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Perhaps this question makes no sense physically, but is it theoretically possible to entangle a photon with an electron, for example?

I know that entanglement links a specific property of particles, but is there any property that maps across particles, e.g. spin, that can be entangled across particles?

As an side, I heard that, in the original German, Schroedinger (?) used the word entwinement which got translated to entanglement in English. Unfortunate, since entwinement sounds so much better.

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  • $\begingroup$ Entwinement, that's interesting Benito. It reminds me of winding numbers. And pair production, and TQFT, which is linked to knot theory. Like, an electron is a 511keV photon entwined with itself. And in annihilation two such fermions with the opposite chirality "unentwine" each other. I must have a look for that. $\endgroup$ – John Duffield Dec 17 '15 at 23:07
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States may be entangled and by extension we say that the particles with these states are entangled. Entwinement is a nice word but it hides a little the basic meaning.

In the references of Quantum entanglement between an optical photon and a solid-state spin qubit

you may find

Several recent experiments demonstrated entanglement of optical photons with trapped

ions

  • Blinov, B. B., Moehring, D. L., Duan, L. M. & Monroe, C. Observation of entanglement between a single trapped atom and a single photon. Nature 428, 153–157 (2004)

atoms :

Volz, J. et al. Observation of entanglement of a single photon with a trapped atom. Phys. Rev. Lett. 96, 030404 (2006) Wilk, T., Webster, S. C., Kuhn, A. & Rempe, G. Single-atom single-photon quantum interface. Science 317, 488–490 (2007)

and atomic ensembles :

Yuan, Z.-S. et al. Experimental demonstration of a BDCZ quantum
repeater node. Nature 454, 1098–1101 (2008)
Matsukevich, D. et al. Entanglement of a photon and a collective atomic excitation. Phys. Rev. Lett. 95, 040405 (2005) Sherson, J. F. et al. Quantum teleportation between light and matter. Nature 443, 557–560 (2006)

This kind of entwinements, following the theory, is used to stock superposed states, ie from a photon to defaults in a crystal.

Precisely, for a photon and an electron, you can read Demonstration of quantum entanglement between a single electron spin confined to an InAs quantum dot and a photon

In this letter, we report an all optical experimental demonstration of quantum entanglement between a single electron spin confined to single charged semiconductor quantum dot and the polarization state of a photon spontaneously emitted from the quantum dot's excited state.

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