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comment Quantum dimension in topological entanglement entropy
@cleanplay: In a non-degenerate ground state the operators applied to the wavefunction as a result of particle exchange are multiplcations by phases. These commute with each other, therefore in a non-degenerate ground state anyons are necessarily abelian. In a degenerate ground state, the operators are Unitary matrices, which in general do not commute, therefore the anyons can be non-abelian, but are not necessarily non-abelian. Since some sets of Unitary matrices do commute, there can be a special case of anyons in a degenerate ground state which are abelian.
Sep
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comment Quantum dimension in topological entanglement entropy
@cleanplay: the fact that there exists a system with abelian anyons in a degenerate ground state does not contradict the statement that anyons in non-degenerate ground states are abelian.
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comment Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain?
Related: physics.stackexchange.com/q/30374/975
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comment Do quantum states contain exponentially more information than classical states?
@user929304 - yes it's analogous. In general, given any quantum state, you can choose what data you want to extract from it by choosing the measurement basis, and after you measure the state collapses. So the question arises whether the state "contains" the information about the distributions of all possible measurements, or just the information about the one measurement that was eventually performed. This is essentially what the OP was asking.
Jan
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comment Do quantum states contain exponentially more information than classical states?
@user929304 - I didn't say the whole book is stored in a single state of superposition of all numbers. The way the book is stored is more complicated and described in the paper cited in my answer. The point is that we can choose any measurement basis we want to perform a measurement. Each phone number has a corresponding measurement basis, so by correctly choosing the basis, we can retrieve any number we like. However, the book is destroyed by the measurement so we can't retrieve more than one number. I hope I clarified the issue.
Dec
29
comment Is the normal force a conservative force?
Wow, indeed there was an error in my proof. I can't believe it was there so long before someone noticed it. @DSinghvi - thanks for pointing it out and good catch! I corrected the error and also improved the answer a bit.
Dec
29
revised Is the normal force a conservative force?
Fixed an error and added an example
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