Schrödinger’s Cat and the Qbit

[RUTA]

The concept of quantum superposition (or superposition for short) is very counterintuitive, as Schr$\ddot{\text{o}}$dinger noted in 1935 writing [1], “One can even set up quite ridiculous cases.” To make his point, he assumed a cat was closed out of sight in a box with a radioactive material that would decay with 50% probability within an hour. If a radioactive decay occurred, a deadly gas would be released in the box killing the cat. Since the decay was represented by a quantum wavefunction in a superposition of 50% “yes” and 50% “no” regarding the decay after one hour, the cat was also represented by a quantum wavefunction in a superposition of 50% “alive” and 50% “dead” (Figure 1). Schr$\ddot{\text{o}}$dinger wrote [1]:

The wavefunction of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

This has become known as Schr$\ddot{\text{o}}$dinger’s Cat...

Continue reading...

 

[Swamp Thing]

Being alive or dead is a macrostate with a huge number of microstates. In fact, the gas capsule being whole or broken is also a macrostate with lots of microstates. Is this relevant / useful to make sense of things?

 

[RUTA]

Being alive or dead is a macrostate with a huge number of microstates. In fact, the gas capsule being whole or broken is also a macrostate with lots of microstates. Is this relevant / useful to make sense of things?

That's certainly true and it's relevant if you want to know the likelihood of decoherence. But, there is no decoherence if you want the box-cat combo to be a Qbit. Of course, no decoherence is ridiculous for something so large (with so many microstates) over an hour, so the thought experiment isn't practical. The point is simply that quantum mechanics says that if you could make the box-cat combo a quantum system and keep it that way (no decoherence), then it's a Qbit and there has to be a measurement whose outcome is the (DeadCat + LiveCat) state, not merely one or the other.

 

[pines-demon]

Lovely article. I agree with much of it, but I think I missed what the conclusion implied.

If the article stating that Schrödinger's cat is a bad analogy/explanation to introduce the topic of quantum superpositions and qubits, I agree.
If the article is stating that Schrödinger's cat is something else then I am missing what the questions at the end are pointing to.

I think that the Schrödinger's cat should be only discussed when the basics of quantum mechanics have been understood and the students are ready to tackle the problem of the classical limit of quantum mechanics and decoherence.

 

[gentzen]

Lovely article. I agree with much of it, but I think I missed what the conclusion implied

I also love the article. I especially love that no conclusion was given, or implied. Of course, I fear that this article is only intended as introduction for another article or book, where a conclusion will be spelled out. But for the moment, without that follow-up, the article is great.

 

[pines-demon]

There is also the claim in the article that we cannot measure in an orthogonal-basis for the Schrödinger's cat state, but I think the questions are even weirder if we allow it. If the box emitted a polarized photon to tell us the state of the cat (horizontal if the cat is dead, vertical if alive), we can then measure the polarization diagonally. What would that tell us?

 

[RUTA]

Lovely article. I agree with much of it, but I think I missed what the conclusion implied.

If the article stating that Schrödinger's cat is a bad analogy/explanation to introduce the topic of quantum superpositions and qubits, I agree.
If the article is stating that Schrödinger's cat is something else then I am missing what the questions at the end are pointing to.

I think that the Schrödinger's cat should be only discussed when the basics of quantum mechanics have been understood and the students are ready to tackle the problem of the classical limit of quantum mechanics and decoherence.

Schrodinger’s cat is used routinely in popular introductions to quantum superposition. However, I’ve never seen any such introduction mention measurements other than opening the box to find the cat alive or dead. As I state in the Insight, you could just as well be talking about a classical situation given that information alone. The difference between a real quantum situation (Qbit) and simple ignorance about a classical situation (Cbit) is profound and needs to be pointed out when trying to introduce quantum superposition. That’s why I wrote this Insight :-)

 

[RUTA]

There is also the claim in the article that we cannot measure in an orthogonal-basis for the Schrödinger's cat state, but I think the questions are even weirder if we allow it. If the box emitted a polarized photon to tell us the state of the cat (horizontal if the cat is dead, vertical if alive), we can then measure the polarization diagonally. What would that tell us?

