6,370 reputation
2044
bio website jfitzsimons.org
location Singapore, Singapore
age 33
visits member for 4 years, 9 months
seen Jun 12 at 16:59

I have just moved to the Center for Quantum Technologies in Singapore, after spending the last 3 years as a Merton College JRF in Theoretical Physics and a Senior Research Fellow in Oxford University Department of Materials. My research focuses largely on theoretical aspects of quantum information processing. In particular I am interested in spin networks, measurement based computation, cryptography and computational complexity.


Apr
18
comment partial trace with sparse matrices
In general, a partial trace of a sparse matrix does not yield a sparse matrix, so you will get only limited improvement by using the fact that the matrix is sparse (maybe a factor of d/s).
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
answered Advice on doing physics under the umbrella of mathematics and the converse
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.
Apr
8
answered What is the physical difference between states and unital completely positive maps?
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
26
answered Multiqubit state tomography by performing measurement in the same basis
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.
Feb
18
answered Constructing a Hamiltonian (as a polynomial of $q_i$ and $p_i$) from its spectrum
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
answered Do any entanglement measures for mixed states exist that use only single site correlation functions?
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
18
answered POVMs that do not require enlargement of the Hilbert space