Russell,

I finally found some confirmation of there being negative quantum (von
Neumann) entropy for entangled systems:

http://en.wikipedia.org/wiki/Joint_quantum_entropy
"The classical joint entropy is always at least equal to the entropy
of each individual system. This is not the case for the joint quantum
entropy. If the quantum state  exhibits quantum entanglement, then the
entropy of each subsystem may be larger than the joint entropy. This
is equivalent to the fact that the conditional quantum entropy may be
negative, while the classical conditional entropy may never be." and:

"The classical joint entropy is always at least equal to the entropy
of each individual system. This is not the case for the joint quantum
entropy. If the quantum state  exhibits quantum entanglement, then the
entropy of each subsystem may be larger than the joint entropy. This
is equivalent to the fact that the conditional quantum entropy may be
negative, while the classical conditional entropy may never be."

The joint quantum entropy  S(A,B) can be used to define of the
conditional quantum entropy:
S(A|B)=S(A,B)-S(B)

This is apparently a result of quantum theory's use of complex variables.
I have not found a source to confirm this,
except for that unfounded(pun intended) video.

Richard

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