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The Schrödinger's cat was regarded as peculiar since we seldom encounter a superposition state in macroscopic scale: $$ | \mathrm{dead \,\,cat} \rangle + | \mathrm{alive \,\, cat}\rangle $$

We more often describe an unknown cat as $$ | \mathrm{dead \,\,cat} \rangle \langle \mathrm{dead \,\,cat} |+ | \mathrm{alive \,\, cat}\rangle \langle \mathrm{alive \,\, cat}| $$

without superposition.

I often heard that it is difficult to prepare and maintain a large-scale superposition state. Similar difficulty also occurs in quantum computing.

My question is, actually what is the reason for the difficulty to prepare and maintain a large-scale superposition state? If it is decoherence, why decoherence happens? Is that because of entropy?

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I don't know the answer but I just wanted to point out that $k\ln N $ and $k \ln 2N $ differ by $k \ln 2$ regardless of the value of $N$. The difference between the entropies is constant (though does become relatively smaller as $N$ increases). –  JeffDror Mar 2 at 17:05
    
Thanks a lot.... –  user26143 Mar 2 at 17:17

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Decoherence happens because in a macroscopic system you are not able to create a small isolated system. In practice you are deal with statistical mixture and not pure state. There's a good description on Wikipedia.

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I briefly read wikipedia about decoherence. My impression is that is an interpretation of experimental result, but does not answer why decoherence happens... –  user26143 Mar 2 at 17:33
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The problem is that in macroscopic system objects are inevitable non-isolated: they are coupled with the external ambient. In particular the system "cat+atom" become immediately entangled with ambient and as a consequence it loses his coherence. –  LC7 Mar 2 at 17:59
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Haroche says: the cat is a complex and OPEN (it cannot be isolated) system, it's impossible to describe it with a wave function. –  LC7 Mar 2 at 18:04
    
Thank you very much for clarifying this point! –  user26143 Mar 2 at 18:41
    
I still have a question. If we consider a hydrogen atom in external field, e.g. Stark and Zeeman effects, the hydrogen atom is not isolated. Why we can still write a wavefunction for the hydrogen atom? Is that because the interaction from external field do not depend on the details of the configuration of radiation field? –  user26143 Mar 2 at 18:54

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