Can I steer myself into one of the Many Worlds like this?

[David Byrden]

Given an ideal "box" as used by Schrodinger;
- have a quantum event occur inside it, e.g. sudden cat death with 50% probability.
- have a machine in it that sends out a qubit, fully entangled with the box' internal state, at regular intervals.
- the qubit is a polarised photon
- outside, use a filter to nudge the photon's polarisation a little, toward a desired angle
- Repeat many times, rotating your filter appropriately.
- By using enough measurements, and small enough angles, you can make the chance of photon absorption in the filter arbitrarily small.

If I understand QM, the measurement of a fully entangled qubit tells you the box' internal state.
Therefore, by choosing a basis for measurement, you are choosing the states that the box may take, when you make the measurement (it is a superposition, so really you are just adjusting the relative amounts of the superposed states in it)
So, you can take an initial superposition of fifty-fifty dead/alive cat, and nudge it with many such measurements into another superposition such as "cat almost certainly alive".
And then you can open the box and recover your cat.

Would this work? Why not? I'm especially interested in how to generate the photons such that the two superposed copies of the photon are coherent, although the two states inside the box will have decohered.

Thank you in advance.

David

 

[DrChinese]

- have a machine in it that sends out a qubit, fully entangled with the box' internal state, at regular intervals.
- the qubit is a polarised photon
- outside, use a filter to nudge the photon's polarisation a little, toward a desired angle
...

So, you can take an initial superposition of fifty-fifty dead/alive cat, and nudge it with many such measurements into another superposition such as "cat almost certainly alive".
And then you can open the box and recover your cat.

Would this work? Why not? I'm especially interested in how to generate the photons such that the two superposed copies of the photon are coherent, although the two states inside the box will have decohered.

Good questions! You are mixing a batch of different scenarios together in ways that they don't fit though.

A photon in a superposition of polarization states is not considered to be polarized. Therefore, a polarized qubit will not be in a superposition. Similarly, an entangled photon is not considered polarized (it is in a superposition of polarization states).

When you measure a photon in a superposition of polarization states, you will get a random outcome on any measurement basis. There are operations you can perform on an entangled photon that does not amount to a measurement, but those do not provide you any useful information and they do not allow you to "nudge" something towards a specific outcome.

Also: "decohere" is not usually used in the same context as "coherent" (i.e. as if they were opposites). I won't attempt to properly define them, as that gets complicated. But generally, entangled particles are said to "decohere" as they interact with the outside environment and cease to be entangled.

 

[David Byrden]

A photon in a superposition of polarization states is not considered to be polarized.

For some reason, I can't find a single authoritative source on the Web that agrees with you. In fact, they all seem to state the opposite.

I'm new to quantum mechanics, so please bear with me if I'm missing something. But I do know what a "mixed state" is, and I'm not talking about that, as I think I made clear. I'm talking about a photon that's in a pure state a|H> + b|V> where H and V are orthogonal polarisations. If this photon is not itself polarised, then what is?

When you measure a photon in a superposition of polarization states, you will get a random outcome on any measurement basis.

Again, you're contradicting every source that I can find. If the superposition has its own polarisation angle, as I thought, then we can align one of the basis vectors with it, and get a guaranteed non-random hit every time. No ?

"decohere" is not usually used in the same context as "coherent"

Hmm. Could you refer me to some source that explains them?
It's not important to my proposal, but I'll explain what I meant: the inside of the box, where the quantum event has happened and information about it has leaked into the wave function of the environment, is now in a superposition of two states. They may be very different ( dead cat vs. live cat) or they may be very similar, but they are likely to be different enough that they don't interfere with each other (in the Young's Slits sense). That's what I understood by the term "decohere".

The two superposed copies of the photon, must not differ in this way. There must be no information you can extract from them (e.g amplitude, timing) that identifies the internal state of the lab as an eigenstate. If such unwanted information were present in the photons, the experiment would behave "classically".

My photon must carry only polarity information. The two superposed copies of the photon must act as one - they must interfere, their polarity vectors must add, like the wave functions that produce Young's fringes. That's what I understood by "coherent".

