Scott: Think of someone who says: “I understand what a complex number does—how to add and multiply one, etc. -- but what does it mean?”
Sounds like a perfectly legitimate question to me. Feynman’s excellent answer is that, in the context of QM, it means a little 2D arrow.
I say this tongue-in-cheek and completely seriously at the same time.
The idea that density matrices summarize locally invariant entanglement information is certainly helpful, but I still don’t know how to start with a density matrix and visualize some physical situation, nor can I take your proof and extract back out an argument that would complete the demonstration in this blog post. I confess this is strictly a defect of my own education, but...
But still, surely you see the difference between saying “Now let this be a trace-preserving operation on this density matrix that is the outer product of the AB state,” and saying “Now split up the joint amplitude distribution on A and B according to distinct states of B, and let anything whatsoever happen to the A side; since the evolution is unitary, it won’t change the squared modulus of any B-group of states, hence it won’t change the perceived probabilities at B.”
Recovering irrationalist, no, I’ve never seen a good calculus textbook in my life. Admittedly my requirements are unusual: The book I’ve always wanted to read is “The Pure Joy of Calculus For People Who Are Good At Math”, rather than “A Giant Dull Tome of Calculus For Students Who Would Rather Be Somewhere Else” or “Calculus for Nitpicking Formalists”.
Scott: Think of someone who says: “I understand what a complex number does—how to add and multiply one, etc. -- but what does it mean?”
Sounds like a perfectly legitimate question to me. Feynman’s excellent answer is that, in the context of QM, it means a little 2D arrow.
I say this tongue-in-cheek and completely seriously at the same time.
The idea that density matrices summarize locally invariant entanglement information is certainly helpful, but I still don’t know how to start with a density matrix and visualize some physical situation, nor can I take your proof and extract back out an argument that would complete the demonstration in this blog post. I confess this is strictly a defect of my own education, but...
But still, surely you see the difference between saying “Now let this be a trace-preserving operation on this density matrix that is the outer product of the AB state,” and saying “Now split up the joint amplitude distribution on A and B according to distinct states of B, and let anything whatsoever happen to the A side; since the evolution is unitary, it won’t change the squared modulus of any B-group of states, hence it won’t change the perceived probabilities at B.”
Recovering irrationalist, no, I’ve never seen a good calculus textbook in my life. Admittedly my requirements are unusual: The book I’ve always wanted to read is “The Pure Joy of Calculus For People Who Are Good At Math”, rather than “A Giant Dull Tome of Calculus For Students Who Would Rather Be Somewhere Else” or “Calculus for Nitpicking Formalists”.