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I have recently found a reference proving the statement from my question. It is: Universal quantum gates Jean-Luc Brylinski and Ranee Brylinski In Mathematics of Quantum Computation, Chapman & Hall (2002) arXiv:quant-ph/0108062 Theorem 1.4, proven in section 8.


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I do know something about the history of the problem, but I don't know the answer. The first reference is S. Lloyd, Almost any quantum logic gate is universal, Phys. Rev. Lett. 10, 346–349 (1995). which gives a "proof" of this... but it isn't strictly correct. I don't know what exactly was wrong with it, because I never looked at it in detail. It doesn't ...


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Any two particles become entangled after an interaction. Entanglement is truly everywhere and occurs constantly. The reaching of equilibrium of the temperature of a coffee cup and the room has not a lot to do with entanglement and more with the irreversibility of the motion of many particles (entropy).


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As was pointed out in the comments most photons are produced individually from deexcitation of electrons from higher energy orbitals, where they had been pushed by heat ( as with heat filament lamps) to lower ones. Since I am a little new to this topic, a little background of entanglement would be appreciated as I might be wrong in my conceptualization. ...


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Suppose $\mathcal{H}=\mathcal{H}_A \otimes \mathcal{H}_B$ and $|\psi \rangle \in \mathcal{H}$ is a pure state which is entangled between the subsystems. Define a 'local' unitary to be $U=U_A \otimes U_B$. Then $U$ cannot change the entanglement entropy independent of what it is, random or not. Expand $|\psi \rangle = \sum_{j,k} a_{j,k} |j_A \rangle \otimes ...


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I'd say: Since entanglement is correlation, randomly changing one part of the system is like adding random noise and should destroy the correlation. But let's make this a bit more formal. You have a system $\rho\in\mathcal{B}(\mathcal{H}_A\otimes \mathcal{H}_B)$ where $\mathcal{H}_{A,B}$ are the Hilbert spaces of qubit A and B (just $\mathbb{C}^2$). Now you ...


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Entanglement is a property, so it doesn't make sense to "entangle entanglements". However you can entangle entangled objects. And indeed, if you have two entangled pairs, you can create four-particle entanglement that way. For example, you could create a four-particle cluster state (cluster states are special entangled states useful for quantum computing) by ...



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