Abstract

The finite dimensional full complex matrix algebra (spin algebra) N is said to be stochastically reducible to the higher dimensional spin algebra M if there is a conditional expectation from M onto N and the conditioned expectation values can be obtained as averages over unconditioned states of M that all have less entropic uncertainty than the entropic uncertainty of the conditioned state. It is shown that no spin algebra is stochastically reducible to a spin algebra of higher dimension.

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