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In this article Bekenstein writes that the amount of information could store in a sphere with diameter of a cm is ~$10^{66}$ bits. If one were to take a set of 1000 entangled electrons and put them into a sphere of about a cm in diameter, due to entanglement a complete description of there spin would be ~$2^{1000}$ continuous variables. How can both of these facts be true?

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As expressed in the question, the Bekenstein bound is a bound on the number of bits — that is, a bound on the entropy, which is the logarithm of the number of mutually orthogonal microstates. ("Orthogonal" here refers to the inner product between state-vectors in the Hilbert space.) A collection of 1000 electron spins provides only 1000 (qu)bits, corresponding to $2^{1000}$ mutually orthogonal microstates. This fits comfortably within the Bekenstein bound. The Bekenstein bound says that the maximum number of mutually orthogonal microstates is $\exp(S)$ with $S\sim 10^{66}$. Our technology won't be running up against that bound anytime soon.

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