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Can someone explain what the deal with qbism even is? Like, I get that when you do weak measurements the random walk the qubit takes [2] looks basically identi

Can someone explain what the deal with qbism even is? Like, I get that when you do weak measurements the random walk the qubit takes [2] looks basically identical to inference. That's not too surprising, given how similar the definition of quantum states is to the definition of probability distributions. But superpositions aren't literally probability distributions. In particular, unlike with probabilities, you can prove that super-logical agents can't rationally disagree about the superposition that a state is in. Superpositions can't be observer-dependent in the way that probability distributions can, because you can create situations where agents who are disagreeing about a superposition must be risking the highest of Bayesian sins: seeing something happen to which they assigned a 0% probability [1]. To me, this directly disagrees with Qbism's tendency to think about quantum states as subjective instead of objective. 1: http://www.scottaaronson.com/blog/?p=822 http://www.scottaaronson.com/blog/?p=822 2: http://algorithmicassertions.com/2016/04/24/eves-quantum-clone-computer.html http://algorithmicassertions.com/2016/04/24/eves-quantum-clo...

n4r9 10y ago
I can try to offer something about the tension between the PBR theorem and QBism. I sat through a conference talk by Chris Fuchs not long after PBR came out, although some of the detail will probably be lost in translation. PBR assumes that the quantum state of a system represents a state of ignorance or partial information concerning an objective, underlying (hidden variable) reality. In QBism the quantum state of a system instead represents an agent's beliefs about what will happen in future interactions with the system. There's no mention of an underlying observer-independent reality. It's not assumed that the physical state of a system can be portrayed with objective, observer-independent variables, nor that a given quantum state assigns probabilities to those variables. A cynical summary might be that QBism weasles out of PBR type issues by sticking to radical/subjective Bayesianism, rather than objective Bayesianism.
- ajb 10y ago
  Does it require the subjective probability to be complex-valued? (as in eg https://arxiv.org/pdf/hep-th/9307019.pdf https://arxiv.org/pdf/hep-th/9307019.pdf, http://physics.bu.edu/~youssef/quantum/quantum_refs.html http://physics.bu.edu/~youssef/quantum/quantum_refs.html)
  - n4r9 10y ago
    I wouldn't say it's required, no. There are many reformulations of quantum probabilities. The approach often taken in QBism is to model the state of a quantum system using a restricted subset of the full probability simplex. For example, a spin-1/2 particle has three degrees of freedom (x, y, z), each of which can be measured to be up or down. The state of the particle is uniquely defined by the probability it associates to each measurement outcome. These are ordinary probabilities between 0 and 1. However certain probability distributions are disallowed, such as deterministically measuring up in all three directions.
  - deleted 10y ago
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- Strilanc 10y ago
  > In QBism the quantum state of a system instead represents an agent's beliefs about what will happen in future interactions with the system. Okay, I think this is my problem. I don't see how these kinds of statement are about quantum mechanics specifically. For example, I could say "In Newtonian mechanics, the classical state of a system represents an agent's beliefs about what will happen in future interactions with the system.". To me, that sentence tracks exactly as well as the quantum variant. But surely qbism is more than just some kind of hardcore solipsism applied to superpositions. It also seems that the claim that a quantum state can't be portrayed with objective, observer-independent variables is simply wrong. We all agree on how to objectively represent the spin of an electron: as a vector in Hilbert space. And different observers doing an experiment will come to agree on which specific vector to use.
- Strilanc 10y ago
  Maybe I should put it this way... what do we gain by accepting qbism? For example, accepting many-worlds gives parsimony of postulates. The number of postulates goes down, because the Born rule is derived from decoherence and unitarity instead of being postulated from directly. Accepting a collapse interpretation gives easy translation between theory and practice. You don't have to justify squaring the amplitudes, you just do it and it works. Accepting a pilot-wave interpretation gives you deterministic rules and an exact single state. Accepting a qbism interpretation gives you...?
  - n4r9 10y ago
    Well, one answer is that it resolves the measurement problem, and variants like Wigners friend, in a coherent way and without the additional issues posed by those other interpretations (although collapse interpretations aren't quite "interpretations" in the same sense). As I understand it - being neither an expert or advocate, just interested in quantum foundations - the QBist attitude is that all those no-go theorems point to quantum theory being little more than a dutch book of the universe. The whole idea is you're barking up the wrong tree if you want to give a direct physical meaning to the quantum state. If you're already welded to the notion that a quantum state corresponds to an external reality then you'll probably never find QBism very satisfying. And that's fair enough. Don't get me wrong here - what you're saying is a very valid criticism and probably what most people have against QBism. I myself find it difficult to see what value it adds, unless you already have a certain approach to scientific knowledge. I was just trying trying to clarify some of the points your original post made. There is a lot of literature about how QBism relates to various results and other interpretations. Chris Fuchs' own writings are very entertaining and worth a read.
  - deleted 10y ago
    [deleted]

