Quantum Bayesianism: Resolving the Interpretation Problem of Quantum Mechanics

[microsansfil]

Hello,

Does Quantum Bayesianism can fix the interpretation problem of Quantum Mechanics?

If we take in account

- the Bayesian approaches to brain function
- QBism: Is quantum uncertainty all in the mind ?
- The work of Jaynes, E. T., `How Does the Brain Do Plausible Reasoning?', in Maximum-Entropy and Bayesian Methods in Science and Engineering, 1, G. J. Erickson and C. R. Smith (eds.)
- The work of J. C. Baez (2003). "Bayesian Probability Theory and Quantum Mechanics".
- And many other more recent work on qbism http://search.arxiv.org:8081/?query=qbism&in=grp_physics


Patrick

 

[bhobba]

Its just another interpretation and like all of them has pro's and con's.

These days when I talk about the foundations of QM I like to reference the modern version of what's known as Gleason's Theorem.

See post 137:
https://www.physicsforums.com/showthread.php?t=763139&page=8

Once you understand the state simply encodes the probabilities of the basic QM axiom Gleason's theorem is applied to, then what the Bayesian view of those probabilities means is pretty clear.

Its not really adding anything except an interpretation of those probabilities. The same thing occurs in many areas of applied math where some prefer probabilities the Bayesian way, while others take a frequentest view. I don't think it's really an Earth shattering revelation - simply what is the best way to view it depending on what makes the most sense to you.

When you view it this way you see Copenhagen, where the state is subjective knowledge, it's really a Bayesian view, and the Ensemble interpretation the frequentest view:
http://en.wikipedia.org/wiki/Copenhagen_interpretation
http://en.wikipedia.org/wiki/Ensemble_interpretation

Basically its nothing of great relevance IMHO.

Thanks
Bill

 

[microsansfil]

See post 137:
https://www.physicsforums.com/showthread.php?t=763139&page=8

Once you understand the state simply encodes the probabilities of the basic QM axiom Gleason's theorem is applied to, then what the Bayesian view of those probabilities means is pretty clear.

Ok Thank.

Gleason's theorem seem to speack about a quantum logic which is a set of events (Eventworlds / Space-time) not a set of state (density opérator in the assiocated Hilbert space). is there an isomorphic between the two representation ?

Patrick

 

[vanhees71]

I don't buy the argument of the Qbists that the probabilities in quantum theory are subjective, at least not for pure states. In the case of pure states a complete set of compatible observables is determined. Then the system is objectively in the corresponding pure state. There is no freedom left to choose a probability distribution due to missing information. Thus the probabilities given by a pure state are objective. The uncertainty in the values of all other observables is not just in our minds but in the system.

 

[bhobba]

Gleason's theorem seem to speack about a quantum logic which is a set of events (Eventworlds / Space-time) not a set of state (density opérator in the assiocated Hilbert space). is there an isomorphic between the two representation

Its the logical consequence of the axiom I gave in its proof:

An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

It's a mapping of observational outcomes to a POVM which is the foundational principle of this approach. What Gleason shows is this implies the existence of a state that aids in calculating those probabilities. It shows exactly what a state is wrt the QM formalism - its a calculational tool - not something fundamental itself.

Interpretations have their own take - but as far as the formalism goes its simply a logical requirement from the fundamental axiom.

BTW I am with Vanhees on this - I don't like this subjective business either - but that's me - once you understand what's going on you can make up your own mind (irony intended ).

Applied mathematicians often use it for areas like credibility theory because it takes into account both "sampling" and "prior" information - but that's not really the situation in physics.

I must also be clear this is my view. The math of Gleason is valid, and no one really doubts that - but whether its telling us something important rather than simply saying the same thing as the usual axioms I mentioned at the end is another thing.

Again you can make up your own mind on that.

Thanks
Bill

 

[microsansfil]

I don't buy the argument of the Qbism.

I am interested on different view point like this one also. I prefer try to distinguish their physics predictive power rather than on philosophical beliefs.

Is only my point of view.

Patrick

 

[atyy]

Regardless of what one thinks of Quantum Bayesianism, it has one solid achievement: a new proof of the quantum de Finetti representation theorem by Caves, Fuchs and Schack. The original method of proof was given by Hudson and Mody. http://arxiv.org/abs/quant-ph/0104088

If one is broadly interested in how quantum states can be subjective, a different approach to defining the question is that of Harrigans and Spekkens. This differs from Quantum Bayesianism in that it asks if there are hidden variables, do the hidden variables uniquely specify the quantum state? http://arxiv.org/abs/0706.2661

Within that line of work, some important constraints are known:
http://arxiv.org/abs/1310.8302
http://arxiv.org/abs/1407.3005

Examples of hidden variables that make the quantum state "epistemic" in the sense of Harrigans and Spekkens are:
http://arxiv.org/abs/1201.6554
http://arxiv.org/abs/1303.2834

Even in a "non-epistemic" case like Bohmian mechanics, where the hidden variables fully determine the quantum state, there can be a use for Bayesian thinking:
http://arxiv.org/abs/0706.2522

 

[microsansfil]

An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

It's a mapping of observational outcomes to a POVM which is the foundational principle of this approach. What Gleason shows is this implies the existence of a state that aids in calculating those probabilities. It shows exactly what a state is wrt the QM formalism - its a calculational tool - not something fundamental itself.

Interpretations have their own take - but as far as the formalism goes its simply a logical requirement from the fundamental axiom.

It seem to be a good approach of QM which minimizes epistemological ambiguity. POVM is it an important special case of measure generalized not obeying the restrictive criteria of ideal projective measurement of von Neumann ?

These measures which provide a more or less partial information on the state of a quantum system are more closer to "real" experience situation than projective measurements experiences situations, isn't it ?

Patrick

 

[bhobba]

It seem to be a good approach of QM which minimizes epistemological ambiguity. POVM is it an important special case of measure generalized not obeying the restrictive criteria of ideal projective measurement of von Neumann ?

Its the other way around. A POVM is a generalisation of a Von-Neumann measurement. A Von-Neumann measurement is a POVM, but the effects are disjoint - its also known as a resolution of the identity. It could be based on Von-Neumann measurements but the version of Gleason that applies just to that is notoriously difficult - I have been through the proof and its reputation is deserved - but still understandable with effort. It also only works in dimension 3 and above.

But these days its well known resolutions of the identity are only one example of more general observation described by POVM - it's what results when you use a probe and do a Von-Neumann measurement on the probe. Not only that but the version of Gleason for POVM's is much simpler and has no limitations on dimension.

These measures which provide a more or less partial information on the state of a quantum system are more closer to "real" experience situation than projective measurements experiences situations, isn't it ?

Indeed they are closer to what usually occurs in practice where you have a probe and you observe the probe rather than make a direct observation.

Thanks
Bill