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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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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 ...

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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 ...

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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 ...

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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 ...

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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 ...

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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 ...

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