n4r9 10y ago

I can try to offer something about the tension between the PBR theorem and QBism. I sat through a conference talk by Chris Fuchs not long after PBR came out, although some of the detail will probably be lost in translation. PBR assumes that the quantum state of a system represents a state of ignorance or partial information concerning an objective, underlying (hidden variable) reality. In QBism the quantum state of a system instead represents an agent's beliefs about what will happen in future interactions with the system. There's no mention of an underlying observer-independent reality. It's not assumed that the physical state of a system can be portrayed with objective, observer-independent variables, nor that a given quantum state assigns probabilities to those variables. A cynical summary might be that QBism weasles out of PBR type issues by sticking to radical/subjective Bayesianism, rather than objective Bayesianism.

ajb 10y ago
Does it require the subjective probability to be complex-valued? (as in eg https://arxiv.org/pdf/hep-th/9307019.pdf https://arxiv.org/pdf/hep-th/9307019.pdf, http://physics.bu.edu/~youssef/quantum/quantum_refs.html http://physics.bu.edu/~youssef/quantum/quantum_refs.html)
- n4r9 10y ago
  I wouldn't say it's required, no. There are many reformulations of quantum probabilities. The approach often taken in QBism is to model the state of a quantum system using a restricted subset of the full probability simplex. For example, a spin-1/2 particle has three degrees of freedom (x, y, z), each of which can be measured to be up or down. The state of the particle is uniquely defined by the probability it associates to each measurement outcome. These are ordinary probabilities between 0 and 1. However certain probability distributions are disallowed, such as deterministically measuring up in all three directions.
- deleted 10y ago
  [deleted]
Strilanc 10y ago
> In QBism the quantum state of a system instead represents an agent's beliefs about what will happen in future interactions with the system. Okay, I think this is my problem. I don't see how these kinds of statement are about quantum mechanics specifically. For example, I could say "In Newtonian mechanics, the classical state of a system represents an agent's beliefs about what will happen in future interactions with the system.". To me, that sentence tracks exactly as well as the quantum variant. But surely qbism is more than just some kind of hardcore solipsism applied to superpositions. It also seems that the claim that a quantum state can't be portrayed with objective, observer-independent variables is simply wrong. We all agree on how to objectively represent the spin of an electron: as a vector in Hilbert space. And different observers doing an experiment will come to agree on which specific vector to use.
Strilanc 10y ago
Maybe I should put it this way... what do we gain by accepting qbism? For example, accepting many-worlds gives parsimony of postulates. The number of postulates goes down, because the Born rule is derived from decoherence and unitarity instead of being postulated from directly. Accepting a collapse interpretation gives easy translation between theory and practice. You don't have to justify squaring the amplitudes, you just do it and it works. Accepting a pilot-wave interpretation gives you deterministic rules and an exact single state. Accepting a qbism interpretation gives you...?
- n4r9 10y ago
  Well, one answer is that it resolves the measurement problem, and variants like Wigners friend, in a coherent way and without the additional issues posed by those other interpretations (although collapse interpretations aren't quite "interpretations" in the same sense). As I understand it - being neither an expert or advocate, just interested in quantum foundations - the QBist attitude is that all those no-go theorems point to quantum theory being little more than a dutch book of the universe. The whole idea is you're barking up the wrong tree if you want to give a direct physical meaning to the quantum state. If you're already welded to the notion that a quantum state corresponds to an external reality then you'll probably never find QBism very satisfying. And that's fair enough. Don't get me wrong here - what you're saying is a very valid criticism and probably what most people have against QBism. I myself find it difficult to see what value it adds, unless you already have a certain approach to scientific knowledge. I was just trying trying to clarify some of the points your original post made. There is a lot of literature about how QBism relates to various results and other interpretations. Chris Fuchs' own writings are very entertaining and worth a read.
- deleted 10y ago
  [deleted]