Joe Fitzsimons
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 Apr 17 comment Advice on doing physics under the umbrella of mathematics and the converse @Moshe: Maybe. I've no idea what the true distribution is like. My sample size is relatively small (10 or 12) and is not all that geographically diverse. Apr 15 comment Advice on doing physics under the umbrella of mathematics and the converse Most string theorists I know are in Mathematics departments. Apr 14 comment What is the physical difference between states and unital completely positive maps? No problem. Hope it helps. Mar 26 comment Multiqubit state tomography by performing measurement in the same basis @Alex: Ah I guess you mean in the correlations. Sorry I forgot to account for that. I'll fix it now. Mar 2 comment Unknown quantum state with promise of classical data Collective measurements tend to do better. But as mentioned in the comments the original question asks about distinguishing states which are indistinguishable: they have the same reduced density matrix. Feb 28 comment Unknown quantum state with promise of classical data In that case, the Holevo quantity bounds the amount of information you can obtain, and hence can be used to upper bound the probability of correctly guessing the correct state. But be warned, it can be an extremely loose bound. Feb 28 comment Unknown quantum state with promise of classical data @PiotrMigdal: Looks like we were typing at the same time about the same thing! Feb 28 comment Unknown quantum state with promise of classical data I'm not quite sure I understand: If $H$ is chosen randomly then $Ha$ is uncorrelated with $a$. Averaging over $H$ you get $\rho = \sum_H p(H) (H a)^{\otimes K} = \sum_H p(H) (H b)^{\otimes K} = \sum_H p(H) (H c)^{\otimes K} = \sum_H p(H) (H d)^{\otimes K}$, so no matter how many copies you have you can't distinguish the initial state, since these states are related by unitary operators (and you've just applied a random unitary). Feb 19 comment Constructing a Hamiltonian (as a polynomial of $q_i$ and $p_i$) from its spectrum @PiotrMigdal: For a finite spectrum there is no unique solution. I suspect this is also true for the infinite case, but I am not sure. Jan 26 comment POVMs that do not require enlargement of the Hilbert space @MateusAraújo: In your case the effective identity operator still collapses the state onto whatever basis you picked, so repeated measurements do nothing. However, my method does not collapse the state in the case of an identity term, which is why multiple rounds makes sense. Jan 26 comment Do any entanglement measures for mixed states exist that use only single site correlation functions? @Calvin: Exactly, although there is no need to restrict to just Pauli operators. Jan 26 comment POVMs that do not require enlargement of the Hilbert space @MateusAraújo: I should have been more careful with my language. You do indeed simply add $pI$ to a particular round. However this is an important difference to your procedure, and allows you to construct a significantly wider range of POVMs: In each round you can choose to implement one POVM element + the scaled identity. Repeating as necessary you can obtain measurements consisting of many POVM elements. Jan 25 comment Solution to the Schrodinger equation for periodically time dependent Hamiltonians Do you want dynamics or average ground state? Jan 17 comment How can one build a multi-scale physics model of fluid flow phenomena? This is not my area at all, so this might be a particularly ignorant comment, but can you not simply simulate a small section at the microscopic level for a range of different conditions for the boundaries, and then piece together these into a solution for a larger volume, repeating several times if necessary? The basic idea being that there are many areas for which exactly the same calculation is necessary, and probably relatively few distinct such calculations, so better to build a lookup table than to calculate anew each time. Jan 13 comment Readable books on advanced topics Ah, I've just looked at a few reviews, and this probably fits my query better than I first thought. Sorry. Jan 13 comment Readable books on advanced topics As I commented on ver's post, I am not looking for popularizations, but rather advanced texts that manage to be readable at the same time. Jan 13 comment Readable books on advanced topics Perhaps I should have made it clearer, but I am not looking for popularizations. Jan 11 comment Readable books on advanced topics Ah yes. Actually, I already have that one! Jan 6 comment Information geometry of 1D Ising model in complex magnetic field regime @WNY: I meant that if you plug such a Hamiltonian into the time dependent Schroedinger equation you get completely unphysical results. I understand from the above comments that you are simply using complex analysis on the conventional Hamiltonian, so I think my confusion has been cleared up. Sorry. Jan 6 comment Information geometry of 1D Ising model in complex magnetic field regime While I have a reasonable amount of experience with the Ising model, I'm not quite clear how exactly it makes sense to make $h$ complex. The dynamics of the system would then not only not be unitary, but would not even conserve total probability. Could you clarify?