Schrödinger’s Cat and the Qbit

[RUTA]

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.

You missed the point of the Insight. If you use Schrodinger's Cat as an example of quantum superposition, then you are claiming it is a qubit and it is incumbent upon you to come up with that complementary measurement and its outcomes. I don't pretend to know what that measurement and its outcomes are, so I wouldn't use Schrodinger's Cat as an example of quantum superposition or claim it is a qubit myself.

 

[PeterDonis]

If you use Schrodinger's Cat as an example of quantum superposition, then you are claiming it is a qubit

Ah, I see. Your viewpoint would then be similar to that of Schrodinger himself (and to my own), since AFAIK he intended the cat thought experiment as a reductio ad absurdum of the claim that QM could be applied to macroscopic objects as if they were qubits.

 

[RUTA]

Ah, I see. Your viewpoint would then be similar to that of Schrodinger himself (and to my own), since AFAIK he intended the cat thought experiment as a reductio ad absurdum of the claim that QM could be applied to macroscopic objects as if they were qubits.

Exactly, although QM doesn't place a size limit on quanta, so maybe a clever experimentalist will someday create a qubit with one measurement equivalent to "open the box" and two outcomes as complex as Live Cat, Dead Cat. They have made quanta from 60-atom buckyballs, but the cat-box system is many orders of magnitude larger than a buckyball, so I doubt I'll live to see that :-)

 

[PeterDonis]

QM doesn't place a size limit on quanta

You seem to be using the term "quanta" in an unusual way:

They have made quanta from 60-atom buckyballs

They have done double slit experiments showing interference using 60-atom buckyballs, but that doesn't mean buckyballs are qubits or that they are elementary quantum systems with no subsystems, which are the two senses in which I'm used to seeing the word "quanta" used.

 

[RUTA]

You seem to be using the term "quanta" in an unusual way:


They have done double slit experiments showing interference using 60-atom buckyballs, but that doesn't mean buckyballs are qubits or that they are elementary quantum systems with no subsystems, which are the two senses in which I'm used to seeing the word "quanta" used.

Anything with a 2-dim Hilbert space is a qubit and any quantum in a double-slit experiment qualifies. The two outcomes for a position measurement in the double-slit experiment are slit 1 or slit 2. [For example, put the detector screen right up against the slits to make the position measurement.] If you're throwing baseballs (classical objects) through the slits, then you have a Cbit and there is no complementary measurement corresponding to slit 1 + slit 2. No matter how far you move the detector screen away from the slits, the baseballs will never start producing an interference pattern. If you have a quantum in the double-slit experiment, then you have a qubit, so there is a measurement with an outcome of slit 1 + slit 2, it's the constructive fringes of your interference pattern giving you a wavelength (lambda) whence momentum = h/lambda. The other momentum outcome is slit 1 - slit 2 corresponding to the destructive fringes. You can get a momentum measurement as the screen gets infinitely far away from the slits, so that the fringes of same order on either side of the center are equal distance from either slit. [Experimentalists typically use a lens such that detector screen locations 2f and f behind the lens give you position and momentum measurements.]

The complexity of the quantum used in the double-slit experiment doesn't matter. The same is true for the Stern-Gerlach experiment where silver atoms become qubits. Send those buckyballs through triple-slits and you have a qutrit. Put an atom in an atomic trap and it's no longer a quantum because it has definite position and momentum. It's exchanging about 100,000 photons per second to become a classical object in that case. It's all context dependent.

 

[PeterDonis]

Anything with a 2-dim Hilbert space is a qubit

As an approximation for analyzing particular experiments, this can work ok--basically you are ignoring all the other degrees of freedom of the particular system (buckyball, silver atom in an S-G experiment, etc.) because you have set up the experiment so those degrees of freedom, to a good enough approximation, do not affect the outcome.

However, if we're talking about a thought experiment like Schrodinger's cat, we're not talking about experimental approximations, we're talking about foundations of QM. And as far as foundations of QM are concerned, a buckyball is not a qubit, nor is a silver atom. For foundational purposes you simply can't ignore all the additional complexity. I thought we had agreed that that was part of Schrodinger's point.

 

[pines-demon]

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.

And I provided a measurement that measures the superposition without perturbing the system. If you want a measurement that measures the alive+dead and that also opens the box then I agree that it is not possible.

 

[RUTA]

As an approximation for analyzing particular experiments, this can work ok--basically you are ignoring all the other degrees of freedom of the particular system (buckyball, silver atom in an S-G experiment, etc.) because you have set up the experiment so those degrees of freedom, to a good enough approximation, do not affect the outcome.

However, if we're talking about a thought experiment like Schrodinger's cat, we're not talking about experimental approximations, we're talking about foundations of QM. And as far as foundations of QM are concerned, a buckyball is not a qubit, nor is a silver atom. For foundational purposes you simply can't ignore all the additional complexity. I thought we had agreed that that was part of Schrodinger's point.

In the reconstruction of QM via information-theoretic principles there is an axiom that states any subspace can be explored independently of the rest. Another axiom states that all subspaces of the same dimension have the same quantum probability structure. So, regardless of what the 2-dim subspace is part of and regardless of what physical situation is responsible for it, when you probe that subspace alone you have a qubit. Let's use this in a pretend situation analogous to Schrodinger's Cat.

Stern and Gerlach tell us that they have a measurement in which a silver atom acted like a qubit (they didn't know about spin, even after they had their result they thought they were exploring the orbital angular momentum of the valence electron). They said that when they passed silver atoms through an inhomogeneous magnetic field, half the time the atoms were deflected up towards the North magnetic pole and half the time they were deflected down towards the South magnetic pole. We're skeptical that they have a qubit with its complementarity from superposition because a silver atom has 47 electrons and a mass number of 108. It seems much more likely that they have only instantiated a Cbit, so we ask them to describe complementary measurements to verify they truly have 2-dim Hilbert subspace behavior, i.e., a qubit.

They answer that when they send atoms first deflected up from vertically-oriented magnets to another pair of vertically-oriented magnets, the atoms are deflected up 100% of the time. And, when they send them to horizontally-oriented magnets, half are deflected left and half are deflected right. Therefore, |V+> = |H+> + |H-> as required of a qubit. We agree they do have an example of superposition via the qubit!

So, by analogy, I'm simply asking those who claim Schrodinger's Cat is an example of superposition to pony up a measurement and outcome complementary to "open the box" and Live Cat or Dead Cat.

[Aside: I'm ignoring the requirement of *continuously* reversible transformations between pure states for simplicity, since I've yet to see complementarity alone for Schrodinger's Cat.]

 

[Devin-M]

I'm simply asking those who claim Schrodinger's Cat is an example of superposition to pony up a measurement and outcome complementary to "open the box" and Live Cat or Dead Cat.