In that case, I believe that my manipulation of the photon will also manipulate the lab's internal state, which is fully entangled with it.
Why?
Because, as asserted in RQM, the state of a quantum system is relative to the observer. I would not be magically reviving an actual dead cat; I would be steering myself into one branch of the "many worlds" rather than another.

So, as I was saying, I can't understand why you seem to disagree with so many other sources?

But, thank you for replying.

David

 

[Nugatory]

Would this work?

No.

The first difficulty will appear even if we start with something much simpler than a cat inside the box - say it's just a single photon inside, so we're just working with a pair of polarization-entangled photons and we're trying to "nudge" the photon inside the box into a particular polarization state.

An entangled state (without worrying about normalization constants) looks something like $|\alpha_1\rangle|\beta_1\rangle+|\alpha_2\rangle|\beta_2\rangle$, a coherent superposition of two vectors from the product space of the two observables; here the $\beta_i$ are polarization states of the photon in the box and the $\alpha_i$ are polarization states of the emitted photon. Your first measurement of the emitted photon will collapse that wave function to either $|\alpha_1\rangle|\beta_1\rangle$ (outside photon measured $\alpha_1$, we know inside photon is in state $\beta_1$) or $|\alpha_2\rangle|\beta_2\rangle$ (outside photon measured $\alpha_2$, we know inside photon is in state $\beta_2$).

But now what? We no longer have an entangled state so another measurement on the same outside photon won't do anything - it will just turn $|\alpha_1\rangle|\beta_1\rangle$ into something like $|\alpha_3\rangle|\beta_1\rangle$.

If instead we try to arrange for the box to emit another entangled photon, we'll need some interaction inside the box to generate a new entangled state. But now we're back to $|\alpha_1\rangle|\beta_1\rangle+|\alpha_2\rangle|\beta_2\rangle$, undoing the effect of our first measurement.

So we cannot "nudge" a single quantum particle into a desired state, and if we cannot do that we surely will not be successful with the $10^{25}$ or so particles that make up a cat. But there's a deeper problem if we were to try. The entire idea is predicated on being able to prepare a superposition of the form $|Live\rangle|\alpha_1\rangle+|Dead\rangle|\alpha_2\rangle$ where as before the $\alpha_i$ are states of the emitted photon and Live/Dead are pure states built up from all the internal degrees of freedom in the box. But such states cannot be prepared and measured because they immediately decohere.

 

[StevieTNZ]

So, as I was saying, I can't understand why you seem to disagree with so many other sources?

Can you please list all sources of the information you are basing your understanding of quantum physics on.

 

[PeterDonis]

I can't find a single authoritative source on the Web

The highlighted words are your problem. Have you looked at any actual textbooks?

I'm new to quantum mechanics

Then you might want to go easy on constructing complicated thought experiments until you have the basics down.

please bear with me if I'm missing something.

It's hard to bear with you when you (a) cite no sources for your knowledge, while insisting that other people give sources for theirs, and (b) seem to be taking the attitude that you are right and everyone else who is trying to explain things to you is wrong. Please take heed.

 

[PeterDonis]

have a machine in it that sends out a qubit, fully entangled with the box' internal state

If the box has a cat in it, this is impossible. The best you can do is, roughly speaking, to entangle the emitted qubit with one qubit of the box's internal state. Since a cat has something like $10^{25}$ qubits' worth of internal state, the emitted qubit tells you basically nothing about the cat, no matter how well entangled it is with one qubit of the box's internal state.

 

[PeterDonis]

as asserted in RQM

What is RQM and what source are you using to learn about it?

 

[stevendaryl]

A photon in a superposition of polarization states is not considered to be polarized.

I sort of get what you're saying, but it doesn't sound exactly right. If we let $|H\rangle$ be a horizontal polarization state and $|V\rangle$ be a vertical polarization state, then the superposition $\alpha |H\rangle + \beta |V\rangle$ (with $|\alpha|^2 + |\beta|^2 = 1$) describes the state of a photon that is polarized at the angle $\theta$ away from horizontal, where $\theta = cos^{-1}(|\alpha|)$.