In order for the polarization of the photon coming from inside the box and measured outside the box to convey information from inside the box, directions in space inside the box would have to be coordinated with directions in space outside the box. How can that be done if the box is truly screened off?

 

[Nugatory]

I think that the Schrödinger's cat should be only discussed when the basics of quantum mechanics have been understood and the students are ready to tackle the problem of the classical limit of quantum mechanics and decoherence.

Agree, but the popularizers get into the discussion first and once they do it’s impossible to silence them.

 

[pines-demon]

In order for the polarization of the photon coming from inside the box and measured outside the box to convey information from inside the box, directions in space inside the box would have to be coordinated with directions in space outside the box. How can that be done if the box is truly screened off?

Does it though? In a real qubit, let's say that it emits a photon to tell which state it is. A state of the form $|0H\rangle+|1V\rangle$ where 0,1 are the states of the qubit and $H,V$ the polarizations. Measuring in the horizontal-vertical basis collapses the qubit but measuring in the diagonal basis does not collapse the superposition (or at least not in the basis that we care).

 

[WWGD]

It's very difficult to tread that line between popularization and rigor without going too far in either direction. I just consider and try to filter that when I run into such accounts.

 

[RUTA]

Does it though? In a real qubit, let's say that it emits a photon to tell which state it is. A state of the form $|0H\rangle+|1V\rangle$ where 0,1 are the states of the qubit and $H,V$ the polarizations. Measuring in the horizontal-vertical basis collapses the qubit but measuring in the diagonal basis does not collapse the superposition (or at least not in the basis that we care).

If the state is (H + V) and you do a V or H measurement, 50% of the photons will pass your polarizer and when they do pass they are then in the V or H state. If you measure in the diagonal (D) basis, 100% will pass and they are in the D = (H + V) state just like when they went in. Likewise, if Schrodinger's cat is a Qbit, there has to be a measurement such that (LC + DC) is the state after measurement.

Now as to conveying information from inside the box, all you know is whether or not a photon passed the polarizer on the outside. After that measurement you know the state of the photon, but you don't know what it was before the measurement. So, you need to have directions in space aligned between the inside and outside of the box and that requires a lot more information transfer which leads to decoherence.

 

[pines-demon]

If the state is (H + V) and you do a V or H measurement, 50% of the photons will pass your polarizer and when they do pass they are then in the V or H state. If you measure in the diagonal (D) basis, 100% will pass and they are in the D = (H + V) state just like when they went in. Likewise, if Schrodinger's cat is a Qbit, there has to be a measurement such that (LC + DC) is the state after measurement.

My version includes entanglement. Suppose that you have some reaction that produces a particle entangled with some photon. So the particle is spin projected up (in the z axis) and the photon is horizontal. Alternatively the spin is down and the photon is vertical. If you measure the photon in the horizontal-vertical basis you do collapse the particle spin in the z axis. But if you measure the photon in the diagonal basis you collapse the spin into a superposition of up and down.

I do not see what would be different with a cat (assuming we can make the box)? A single photon will not make the superposition go away unless you measure in the right basis.

Now as to conveying information from inside the box, all you know is whether or not a photon passed the polarizer on the outside. After that measurement you know the state of the photon, but you don't know what it was before the measurement.

With the escaping photon you might not know what the state was before you measure the photon, but at least you know what the cat state is before opening the box.

So, you need to have directions in space aligned between the inside and outside of the box and that requires a lot more information transfer which leads to decoherence.

What do you mean by this?

 

[RUTA]

My version includes entanglement. Suppose that you have some reaction that produces a particle entangled with some photon. So the particle is spin projected up (in the z axis) and the photon is horizontal. Alternatively the spin is down and the photon is vertical. If you measure the photon in the horizontal-vertical basis you do collapse the particle spin in the z axis. But if you measure the photon in the diagonal basis you collapse the spin into a superposition of up and down.

I do not see what would be different with a cat (assuming we can make the box)? A single photon will not make the superposition go away unless you measure in the right basis.

With the escaping photon you might not know what the state was before you measure the photon, but at least you know what the cat state is before opening the box.

What do you mean by this?

