On Saturday, June 22, 2019 at 11:08:50 AM UTC-5, John Clark wrote: > > On Fri, Jun 21, 2019 at 8:13 PM Lawrence Crowell <[email protected] > <javascript:>> wrote: > > *> A Hadamard gate is not a unitary operation* > > > I don't quite understand that. I thought all quantum logic gates could be > represented by a symmetric Hermitian matrix, and if all the probabilities > don't add up to exactly 1 it's hard to see how it could be of much use to > physics. What does a probability of 110% mean? > > > *and so one can prepare or duplicate states that way.* > > > If you could do that then you could get around the Heisenberg Uncertainty > Principle. If you could make 2 copies you could measure the position of one > particle to arbitrary precision and not worry about velocity, and then > measure the velocity of the other copy to arbitrary precision and not worry > about position. And they you'd know both position and velocity to arbitrary > precision. > > It also seems to me that not being able to duplicate a quantum state is > the only thing that prevents you from sending messages faster than light. > Suppose Alice and Bob are many light years apart and have entangled > electrons. Bob makes lots of clones of his electron and measures them, if > they're all spin up then Bob instantly knows that Alice has measured her > electron, if there is a 50 50 mix then Bob instantly knows that Alice has > not measured her electron. Measuring could mean dot and not measuring could > mean dash, and presto you've got a faster than light telegraph. > > I must therefore conclude that it's impossible for Bob to make lots of > clones of his electron. >
Hadamard gates are used to prepare quantum states, to establish or remove entanglements. They are not unitary. I might just come down to Bohr when he said one must have classical operations to measure and understand QM. A Hadamard matrix is such that HH^T = nI, which is sort of close to being unitary. > > >> *> The computer of the year 2030 will have a network of processors. There >> will continue to be a straight up von Neumann type processor, but what can >> run in parallel with neural networks, quantum processors and other >> specialized processors. The Ras-Tal theorem illustrates a reduction in the >> need for oracle input.* > > > I've never heard of the Ras-Tal theorem, I Googled it but all Google > could find was your very post mentioning it, Bing couldn't even find that. > > John K Clark > https://www.intriq.org/uploads/Documents/Presentations/2018/Fall_2018/Avishay%20Tal.pdf -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/45cd05bc-df4f-4251-9ba8-b230ee9124d5%40googlegroups.com.
