Is the Reduced Spin State of an Entangled Particle an Improper Mixture?

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Hi there -- can anyone give me, or point me to, an argument that the reduced state density matrix corresponding to one of a pair of entangled particles is an `improper mixture' -- that is, that the particle with that reduced state (a reduced spin state, say) cannot be understood as being in some spin state with some (classical) probability, but we just don't know which?

Any help much appreciated!
 
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Thank you! That is indeed helpful.
 

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