A Fock space constructed via a separable Hilbert space is separable, however the tensor product of a countable set of separable Hilbert spaces is not (infinite qbit chain). How is the previous statement correct, I thought the two spaces would be separable they seem to be quite literally the same.
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$\begingroup$ It is not clear what you're asking. $\endgroup$– Tobias FünkeJan 10 at 14:02
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$\begingroup$ This might be better on a math site. $\endgroup$– mike stoneJan 10 at 14:03
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1$\begingroup$ @TobiasFünke Prove that the tensor product of a countably infinite set of separable Hilbert spaces is not separable. $\endgroup$– TheDawgJan 10 at 14:09
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$\begingroup$ This is not a question. $\endgroup$– Tobias FünkeJan 10 at 14:11
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$\begingroup$ I think that a countable product of seperable topological spaces is separable:math.stackexchange.com/q/244427. Who says that iot is not? $\endgroup$– mike stoneJan 10 at 14:11
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