But in order to know that the directions in space corresponding to V and H outside the box align with V and H inside the box, lots more information has to be shared.

 

[pines-demon]

But in order to know that the directions in space corresponding to V and H outside the box align with V and H inside the box, lots more information has to be shared.

Why the argument on the "directions in space aligned between the inside and outside" does not matter for the spin qubit entangled with the photon case?

 

[RUTA]

Why the argument on the "directions in space aligned between the inside and outside" does not matter for the spin qubit entangled with the photon case?

That's my question, too.

In quantum mechanics, the state providing the distribution of outcomes among the detectors contains information about the entire spatiotemporal context of the experiment given a particular source and its detectors (usually just implied, but necessary for understanding what the state is describing). I'm not talking about hidden variables, what I'm saying applies to the quantum state even if it is assumed to be complete. You have to know what the symbols in the mathematical representation of the state mean in terms of detectors for a source and their locations and/or orientations in space, so as to make physical sense of the distribution of outcomes for the experiment.

For example, the singlet state says when the detector settings are the same Alice and Bob will get opposite outcomes. So, you need to know what a detector and its settings are, what an outcome means for that detector, and you need a source that produces those outcomes for those detectors.

Anyway, if the box-cat system is screened off, then it's not sharing information with us (its environment). But, we need (a lot of) information to coordinate common directions in space between the inside and outside of the box in order to make sense of the quantum state.

 

[pines-demon]

That's my question, too.

In quantum mechanics, the state providing the distribution of outcomes among the detectors contains information about the entire spatiotemporal context of the experiment given a particular source and its detectors (usually just implied, but necessary for understanding what the state is describing). I'm not talking about hidden variables, what I'm saying applies to the quantum state even if it is assumed to be complete. You have to know what the symbols in the mathematical representation of the state mean in terms of detectors for a source and their locations and/or orientations in space, so as to make physical sense of the distribution of outcomes for the experiment.

Can reformulate this in terms of a (non macrocat and non photonic) qubit? Let us take a superconducting qubit, its state does not depend on the direction of space (contrary to a spin qubit). Now I can get the state of the qubit by sending some microwave signal and getting its reflection. What has this to do with space?

If you mean that this has to do with the observable you measure, sure I am telling you my analogy with a qubit and a photon is correlated. The qubit has state 0 if H is measured, 1 if vertical. But I could replace the photon with some particle with two degrees of freedom that are not spatial.

 

[RUTA]

Can reformulate this in terms of a (non macrocat and non photonic) qubit? Let us take a superconducting qubit, its state does not depend on the direction of space (contrary to a spin qubit). Now I can get the state of the qubit by sending some microwave signal and getting its reflection. What has this to do with space?

If you mean that this has to do with the observable you measure, sure I am telling you my analogy with a qubit and a photon is correlated. The qubit has state 0 if H is measured, 1 if vertical. But I could replace the photon with some particle with two degrees of freedom that are not spatial.

There has to be a source of microwaves that after emission reflect off of some 'thing' and are subsequently detected by some other 'thing'. That's a spatial (and temporal) configuration of objects (and events).

 

[pines-demon]

There has to be a source of microwaves that after emission reflect off of some 'thing' and are subsequently detected by some other 'thing'. That's a spatial (and temporal) configuration of objects (and events).

Ok. However I still do not see what is the point that you are trying to make.

What I say is that you can have a qubit that emits a photon and by that photon we can understand the state of the qubit. You seem to imply that this principle is not possible with the cat-box thought experiment.
The whole cat-box experiment is impossible for an large number of practical reasons I do not see why a single photon escaping the box makes it more or less attainable.

 

[RUTA]

Ok. However I still do not see what is the point that you are trying to make.

What I say is that you can have a qubit that emits a photon and by that photon we can understand the state of the qubit. You seem to imply that this principle is not possible with the cat-box thought experiment.
The whole cat-box experiment is impossible for an large number of practical reasons I do not see why a single photon escaping the box makes it more or less attainable.

That single photon conveys the state of the qubit because it's polarization has meaning in the context of the source, detectors, and measurement settings. Since the box is screened off, you don't have that contextual information.

