  We apply algorithmic information theory to quantum mechanics in order to shed
light on an algorithmic structure which inheres in quantum mechanics.
  There are two equivalent ways to define the (classical) Kolmogorov complexity
K(s) of a given classical finite binary string s. In the standard way, K(s) is
defined as the length of the shortest input string for the universal
self-delimiting Turing machine to output s. In the other way, we first
introduce the so-called universal probability m, and then define K(s) as -log_2
m(s) without using the concept of program-size. We generalize the universal
probability to a matrix-valued function, and identify this function with a POVM
(positive operator-valued measure). On the basis of this identification, we
study a computable POVM measurement with countable measurement outcomes
performed upon a finite dimensional quantum system. We show that, up to a
multiplicative constant, 2^{-K(s)} is the upper bound for the probability of
each measurement outcome s in such a POVM measurement. In what follows, the
upper bound 2^{-K(s)} is shown to be optimal in a certain sense.