 

[David Byrden]

The best you can do is, roughly speaking, to entangle the emitted qubit with one qubit of the box's internal state. Since a cat has something like $10^{25}$ qubits' worth of internal state, the emitted qubit tells you basically nothing about the cat, no matter how well entangled it is with one qubit of the box's internal state.

I can't quite square this with what I'm told about the Schrodinger experiment.
Let's call my box a Byrden box. It has the same isolating ability as the Schrodinger box, plus the machinery to emit photons and measure them as I described.

Now, take a standard Schrodinger box and replace the usual radioactive source with a device that emits two fully entangled particles at a predetermined time.
One of the particles goes to the poison vial, where it gets measured, and it breaks the vial only if one of the two possible results is measured.
If I understand correctly, this will put the cat in a superposition of "alive" and "dead", like a standard Schrodinger box.

The other entangled particle has already been guided out of the box. Upon measuring it with external (but aligned) equipment, we learn the state of the internal particle.
And therefore we learn whether the cat is alive or dead - don't we?

To put it another way:
you're saying that the state of the cat simply cannot be embodied in the state of the particle. But, even in a standard Schrodinger box, there is a moment when the radioactive source decays and is about to kill the cat; and in that moment, the cat's destiny (not its entire final state) is fully embodied in that particle.
You see, I'm not asking for the entire state of the cat to be carried by the particle. I'm asking for one bit of its state. It happens to be a very interesting bit, picked out from trillions of unimportant bits, but nevertheless it is one bit.
I'm an electronics engineer. I studied Shannon's Information Theory. I wouldn't feed you nonsense.

So it seems to me that if the Byrden box doesn't work, then the Schrodinger box can't work either, not even the standard Schrodinger box. I hope you will resolve this for me?

Thank you for responding.

David

 

[stevendaryl]

If the box has a cat in it, this is impossible. The best you can do is, roughly speaking, to entangle the emitted qubit with one qubit of the box's internal state. Since a cat has something like $10^{25}$ qubits' worth of internal state, the emitted qubit tells you basically nothing about the cat, no matter how well entangled it is with one qubit of the box's internal state.

I don't understand what you're saying here. Let's make it more concrete. Suppose that you create a correlated electron/positron pair. The electron leaves the box. The positron goes into a detector in the box that measures its spin relative to the z-axis. If the detector measures spin-up, then the poison gas is released, killing the cat.

In that case, the spin of the positron reveals a huge amount of information about the state of the cat.

 

[David Byrden]

I sort of get what you're saying, but it doesn't sound exactly right. If we let $|H\rangle$ be a horizontal polarization state and $|V\rangle$ be a vertical polarization state, then the superposition $\alpha |H\rangle + \beta |V\rangle$ (with $|\alpha|^2 + |\beta|^2 = 1$) describes the state of a photon that is polarized at the angle $\theta$ away from horizontal, where $\theta = cos^{-1}(|\alpha|)$.

That is exactly what I learned from multiple seemingly reliable sources. Should I link to some of them?

David

 

[David Byrden]

What is RQM and what source are you using to learn about it?

Relational Quantum Mechanics. You could begin here;

https://en.wikipedia.org/wiki/Relational_quantum_mechanics

I find that some experiments simply can't be explained unless you allow different observers to hold different states for the same system at the same time. For example, the experiment that is detailed in this Renner-Frauchiger paper;

https://arxiv.org/pdf/1604.07422v1.pdf

The "agents" simply cannot all see the same state. (But bear in mind that Renner's own analysis, in that paper, contains an error.)David

 

[David Byrden]

The best you can do is, roughly speaking, to entangle the emitted qubit with one qubit of the box's internal state.

You're correct. I should have spoken more clearly.

I should have said; "fully entangled with the one qubit of the box' internal state that distinguishes between "Live" and "Dead".

In practice; the box will contain those two eigenstates in superposition. The photon-emitting machine will be identical in both states, except for its filter bank that gives the desired polarity to the emitted photon. That polarity was earlier determined by the alive/dead decision, therefore the machine entangles the photon with exactly that one bit of information.