 

[pines-demon]

That single photon conveys the state of the qubit because it's polarization has meaning in the context of the source, detectors, and measurement settings. Since the box is screened off, you don't have that contextual information.

The qubit is also screened off, if not you lose the state of the qubit....

 

[RUTA]

The qubit is also screened off, if not you lose the state of the qubit....

Yes, but to know the state of the qubit, so as to acquire information from it, you need information about its source. If a random photon passes thru your vertically-oriented polarizer, you know it's now a V photon, but that doesn't tell you anything about what it was before you measured it, except it wasn't an H photon. And for that to convey information about its source, those directions in space have to be established between the source and your polarizer. The cat-box system is screened off, so you can't even see it let alone establish a common vertical direction in space.

 

[pines-demon]

Yes, but to know the state of the qubit, so as to acquire information from it, you need information about its source. If a random photon passes thru your vertically-oriented polarizer, you know it's now a V photon, but that doesn't tell you anything about what it was before you measured it, except it wasn't an H photon. And for that to convey information about its source, those directions in space have to be established between the source and your polarizer. The cat-box system is screened off, so you can't even see it let alone establish a common vertical direction in space.

Make the qubit trigger the poison and emit the photon. You can calibrate the measurement of the photon without the cat, and then perform the experiment with the cat.

 

[RUTA]

Make the qubit trigger the poison and emit the photon. You can calibrate the measurement of the photon without the cat, and then perform the experiment with the cat.

Yeah, I don't think you need polarization info, you just need to know if the poison is released. For that the photon alone will work. The problem is, you can't see the box and you don't know where it is, so you'd have to somehow distinguish the photon from the box from all those you're receiving from all directions otherwise. Once you figure out a configuration for doing that (measurement producing either LC or DC), maybe you will know how to change the configuration to get (LC + DC) as the outcome. Then Schrodinger's Cat would be a qubit :-)

 

[pines-demon]

The problem is, you can't see the box and you don't know where it is, so you'd have to somehow distinguish the photon from the box from all those you're receiving from all directions otherwise.

Make the photon be a gamma photon or some frequency that you recognize easily. Coordinate the direction of emission of the photon from the box with the axis given by one of the vertices of the box.

I am sorry if this is getting tiresome and off-topic.
Mentors: Maybe this back-and-forth can be thrown into a different thread (beginning in post #6 or #8).

 

[RUTA]

Make the photon be a gamma photon or some frequency that you recognize easily. Coordinate the direction of emission of the photon from the box with the axis given by one of the vertices of the box.

I am sorry if this is getting tiresome and off-topic.
Mentors: Maybe this back-and-forth can be thrown into a different thread (beginning in post #6 or #8).

Don't worry about being off topic. It's relevant to my Insight and it's an interesting conversation :-)

I don't know how many gamma rays impinge on any cm^2 at the surface of Earth per unit time, so I can't speak to that. However, again, we don't see the box and have no way to coordinate directions in space between the inside and outside of the box (until after decoherence), so it will be difficult to figure out where and when a gamma ray detection is relevant to the measurement.

 

[pines-demon]

Don't worry about being off topic. It's relevant to my Insight and it's an interesting conversation :-)

I don't know how many gamma rays impinge on any cm^2 at the surface of Earth per unit time, so I can't speak to that. However, again, we don't see the box and have no way to coordinate directions in space between the inside and outside of the box (until after decoherence), so it will be difficult to figure out where and when a gamma ray detection is relevant to the measurement.

Shield the lab with lead. If a photon comes from inside the box to the outside of the box, in the calibrated direction, then that is the detection that we need. Again if we can make the box, we can allow the box to let a single photon pass through.

 

[RUTA]

Shield the lab with lead. If a photon comes from inside the box to the outside of the box, in the calibrated direction, then that is the detection that we need. Again if we can make the box, we can allow the box to let a single photon pass through.

Ok, time to address the real question: how do we do an actual measurement where the outcome is |LC> + |DC> rather than |LC> or |DC>?

 

[pines-demon]

Ok, time to address the real question: how do we do an actual measurement where the outcome is |LC> + |DC> rather than |LC> or |DC>?

