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Crash course in entanglement: The state of each qbit is represented by a state vector of two complex numbers [a, b] where |a|^2 + |b|^2 = 1. There are two spec

Crash course in entanglement: The state of each qbit is represented by a state vector of two complex numbers [a, b] where |a|^2 + |b|^2 = 1. There are two special qbit values called the classical basis: [1, 0] which is the classical bit 0, and [0, 1] which is the classical bit 1. If a qbit is not in one of the two classical states, we say it is in superposition. When a qbit is in superposition, we can measure it[0] and it will collapse probabilistically to 0 or 1; for a qbit [a, b], the probability that it collapses to 0 is |a|^2 and the probability that it collapses to 1 is |b|^2. Things get more interesting when we have multiple qbits. If we have two qbits [a, b] and [c, d], we define their product state as their tensor product [ac, ad, bc, bd]. For example, if we have two qbits both in state [1/sqrt(2), 1/sqrt(2)], their product state would be [1/2, 1/2, 1/2, 1/2]. We use the product state to calculate the action of a quantum logic gate that operates on multiple qbits - for a gate which operates on two qbits, we can always represent its action as a 4x4 matrix. Usually we can move back and forth between the product state representation and writing out the individual qbits states. However, in certain scenarios something very special happens: we cannot factor the product state back into the individual state representation! Consider the product state [1/sqrt(2), 0, 0, 1/sqrt(2)]. If you try to write this as a tensor product of two states [a, b] and [c, d], you cannot! It cannot be factored; the qbits have no individual value, and we say they are entangled. Well, what does this mean? It means when you measure one qbit, even if the qbits are very far apart, you instantly know the value of the other qbit. So if I entangled two qbits in the state [1/sqrt(2), 0, 0, 1/sqrt(2)], give you one, then we go to opposite ends of the universe, if I measure my qbit and see a 0 I'll know your qbit instantly also collapsed to 0 (or collapsed to 1 if I measured 1). This phenomenon has been experimentally-verified to occur faster than light. It is instantaneous, as far as we can tell. So, local realism is wrong! Spooky action at a distance is real! There is an important caveat: while the qbits seem to coordinate in some faster-than-light way, you cannot use this to communicate in a faster-than-light way. All we have is a shared random number generator. I can't send some chosen bit from my reference frame to yours. This is called the no-communication theorem. If you found this interesting, I have a full video on quantum computing for computer scientists here: https://youtu.be/F_Riqjdh2oM https://youtu.be/F_Riqjdh2oM [0] IDGAF about your chosen quantum mechanics interpretation, don't @ me

bdamm 8y ago
The part I don't understand is the "spooky action at a distance." Isn't this just the same as if the qbits were already in whatever their final state was as soon as they were entangled? Or in other words, is there any experimental basis for determining that the "cat" stayed alive at all? It seems a lot less magical when we just determine that in fact the value is the same no matter when or where you measure it, although it may not be predictable. And since the "entangled" qbit always had the same value, no matter when you measured it, then there is no "spooky action at a distance". The action occurred when d=0, and what you actually have is two copies of the same ROM.
- ahelwer 8y ago
  The idea that the qbits choose which value they'll collapse to at time of entanglement is called local hidden variable theory, which John Bell disproved in 1964: https://en.wikipedia.org/wiki/Local_hidden_variable_theory https://en.wikipedia.org/wiki/Local_hidden_variable_theory In more practical terms, the theory also falls apart when you start doing more complicated things with entangled qbits than just measuring them, like quantum teleportation or error correction.
  - madeuptempacct 8y ago
    So, it's kind of like closures in JavaScript? "A Bell test experiment or Bell's inequality experiment, also simply a Bell test, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to two other concepts: the principle of locality and Einstein's concept of "local realism". The experiments test whether or not the real world satisfies local realism, which requires the presence of some additional local variables (called "hidden" because they are not a feature of quantum theory) to explain the behavior of particles like photons and electrons. According to Bell's theorem, if nature actually operates in accord with any theory of local hidden variables, then the results of a Bell test will be constrained in a particular, quantifiable way. If a Bell test is performed in a laboratory and the results are not thus constrained, then they are inconsistent with the hypothesis that local hidden variables exist." Spooky private method scope is spooky.
  - 8y ago

bdamm 8y ago

The part I don't understand is the "spooky action at a distance." Isn't this just the same as if the qbits were already in whatever their final state was as soon as they were entangled? Or in other words, is there any experimental basis for determining that the "cat" stayed alive at all? It seems a lot less magical when we just determine that in fact the value is the same no matter when or where you measure it, although it may not be predictable. And since the "entangled" qbit always had the same value, no matter when you measured it, then there is no "spooky action at a distance". The action occurred when d=0, and what you actually have is two copies of the same ROM.

ahelwer 8y ago
The idea that the qbits choose which value they'll collapse to at time of entanglement is called local hidden variable theory, which John Bell disproved in 1964: https://en.wikipedia.org/wiki/Local_hidden_variable_theory https://en.wikipedia.org/wiki/Local_hidden_variable_theory In more practical terms, the theory also falls apart when you start doing more complicated things with entangled qbits than just measuring them, like quantum teleportation or error correction.
- madeuptempacct 8y ago
  So, it's kind of like closures in JavaScript? "A Bell test experiment or Bell's inequality experiment, also simply a Bell test, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to two other concepts: the principle of locality and Einstein's concept of "local realism". The experiments test whether or not the real world satisfies local realism, which requires the presence of some additional local variables (called "hidden" because they are not a feature of quantum theory) to explain the behavior of particles like photons and electrons. According to Bell's theorem, if nature actually operates in accord with any theory of local hidden variables, then the results of a Bell test will be constrained in a particular, quantifiable way. If a Bell test is performed in a laboratory and the results are not thus constrained, then they are inconsistent with the hypothesis that local hidden variables exist." Spooky private method scope is spooky.
- 8y ago