From: on behalf of Seth Lloyd Sent: Monday, July 6, 2015 7:59 AM To: Jeffrey E. Subject: Re: Dear Jeffrey, My apologies for not resp=nding sooner. I took an email vacation for a week plus which =urned out to be a mistake because I fell irrevocably behin=. That was a very fun conversation with Noam in C=mbridge: he is an amazing thinker (if a tad inflexible at times). Your question about entropy is an important one. Th= second law of thermodynamics tells us that systems go to states=of high entropy where events are random and uncorrelated, so that thermal<=div> fluctuations appear to be statistically independent. Howev=r, if you look under the hood of the second law, you find that w=at is really going on is that the dynamics that leads you to thi= high entropy state is actually generating huge amounts of correlations between the different parts of the system. In f=ct, the apparently random and independent fluctuations of the pa=ts reflect large correlations with the other parts of the system. B=t these correlations are effectively smeared out over the whole =ystem: to reveal the fact that they are not truly independent, o=e would have to make measurements on all the parts together, and For example, even though the apparent high entrop= of a gas of molecules reflects all the correlations that are ge=erated by the collisions of molecules over time, if one looks at=just two molecules in the gas, their motions will be statistically indepen=ent to a high degree of accuracy. adiv> On your second question, quantum superposition is indeed closely =nalogous to a chord in music: the strangeness and power of quant=m superposition arises out of the interference between the diffe=ent waves in the superposition. A classical computer can o=ly register one set of logical values for its bits at any given =ime. So a classical computation is like plain chant: a <=div> single sequence of tones without interference. By co=trast, a quantum computation is lik