Re: A theoretical physics FAQ (information in a particle)

Arnold Neumaier wrote:

[..]

Specifying a mixed state _exactly_ provides already an infinite amount
of information, since the density matrix rho must be specified to
infinite precision.

Perhaps an analogy can be made with throwing a slightly biased die.
If the die is thrown and temporarily kept hidden (as in some dice
games), the observer needs an infinite amount of information to
describe his knowledge of the state of the die: A probability
distribution consisting of real numbers. On the other hand the state of
the die can also be thought of consisting of much less information: Just
a choice of 1 from 6.

In this case, the exact description of ignorance about a system requires
much more information than the system itself contains.

Gerard

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