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The previous answers have explained the difference between quantum superposition of states and mixture of states(mixed states) mathematically and experimentally. Here, I would try to explain it in a more intuitive way, focusing more on the philosophical difference. The pure state $$|\psi\rangle=\frac{|\psi_{1}\rangle+|\psi_{2}\rangle}{\sqrt{2}}$$ is in a ...


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Convolver, you commented PM 2Rings answer as follows: In that case, I think superposition doesn't really exist... Take the case of two colored marbles. Indeed there isn’t a superposition. Different from two photons, made by Spontaneous parametric down-conversion. The photons directions are entangled, but the directions (together) are random around 360°. ...


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Can you know the exact time at which the particle B goes from superposition into a known state due to the remote measurement of particle A, only by waiting on particle B without knowledge of A? No, you cannot tell if particles B & A are entangled without measuring both particles and comparing the measurements, and to compare the measurements you need to ...


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Generaly, a qubit is a quantum system having two distinguishable states. The qubit can be implemented in many ways - electron spin, photon polarization, ions spin, quasiparticles called anyons ("transitional" entities between fermions and bosons, so far only theory) etc. As any quantum system, when the qubit is measured, it collapses into one of ...


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States with different charges cannot be superposed, because they are in different superselection sectors. This is because charge is a globally conserved quantity. Consider two states $| \psi_+ \rangle$ and $|\psi_-\rangle$, where the first has a charge of $+1$ and the second of $-1$. Charge conservation implies that $$\langle \psi_+ |A|\psi_-\rangle = 0$$ ...


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In the middle of a quantum algorithm there are indeed superpositions involving a large number of terms. But then we do an interference effect in which all these terms come together and interfere with one another, some reinforcing and some cancelling out. It is this reinforcement and cancelling which is doing a major part of the whole computational process. ...


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Superposition is NOT uncertainty. The state \begin{align} \vert +;\hat x\rangle = \frac{1}{\sqrt{2}}\vert +;\hat {z}\rangle +\frac{1}{\sqrt{2}}\vert -;-\hat{z}\rangle. \tag{1} \end{align} will certainly be detected with its spin up along $\hat x$. It is however a superposition of states with spins along $\hat z$, and the probability of detecting the spin ...


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Quantum mechanics is random or, more accurately, probabilistic, because nature is fundamentally not deterministic. Of course there are those clinging to deterministic explanations, like Bohmian mechanics, by ignoring mathematical proofs, just as there are those clinging to Dingle's argument against relativity. But the argument "I don't understand the ...


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Quantum Indeterminacy is Key to the Arrow of Time There is no machinery to explain the randomness (as Mr. Anderson answered from Feynman), but maybe a connection to other phenomena can help. I'm going to go out on a limb here, because answers in this forum are supposed to be from established science. But I think I can make a case for an important ...


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Assuming the electrons are prepared correctly, we know nothing at all about their spins prior to our measurement with the Stern-Gerlach device. (Except, of course, that each spin is $\pm\hbar/2$ along some direction.) That ignorance is captured by the idea of the equal superposition. Using that idea, when we calculate measurement probabilities in quantum ...


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You are asking why QM is random (which in your case given the context is used as probabilistic), and what is correct to say is that QM is probabilistic in nature, and our underlying world, and our universe seems to us to be quantum mechanical, and truly probabilistic. is there a way to understand the system as having an initial state which forced it to come ...


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We don't even know that the universe is fundamentally random. That's just the most popular interpretation (called the Copenhagen Interpretation). In this interpretation, the behavior of particles is probabilistic with no deeper reasoning, and the "why" is left to philosophers (or, possibly, a future Theory of Everything). There are other ...


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It's weirder than you thought. The wavefunction itself is fully deterministic. People often say "it's the measurements that are probabilisitic" but that isn't right either. The measurement is deterministic if you include the measurement apparatus in the wavefunction. And therein is the core of the great mystery, and the big philosophical questions ...


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If it helps, it's not that the nature of the universe is random, it's that we model it as random in Quantum Mechanics. There are many cases in science where we cannot model the actual behavior of a system, due to all sorts of effects like measurement errors or chaotic behaviors. However, in many cases, we don't need to care about exactly how a system ...


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As Feynman said when laying out the first principles of quantum mechanics: How does it work? What is the machinery behind the law?” No one has found any machinery behind the law. No one can “explain” any more than we have just “explained.” No one will give you any deeper representation of the situation. We have no ideas about a more basic mechanism from ...


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a) I wouldn't call it "random" but "probabilistic". b) The evolution of a system is fully deterministic. It's the outcome of measurements that is probabilistic. c) Your reasoning is wrong. The probabilistic nature of measurements' outcomes is something intrinsic to quantum mechanics (the measurement problem), independent of the specifics ...


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In quantum mechanics, the superposition principle tells us that quantum states can be added together and the result will be another valid quantum state. Conversely, every quantum state can be represented as a sum of two or more distinct quantum states. Essentially the superposition principle says that if you have two quantum states $|\psi_1\rangle$ and $|\...


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Does the superposition principle actually tell us about our inability to predict what happens during the course of the experiment? No, it tells us that what we can predict is the probability distribution of a large number of experiments with the same boundary conditions. The single electron trajectory and footprint cannot be predicted , but the accumulated ...


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The answer is no -- Schrodinger's Cat is not possible, even in principle. In the following analysis, all of the superpositions will be location superpositions. There are lots of different types of superpositions, such as spin, momentum, etc., but every actual measurement in the real world is arguably a position measurement (e.g., spin measurements are done ...


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