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that two entangled particles have opposite characteristics that is kept regardless of distance: e.g. if one of them is detected to have a up spin then other is bound to have a down spin. Firstly: as your description shows, the relevant correlation is pair by pair. It must be (ideally) unambiguous whether a given detection indication of the one analyzer ...

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One way to facilitate this discussion is to think of what's classically forbidden but quantumly permissible. My favorite so far is a game that I call Betrayal. Let me explain that in this answer. Betrayal: Game Rules The players are a cooperative three-person team, they will either all win or they will all lose. They will be put through some number $N \gg ... 1 I still don't quite understand the reasoning behind the conclusion that entangled particles somehow can communicate their state to each other instantaneously, even though they are separated by a substantial distance This isn't correct, they occupy a joint state. From what I gather [...] upon observation of one of the particles, it immediately (and ... 0 Entanglement is the term used for quantum mechanical correlation, and as always "correlation does not mean causation". In quantum mechanics most yes/no correlations come from conservation of quantum numbers. Conservation laws are strict as for example angular momentum conservation. If two electrons are set up to have spin up and spin down, the total spin ... 0 It does seem like you have some misconceptions. You don't have to measure them simultaneously, in fact the whole idea of "being simultaneous" turns out to be subjective and observer dependent in relativity. But the real issue is that there are many measurements you can do. For instance you could measure the z component of spin, or you could measure the y ... 2 Firstly, the notation$|\Phi\rangle = \frac{1}{\sqrt 2}(|1\rangle_A|1\rangle_B + |0\rangle_A|0\rangle_B)$already assumes away anything spatial because you are only writing the spin degrees of freedom. Secondly you mention superposition as if it avoids being a pure state. A superposition is still a pure state. Superposition is like a sum. You don't look ... 0 An entangled state has to such that it can't be written in the form$|i\rangle_A|j\rangle_B$. If the state can't be written in that form, then neither system alone has a pure reduced density matrix, i.e. - a density matrix of the form$|i\rangle\langle i|$as opposed to a density matrix of the form$\sum_ip_i|i\rangle\langle i|$, which is called a mixed ... 0 You seem to think that when you measure one entangled particle, the other is affected even if you have not interacted with it. If that were true, then the result of the measurement on the first particle would determine the result of the measurement on the second. And then if you measure them at the same time, there is a problem of how to determine the tie ... 1 Measurements are never instantaneous, only idealizations of actual measurements are modeled as instantaneous. Measuring one particle in a entangled pair destroys the entanglement, after a measurement they are no longer entangled. Doing repeated measurements quicker and quicker can exert a quantum Zeno effect where the no-measurement evolution away from a ... 1 If you do a strong measurement of a particle in an entangled pair, then they are no longer entangled, they get the correlation they have and thereafter you can measure or affect one without affecting the other (except to the degree that they interact). If you want to do weak measurements you might get a different story. In either case, you can (if you ... 1 First I'll describe what happens when you measure the spin of just one particle. Say you setup a some magnets to make a region of inhomogeneous field so that when a spin up particle heads forward into the region it ends up deflect right. And a spin down heads forward it ends up deflected left. Then if you have a superposition of up and down such as ... 0 I'm going to try to teach you the right way to think about this, but possibly that will be very difficult to visualize. So I wanted to give you a starter course on what you're getting wrong. What you're getting wrong Your colors are indeed orthogonal states that can be measured differently. On your second screen you'll see green and orange light hit the ... 0 If thing A has multiple states it can be in, and thing B has multiple states it can be in, then thing A and thing B can, in theory, be entangled. They could, in principle, have been made that way. And depending on how they interact they might become entangled even if they started out not entangled. Measurements, in fact, are examples of situations where ... 1 This is interesting! Just want to ask a few questions for clarification: (1) Which geometry did you use for the states? disk, sphere, torus? (2) Which set of Slater determinants did you computed overlaps with? for example, did you use a fixed single particle basis and did the optimization over occupation numbers only, or did you allow for changes of the ... 3 The entanglement of any region in a matrix product state of bond dimension$D$is bounded by$S\le 2\log D$. Thus, in order to simulate a system with a lot of entanglement, the bond dimension (and thus the memory and time of the computation) will grow exponentially with the entropy. Conversely, we know that if for a state$\vert\psi\rangle\$ the ...

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Let us start from the beginning. Elementary particles are quantum mechanical entities. They can be described with the quantum mechanical solutions of the appropriate equations for the set up under consideration with the constants taken from the boundary conditions of the problem. In this it is not different than the situation with classical mechanics ...

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