Comments by "EebstertheGreat" (@EebstertheGreat) on "How Does a Quantum Computer Work?" video.

  1. Dang Pham hazonku The coefficients are actually called probability amplitudes, and are complex numbers. The probability of a particular state is the square of the modulus of the probability amplitude (that is to say, the product of the amplitude ϕ with its complex conjugate ϕ*). Note that this means the phase can't actually be observed and isn't particularly meaningful in an absolute sense, but is necessary for performing calculations.
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  2. Checkedbox It is not in a pure state. It and the other entangled particle are both in a mixed state, although with the same total entropy of two pure states. Particles can be generated with certain properties, such as spin, correlated. For instance, if a gamma ray passes close to an atomic nucleus and produces an electron and positron pair, the total spin of the two new particles must be zero. So either the electron has spin 1/2 about any given axis and the positron has spin -1/2, or vice-versa. Until they interact further, the two states cannot be separated. Once you do interact with one of them through some sort of quantum observation, the whole system collapses to a single pure state, regardless of how far apart the particles are.
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  3. Checkedbox Unfortunately, spin doesn't have a classical analog. There is nothing like spin in classical mechanics, so it's not easily understood. It is best understood mathematically in the context of quantum mechanics. There are lots of attempts out there at explaining spin to lay people, some better than others, but ultimately I don't think you can really get a feel for it without delving into group theory. But spin is not the only quantum number we can use to give examples of entanglement. There is also an uncertainty in the momenta of particles, for instance, but this uncertainty can also be correlated. The point is that there is some property of both particles with limited degrees of freedom. Your idea that the particles already had classical observables but that we simply didn't know what they were until we measured them is a typical response. However, it is not true. The mixed states can interfere with each other and give indisputable indirect evidence of their existence even before the particles are directly observed. For an example of this, look into the "two-slit experiment." However, that doesn't prove that the two particles didn't already have some "hidden variables" that determined how they would collapse all along, i.e. that it was never really random to begin with. This position was advanced by Einstein, Podolsky, and Rosen in a famous paper and thought experiment. The paper demonstrated that quantum entanglement was inconsistent with local realism, the idea that all interactions only occur over short distances (e.g. by exchanging particles) and that the particles had definite properties (e.g. spin, momentum) before they were measured. That "EPR" paper had tremendous influence, and resulted in John Bell publishing famous inequalities that showed we could test local realism experimentally. Incredibly, the tests found local realism to be an incorrect assumption, that is, either the universe is non-local (interactions can occur at a distance) or particles do not have definite properties before they are "observed". Note that Schrodinger's Cat is just an analogy, as TLJGames said. The superposition of the quantum system would collapse long before anybody had a chance to look into the box, just due to the many interactions with the environment. Physicists believe it is a particle interacting with its environment, and thus becoming heavily entangled, that eventually leads to collapse, although the details are not at all understood. They certainly do not believe an entire cat could simultaneously be alive and dead until we looked at it. E: You made another post... Angular momentum relates to an object's angular motion. It is related to the product of its linear momentum (p=mv) and the distance to the point about which it is rotating. You also have to multiply by the sine of the angle, since if the object is just moving straight toward or away from the point, obviously there's no angular momentum there. The angular momentum is related to how the angle it makes with the point changes. The exact definition is L = r x p, where L is the angular momentum pseudovector, r is the displacement vector to the reference point, p is the momentum vector, and x is the cross-product.
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