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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.


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 ...


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).


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. ...


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 ...


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 ...


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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