I hope there's no theoretical reason why this can't be built? I can see practical problems. I can see us having to fire the photon at a time precisely determined by an atomic clock, for example, so that the "alive" and "dead" copies of the machine will fire at exactly the same time. But I'm asking for a theoretical reason why it can't be done.

Anyway, thank you for pointing that out.

David

 

[DrChinese]

I sort of get what you're saying, but it doesn't sound exactly right. If we let $|H\rangle$ be a horizontal polarization state and $|V\rangle$ be a vertical polarization state, then the superposition $\alpha |H\rangle + \beta |V\rangle$ (with $|\alpha|^2 + |\beta|^2 = 1$) describes the state of a photon that is polarized at the angle $\theta$ away from horizontal, where $\theta = cos^{-1}(|\alpha|)$.

A photon polarized at 0 degrees does not have a specific polarization at 45 degrees. I think most would say it is not polarized at 45 degrees. There might be some who would assert it has such a polarization, but it is unknown. Ditto for the polarization of entangled photons. I don't think there is anything controversial about this. The point is that if something is in a superposition on a basis: you can either maintain the superposition or you can reduce it to a more "known" state.

 

[Nugatory]

So it seems to me that if the Byrden box doesn't work, then the Schrodinger box can't work either, not even the standard Schrodinger box. I hope you will resolve this for me?

That's right, a "standard" Schrodinger box doesn't work with cats either.

Schrodinger proposed his thought experiment to indicate a problem in the then-current understanding of quantum mechanics. He wasn't arguing that the cat would remain in a dead/alive superposition until the box was opened; he was arguing that something was wrong because QM seemed to require this untenable result. It was several decades later (and after a wrong turn through the consciousness-causes-collapse swamp) before the discovery of quantum decoherence resolved the problem: ordinary unitary evolution rapidly turns superpositions of cats and other macroscopic systems into improper mixed states.

If you have something much simpler inside the box (a single particle is easy to reason about, so that's what I considered in my previous post) then long-lived superpositions can exist, but your suggested "nudging" technique still won't work for the reasons given in that post.

 

[David Byrden]

say it's just a single photon inside, so we're just working with a pair of polarization-entangled photons and we're trying to "nudge" the photon inside the box into a particular polarization state.
...
Your first measurement of the emitted photon will collapse that wave function to either $|\alpha_1\rangle|\beta_1\rangle$ (outside photon measured $\alpha_1$, we know inside photon is in state $\beta_1$) or $|\alpha_2\rangle|\beta_2\rangle$ (outside photon measured $\alpha_2$, we know inside photon is in state $\beta_2$).

Exactly. And, as I said, I choose $\alpha_1$ to be almost unity, so that I am almost certain to measure it. In that case, I have "nudged" the internal photon into the state $\beta_1$, have I not ? It's slightly different to its original state, and it's in a direction of my choosing. Therefore I call it "nudging".

We no longer have an entangled state so another measurement on the same outside photon won't do anything.

Correct. That's why I have the machine inside the box emitting photons at regular intervals, and I measure each photon only once.

If instead we try to arrange for the box to emit another entangled photon, we'll need some interaction inside the box to generate a new entangled state.

No, that's not the idea.
I proposed to leave the machine in a state determined by the first and only interaction with a quantum randomness generator, or radioactive emitter, or whatever you may call it.
Based on that interaction, the machine will configure itself to give an emitted photon one of two orthogonal polarities. And it will remain in that configuration for all the subsequent photons. And since the machine's configuration is entangled with the quantum measurement, it will fully entangle all those photons with the measurement. No?
The only difficulty here is that I need the two copies of the machine, which are in superposition, to generate coherent photons that interfere. But this is the kind of difficulty that the designers of quantum computers face and defeat, is it not?

... $|Live\rangle|\alpha_1\rangle+|Dead\rangle|\alpha_2\rangle$ where as before the $\alpha_i$ are states of the emitted photon and Live/Dead are pure states built up from all the internal degrees of freedom in the box. But such states cannot be prepared and measured because they immediately decohere.

