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Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently — instead, a quantum state must be described for the system as a whole. Measurements of physical properties such as position, momentum, spin, ...


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Quantum entanglement is the property of two objects $A,B$ – more precisely two subsystems – or a relationship between these two objects whose quantities or observables aren't independent of each other. It means that there exist some quantities $a_j$ and $b_k$ describing $A,B$, respectively, such that the probability distribution for these observations ...


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I think this is approach is the correct one. Here is from a paper I have written: The primary insight of this is that if we modify our concept of ‘local’, much of the strangeness may disappear. Specifically, consider that 4-dimensional space-time is a construct that is projected onto an underlying topology that I will call ‘true space’. The fundamental idea ...


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I finally figured it out, at least for the simple case where the two atomic states have the same angular momentum: In this case the photons are always opposite in angular momentum (meaning they are either both left or both right handed). Regarding linear polarization, it depends on the parity of the system. In one case the linear polarizations are 100% ...


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The articles by Chris Monroe describe the following situations: (1) use of an already entangled pair of photons to transfer the entanglement, resulting in ion-ion entanglement; (2) interference of photons from independent sources, A, B, not previously entangled, such that no experiment can determine from which source a particular photon originated. Method ...


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No, but a mercury lamp does. Each mercury and calcium atom emits two indistinguishable photons out of a single atom, instead of one, like the rest of the atoms. The photons emitted by a single atom at the same time are entangled. Do not expect entangled photons out of atoms that emit a single photon at the time. Also the mercury lamp must not have a ...


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This can be explained with a classical description of particles; quantum physics is overkill. The explanation stems from the physical constraints of the system, and therefore the specific details are completely system-dependent. Generally speaking, it involves some form of non-random selection of a subset of the random motion. To give you an example of how ...


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Concerning the question: "Is it theoretically impossible to realize entanglement-like phenomena (e.g. non-local behavior or violation of some sort of Bell inequality) using a Couder-Fort experiment?", I have recently discussed this with John Bush from MIT, one of the experts of these experiments. I believe it is possible that a Bell inequality can indeed be ...


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Let me rewrite $A=|H\rangle_1$, $B=|V\rangle_1$, $X=|H\rangle_2$, $Y=|V\rangle_2$ for typographical clarity. Then $A$ is (by assumption) orthogonal to $B$, so $A\otimes X$ is orthogonal to $B\otimes X$, and $A\otimes Y$ is orthogonal to $B\otimes Y$. Also $X$ is (by assumption) orthogonal to $Y$, so $A\otimes X$ is orthogonal to $A\otimes Y$, and $B\otimes ...


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The quantum field is first and foremost theory. Like any theory it's believability rests on it's logical correlation to things we can see. So I don't think this is necessarily too broad a question. In fact it might be a good question to simplify the theory in general. Quantum entanglement is simply the notion that sometimes the math doesn't work. Or ...


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In all these discussions about entanglement, all the measured observables of Alice always commute with those of Bob. Their degrees of freedom describe two factors ${\mathcal H}_A$ and ${\mathcal H}_B$ of the overall Hilbert space of possibilities which is the tensor product $$ {\mathcal H} = {\mathcal H}_A\otimes {\mathcal H}_B $$ This factorization of the ...


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Other answers paraphrase it well in technical terms. It might be easier to see if you remember that when two particles interact they must do so in a way so that the momentum, energy, spin, etc. are conserved. After the interaction the two particles still remain in a superposition state but if you measure one of them after an interaction you can find out ...


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It's funny how people keep saying "the Copenhagen Interpretation says such-an-such and that's really weird and makes no sense". Such an embarrassing string of bad explanations really ought to make one think twice about accepting it as an explanation. There is NOTHING in the equations which says the wavefunction collapses, that's a superfluous idea added by ...


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Asking a question about the foundations of statistical mechanics is a good way to start a fight, so don't expect a clear consensus on this. Stripping away the hype, what these papers try to do is establish that an isolated quantum system will, under certain (but general) conditions, evolve to a state that looks like thermodynamic equilibrium locally, even ...


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Can someone tell me the practical difference of "world splitting" in MWI, and the original "wavefunction collapse"? Even if there is no such thing as an "abrupt" split, I don't see why you couldn't also argue the same for the "collapse". There is no world splitting. A state that starts out as having a single value for some relevant observable gradually ...


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If you want to use nonrelativistic quantum mechanics you have to first start with the basics. Firstly it doesn't handle particle creation or destruction, so you need to fix how many particles you have of each type. Then you want a function from the configuration space $\mathbb R^{3n}$ into the joint spin state $\mathbb C^{k_1}\otimes\mathbb C^{k_2}\otimes ...


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Your question has nothing to do with entanglement. You might as well ask this instead: Physics predicts that two positive charges will repel each other. Suppose I bring two positive charges into close proximity and find that they attract each other instead. How can this contradiction be resolved? Or you could posit any other experimental result that ...


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This is one of the most misunderstood things about entanglement, which is that it doesn't matter who goes first. Neither measurement actually affects the other one, contrary to the intuitive implications of "wave function collapse". Entanglement is correlation, not causation.


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Even if Alice and Bob are both first to measure their spin (according to their respective reference frames), two spins entangled into the singlet state will still give opposing results. That's what quantum mechanics predicts. Finding out that the entangled spins gave agreeing results would falsify a prediction of quantum mechanics. People would be very ...


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An ensemble of interacting particles will, over time, develop entanglement between widely separated parts*, so this is similar to asking whether an interacting system can still be a BEC. The short answer is yes, but a subtlety is that various authors define BEC in slightly different ways. One way of defining BEC, as I mention in a recent answer, is the ...


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The answer to your first question is interpretation-dependent. In many-worlds, the other state is unaffected. In the Copenhagen interpretation, the other state is affected. Since interpretations all give the same predictions, and they disagree about the answer to your first question, the answer can't be determined experimentally or mathematically. What is ...


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Let $\lambda_i$ be the eigenvalues of $\rho_A$. Then $$ \log \text{tr} \rho_A^n = \log \left( \sum_i \lambda_i^n \right) $$ Now, let is differentiate w.r.t. $n$. We find $$ - \frac{\partial }{ \partial n} \log \text{tr} \rho_A^n \bigg|_{n=1} = - \frac{\sum_i \lambda_i^n \log \lambda_i }{\sum_i \lambda_i^n } \bigg|_{n=1} = - \frac{ \sum_i \lambda_i \log ...


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Well, the trite answer is "no" because every bit of matter we see around us is in an entangled state. It's the normal classical world.



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