I was suggesting that the photon comes up polarized vertical if the cat is alive and horizontal if the cat drops dead (think of the cat as made of transparent sugar water that rotates the polarization , if the cat stands the photon rotates into vertical). Of course measuring in this basis tells you nothing about the experiment.

However if you measure in the diagonal basis and you get a consistent 100% antidiagonal photons, then your cat is in superposition. Of course you need to convince your funding agency that you need that many sugary cats for your experiment.

 

[PeterDonis]

how do we do an actual measurement where the outcome is |LC> + |DC> rather than |LC> or |DC>?

If you're pretending the cat is a qubit, we already know how to do this for qubits; it's just measuring in, say, the spin-x basis instead of the spin-z basis. So I don't see what the difficulty is. Once you've discarded all the actual complexity in the problem, by pretending the cat is a qubit instead of actually dealing with the fact that it's a huge system composed of the equivalent of something like $10^{25}$ qubits with all kinds of interactions between them, you can't then pretend that there is any difficulty left in the measurement.

 

[RUTA]

If you're pretending the cat is a qubit, we already know how to do this for qubits; it's just measuring in, say, the spin-x basis instead of the spin-z basis. So I don't see what the difficulty is. Once you've discarded all the actual complexity in the problem, by pretending the cat is a qubit instead of actually dealing with the fact that it's a huge system composed of the equivalent of something like $10^{25}$ qubits with all kinds of interactions between them, you can't then pretend that there is any difficulty left in the measurement.

In order for the cat-box system to be a qubit (not a simple Cbit), there has to be a "vertical spin" measurement corresponding to its "horizontal spin" representation (where the "horizontal spin" measurement is "open the box" and the two possible outcomes are LC and DC). What is that measurement? I'm not pretending to know.

 

[RUTA]

I was suggesting that the photon comes up polarized vertical if the cat is alive and horizontal if the cat drops dead (think of the cat as made of transparent sugar water that rotates the polarization , if the cat stands the photon rotates into vertical). Of course measuring in this basis tells you nothing about the experiment.

However if you measure in the diagonal basis and you get a consistent 100% antidiagonal photons, then your cat is in superposition. Of course you need to convince your funding agency that you need that many sugary cats for your experiment.

We have to be able to make an actual measurement that produces Live Cat + Dead Cat comparable to "open the box" where the outcomes are Live Cat or Dead Cat. You can't do that with a single photon, we need something the size of a cat in the outcome someplace. As I said to Peter Donis, I have no idea what such a measurement would be, but there has to be one if Schrodinger's Cat is a qubit not a Cbit.

 

[pines-demon]

We have to be able to make an actual measurement that produces Live Cat + Dead Cat comparable to "open the box" where the outcomes are Live Cat or Dead Cat. You can't do that with a single photon, we need something the size of a cat in the outcome someplace. As I said to Peter Donis, I have no idea what such a measurement would be, but there has to be one if Schrodinger's Cat is a qubit not a Cbit.

The measurement of the photon in another basis is the measurement of the superposition. If you want to open the box and see an alive+dead cat that is not possible, it is like asking to see both spin up-z and spin down-z with a Stern-Gerlach measurement oriented in z, it is not possible.

 

[PeterDonis]

In order for the cat-box system to be a qubit (not a simple Cbit), there has to be a "vertical spin" measurement corresponding to its "horizontal spin" representation (where the "horizontal spin" measurement is "open the box" and the two possible outcomes are LC and DC). What is that measurement? I'm not pretending to know.

Well, you're the one who said we can pretend that the cat-box system is a qubit. So the burden is on you to produce such a measurement. If you can't, then maybe you need to rethink your claim that the cat-box system can be treated as a qubit.

 

[RUTA]

The measurement of the photon in another basis is the measurement of the superposition. If you want to open the box and see an alive+dead cat that is not possible, it is like asking to see both spin up-z and spin down-z with a Stern-Gerlach measurement oriented in z, it is not possible.

No, when people use Schrodinger's Cat as a example of superposition, they say the measurement is "open the box" and the outcomes are Live Cat or Dead Cat, so if you want that to be a qubit, then you need a measurement and outcomes equivalent in scale and constituents to "open the box" and Live Cat, Dead Cat. That's the point of the Insight.