3 ms·

> - quantum mechanics cannot be exploited for exponential computation As far as we know for now, [a variant of [0] ] this one is the wrong claim: we do have al

> - quantum mechanics cannot be exploited for exponential computation As far as we know for now, [a variant of [0] ] this one is the wrong claim: we do have algorithms (Shor's, Grover's) that are faster on Quantum Computers than any known classical algorithm. Of course, we do not yet have any proof that a faster classical algorithm can't exist, so the possibility remains open that this claim remains true. BUT, if this claim turns out to be true, then it is extremely likely that either one or both of the other 2 claims will immediately turn out to be wrong. [0] I would note that the "exponential" part is somewhat of a red herring. If there is any kind of asymptotic speed-up that QCs fundamentally have over classical computers, even if it's just quadratic, then the larger point will remain valid. > In a sense, the sci-fi concept of the ansible, where quantum collapse effects are exploited for FTL signaling, is more plausible than the view where quantum systems collapse instantly, but cannot be exploited for FTL. This is also what rubs me the wrong way about entanglement, and seems a very tantalizing thread to pull at if one wanted a more fundamental theory. The other thread of course is the measurement problem.

eigenket 6y ago
Your two threads seem to be essentially the same thread. The "weird stuff" in entanglement comes pretty directly from collapse as part of measurement. If you drop this and go to something like many worlds then things look a bit nicer, but then you have so solve the measurement problem in many worlds, which seems quite hard.
- Koshkin 6y ago
  But collapse is fake news, as it were. A state can be called a “superposition” only relative to a particular set of basis states, which, in turn, depends on what observable we are talking about, and the “collapse” is simply yet another way a state can change.
  - simiones 6y ago
    No, collapse or some alternative to it is a fundamental component of quantum mechanics. Without it, quantum mechanics makes wildly wrong predictions. The Schrodinger equation almost always predicts that a particle has some particular amplitude at many different locations. However, if you try to detect a particle, you will never find it at more than one location. Furthermore, once the particle is detected at one particular location, you need to update the Schrodinger equation to give it amplitude 1 at that location and 0 everywhere else - if you don't perform this nonlinear update and instead use the old wave-function, the predictions for further experiments will be completely off. Now, the physical interpretation of this collapse varies wildly between different interpretations of QM, but some variant of it is always required - otherwise, the observations simply do not match the math. We don't yet have any theory consistent with QM that can make predictions without applying the Born rule.
    - FeepingCreature 6y ago
      I believe in Many-Worlds, the update step falls out of decoherence "for free." Because you are also in superposition after the measurement, the "you have measured 1" part of your wavefunction of course measures amplitude 1. That doesn't give you the Born rule though - I believe there's some attempts to get it out of game theory [1], where they show that given sufficiently long timespans, "almost every" worldline has a history with quantum measurements whose distribution matches the Born probabilities. [1] https://arxiv.org/abs/0906.2718 https://arxiv.org/abs/0906.2718

eigenket 6y ago

Your two threads seem to be essentially the same thread. The "weird stuff" in entanglement comes pretty directly from collapse as part of measurement. If you drop this and go to something like many worlds then things look a bit nicer, but then you have so solve the measurement problem in many worlds, which seems quite hard.

Koshkin 6y ago
But collapse is fake news, as it were. A state can be called a “superposition” only relative to a particular set of basis states, which, in turn, depends on what observable we are talking about, and the “collapse” is simply yet another way a state can change.
- simiones 6y ago
  No, collapse or some alternative to it is a fundamental component of quantum mechanics. Without it, quantum mechanics makes wildly wrong predictions. The Schrodinger equation almost always predicts that a particle has some particular amplitude at many different locations. However, if you try to detect a particle, you will never find it at more than one location. Furthermore, once the particle is detected at one particular location, you need to update the Schrodinger equation to give it amplitude 1 at that location and 0 everywhere else - if you don't perform this nonlinear update and instead use the old wave-function, the predictions for further experiments will be completely off. Now, the physical interpretation of this collapse varies wildly between different interpretations of QM, but some variant of it is always required - otherwise, the observations simply do not match the math. We don't yet have any theory consistent with QM that can make predictions without applying the Born rule.
  - FeepingCreature 6y ago
    I believe in Many-Worlds, the update step falls out of decoherence "for free." Because you are also in superposition after the measurement, the "you have measured 1" part of your wavefunction of course measures amplitude 1. That doesn't give you the Born rule though - I believe there's some attempts to get it out of game theory [1], where they show that given sufficiently long timespans, "almost every" worldline has a history with quantum measurements whose distribution matches the Born probabilities. [1] https://arxiv.org/abs/0906.2718 https://arxiv.org/abs/0906.2718