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Quantum entanglement occurs when particles such as photons, electrons, molecules as large as buckyballs, and even small diamonds interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description (state), which is indefinite in terms of important factors such as position,momentum, spin, polarization, etc. Source: Wikipedia

All objects can get quantumly entangled, but to get a more sustained quantum entanglement with a long dechoherence time, the objects has to have equal properties. Do all properties have to be equal or could some properties be different?

For instance: Form seem to be important for quantum entanglement, but is size important? Could a small diamond be quantum entangled with a larger diamond with the same shape?

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Question updated and clarified with information from John's answer. –  Enos Oye Mar 6 '13 at 11:21

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Any two interacting systems can become entangled in principle. Entangled simply means the two objects cannot be described by two separate wavefunctions, but must be described by a single wavefunction that encompasses both systems.

The problem is not that your two systems don't become entangled, but that the wavefunction collapses due to decoherence and the entanglement is lost. The rate at which decoherence happens increases rapidly as the system gets bigger (strictly speaking, as the degrees of freedom increase). This is why we can normally only detect entanglement for microscopic objects.

I can't get at the original paper describing the experiment because it's behind a paywall, but some Googling for related papers like this one suggests that the vibrational excitations in diamond are unusually resistant to decoherence for technical reasons that I must admit I didn't really grasp. The decoherence time is around 23$\mu$s, which is eternity as decoherence times for macroscopic objects go!

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Thanks for your clarification. So the more equal in size and shape the diamonds get, the longer decoherence time they have. What if the small diamond has a shape/form which is repeated in the larger diamond, could we then have a long decoherence time? –  Enos Oye Mar 6 '13 at 10:31
The diamonds don't need to be equal sizes. From what I could understand of the paper I mentioned, it's hard to excite the vibrational mode the experiment uses, so there is very little interaction of the vibration with the environment. This is what produces the long decoherence lifetime. –  John Rennie Mar 6 '13 at 11:07
Ok, so lower rate of energy loss increases decoherence time and size doesn't matter. Let me ask a wild one, could the iron nickel sphere crystal core of a rocky planet have a sustained quantum entanglement with the core of another planet? –  Enos Oye Mar 6 '13 at 11:29
No, the Earth's core interacts strongly with it's environment and its decoherence time is likely to be effectively zero. A more interesting question is could a diamond the size of the Earth's core entangle with the core of another diamond of the same size? I don't know the answer. –  John Rennie Mar 6 '13 at 11:46
@Enos Oye any two objects can be entangled, they do not need to be similar, but your example is weird because you were told that the greater the objects are and the hotter they are, the less time the entanglement lasts. –  Anixx Oct 8 '13 at 9:17

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