On Fri, Dec 07, 2012 at 10:51:49AM -0500, Richard Ruquist wrote: > 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) >
Put this way, I can see it is related to the fact that acquisition of information may well reduce the information you have, subject to the triangle inequality. But this seems to go further, in saying that the triangle inequality may be violated, but I'm not sure. Will need to read the paper (below) to comment further. But it is mutual entropy (or mutual information) that goes negative, not entropy itself... > 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. Bruno found a reference to a paper by Cerf and Adami, which looks like the one. I have added it to my reading list. > > Richard > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