Yes, the two eigenstates of the contents of the Byrden Box will immediately decohere. A live cat is very, very different to a dead cat. I don't expect to see cat interference fringes!
But what I propose is to design the photon-emitting machine such that it can emit coherent photons. Only the photons need to be identical across the two eigenstates, differing only in their polarity, not bearing any other information about the contents of the Byrden Box.

I know that the "many worlds" interpretation is distasteful to some, so the concept of arranging a collaboration between machines in two of the "many worlds" really won't be popular.
But all I care about is; does QM forbid it?

Thank you.

David

 

[David Byrden]

ordinary unitary evolution rapidly turns superpositions of cats and other macroscopic systems into improper mixed states.

Thank you, thank you, this is what I'm looking for! Can you refer me to a good textbook etc. that explains this properly?

David

 

[Nugatory]

Thank you, thank you, this is what I'm looking for! Can you refer me to a good textbook etc. that explains this properly?

An acceptable popularization is David Lindley's "Where does the weirdness go?" but it's not a textbook.
The references section of the Wikipedia article on "quantum decoherence" contains links to some of the important papers; start with Zeh, and also pay attention to the later Zurek ones.

 

[stevendaryl]

A photon polarized at 0 degrees does not have a specific polarization at 45 degrees. I think most would say it is not polarized at 45 degrees. There might be some who would assert it has such a polarization, but it is unknown. Ditto for the polarization of entangled photons. I don't think there is anything controversial about this. The point is that if something is in a superposition on a basis: you can either maintain the superposition or you can reduce it to a more "known" state.

This might be a matter of semantics, but to me, saying that a photon is polarized means that there exists a filter orientation such that the photon is guaranteed to pass the filter. Unpolarized means that there is no such orientation. So an entangled photon is unpolarized by that definition, while a photon that is in a superposition of $|H\rangle$ and $|V\rangle$ is polarized by that definition.

What you are saying is that for a particular filter orientation it may neither be the case that the photon is polarized at that orientation, nor at the orthogonal orientation. But that's not particularly a quantum issue. That's true with classical polarizations, as well.

 

[David Byrden]

An acceptable popularization is David Lindley's "Where does the weirdness go?" but it's not a textbook.

Thanks again.
The moment I saw the words "mixed state", I knew the game was up.

David

 

[PeterDonis]

I can't quite square this with what I'm told about the Schrodinger experiment.

What you're told by what source? You still have cited no sources.

 

[PeterDonis]

"fully entangled with the one qubit of the box' internal state that distinguishes between "Live" and "Dead".

One qubit of the box's internal state does not distinguish between "Live" and "Dead". If it did, you would be able to tell whether the cat was alive or dead by measuring just one qubit of its internal state. You can't.

 

[PeterDonis]

even in a standard Schrodinger box, there is a moment when the radioactive source decays and is about to kill the cat; and in that moment, the cat's destiny (not its entire final state) is fully embodied in that particle.

But you can't tell the state of that particle by making measurements on the cat, because there is no single qubit of the cat's internal state that is fully entangled with the particle's one qubit (assuming the particle's state is equivalent to one qubit, which shouldn't be problematic), and there is no yes/no measurement you can make on the cat as a whole that tells you the state of the particle's one qubit.

 

[PeterDonis]

Based on that interaction, the machine will configure itself to give an emitted photon one of two orthogonal polarities. And it will remain in that configuration for all the subsequent photons. And since the machine's configuration is entangled with the quantum measurement, it will fully entangle all those photons with the measurement. No?

No. This basically allows you to make multiple copies of the same qubit, which violates the no-cloning theorem.

 

[PeterDonis]

This basically allows you to make multiple copies of the same qubit

Or, alternatively, it allows you to fully entangle arbitrarily many qubits with a single qubit, which isn't possible. You can only fully entangle a single qubit with one other qubit.

 

[David Byrden]

But you can't tell the state of that particle by making measurements on the cat, because there is no single qubit of the cat's internal state that is fully entangled with the particle's one qubit (assuming the particle's state is equivalent to one qubit, which shouldn't be problematic), and there is no yes/no measurement you can make on the cat as a whole that tells you the state of the particle's one qubit.

