14. Jan 22, 2016

### cube137

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"

15. Jan 22, 2016

### Staff: Mentor

Thanks
Bill

16. Jan 22, 2016

### cube137

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.

17. Jan 22, 2016

### 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.

18. Jan 22, 2016

### Staff: Mentor

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

19. Jan 22, 2016

### Staff: Mentor

It's not really a good idea to discuss superposition's unless you know the difference between a pure and a mixed state:

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

Last edited: Jan 22, 2016
20. Jan 22, 2016

### cube137

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 learnt it from him when I read it yesterday. So atyy was wrong (hope atyy can defend it).