Once again I must apologise for not making myself clear.
My intent was:
1. a quantum measurement with 2 outcomes, is made inside the box, by the machine
2. the machine kills the cat, or not, according to the result
3. the machine configures its filters according to the same result, and begins to send out photons

David

 

[David Byrden]

No. This basically allows you to make multiple copies of the same qubit, which violates the no-cloning theorem.

From Wikipedia; "amplification of a quantum signal can only happen with respect to some orthogonal basis".
https://en.wikipedia.org/wiki/No-cloning_theorem

The original qubit which determines the cat's fate has 2 states. They are, to my understanding, known and orthogonal. Does that not allow me to clone it?

David

 

[DrChinese]

So an entangled photon is unpolarized by that definition, while a photon that is in a superposition of $|H\rangle$ and $|V\rangle$ is polarized by that definition.

How would you describe the polarization of a photon emitted by an electron dropping to a lower orbital? I would say it has no polarization until measured on some basis.

 

[PeterDonis]

The original qubit which determines the cat's fate has 2 states. They are, to my understanding, known and orthogonal. Does that not allow me to clone it?

No, because you don't know which of the two possible outcome states the qubit has. So the actual state of the qubit is not known.

the machine configures its filters according to the same result

Can you explain this in more detail?

 

[David Byrden]

How would you describe the polarization of a photon emitted by an electron dropping to a lower orbital? I would say it has no polarization until measured on some basis.

Just guessing, but would that one be in a "mixed state" ?

David

 

[David Byrden]

Can you explain this in more detail?

Well, I'm not expert in how such apparatus need to be configured, but as a general approach:
The machine measures some quantum observable (?) that has 2 orthogonal values.
The machine sets a filter to one of two positions, depending on the measured value.
The positions are 90 degrees apart.
A pulse of photons is fired through the filter.
The photons that transit it are then in one of two orthogonal polarities, depending on what value was measured.

If we need to use a single photon rather than a pulse of photons, we would create the photon with a known polarisation, and use a series of filters to rotate its polarity gradually. Setting the filters at small angles apart, we can make the probability of absorption arbitrarily small by adding more filters.

David

 

[DrChinese]

...we would create the photon with a known polarisation, and use a series of filters to rotate its polarity gradually. Setting the filters at small angles apart, we can make the probability of absorption arbitrarily small by adding more filters.

Using the technique you describe, you cannot make the probability of absorption arbitrarily small by adding more filters. Obviously, arbitrarily small would include 0 probability. However, you can rotate the polarization state using a wave plate.

 

[Nugatory]

Once again I must apologise for not making myself clear.
My intent was:
1. a quantum measurement with 2 outcomes, is made inside the box, by the machine
2. the machine kills the cat, or not, according to the result
3. the machine configures its filters according to the same result, and begins to send out photons

That's fine, but I'm not clear on where you are going here (certainly not any sort of "steering" or "nudging" from outside the box).

Once the measurement in step #1 has been performed, we have a box with either a dead cat in it or a live cat, and filters configured in such a way that the box emits photons in one state if the cat is alive and in an orthogonal state if the cat is dead. There's no superposition or entanglement here, we just have an unusually complex apparatus (the cat is an inhumane alternative to a recording device attached to a photon detector, the emitted photon tells us what the measurement result was just as surely as if it were being reflected from the cat through a window in the box to our eyes) for measuring the polarization of the photon in the box.

If the photon measured in step #1 was entangled with a photon outside the box before the measurement, then a measurement of that photon will of course tell us the dead/live state of the cat (as will any photons sent later, as step #3). But our measurement of that photon has no effect on what's going on inside the box (otherwise the no-signalling theorem would be violated). All we have is two possibilities: 1) The cat is now dead and our external measurement says the cat is dead; 2) The cat is now alive and our external measurement says the cat is alive.

 

[David Byrden]

Once the measurement in step #1 has been performed, we have a box with either a dead cat in it or a live cat

Are you asserting that the Schrodinger's Cat experiment does not produce a cat in a superposition of "alive" and "dead" ? Because my box, in case I wasn't clear, is the same kind of box, with the added mechanisms that I described.

Davd