# Joe Fitzsimons

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website        jfitzsimons.org
location       Singapore, Singapore
age            31
member for     2 years, 6 months
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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.

|             |                  | bio                  | visits          |            |                   |
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|             | 5,596 reputation | website              | jfitzsimons.org | member for | 2 years, 6 months |
| 1237 badges | location         | Singapore, Singapore | seen            | 1 hour ago |                   |

# 257 Comments

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| Dec7  | comment | Uniqueness of eigenvector representation in a complete set of compatible observables@Moshe: I didn't bother looking at the Physics.SE link before answering, but now you've pointed it out I agree that genetth's answer was perfect.                                                                                                                                                                                                                                                                                                                                                                                                                                              |
| Dec6  | comment | Uniqueness of eigenvector representation in a complete set of compatible observablesSecondly, in quantum mechanics observable and Hermitian operator are synonymous. You can construct a physical measurement (in principle at least) for any Hermitian operator, and any physical observable is Hermitian.                                                                                                                                                                                                                                                                                                                                                                        |
| Dec6  | comment | Uniqueness of eigenvector representation in a complete set of compatible observables$\psi_i$ above are a basis for the Hilbert space in which all measurements are diagonal. If the set of measurements is maximal then it necessarily contains $D$ for some specific choice of basis. Since you specify the set of observables by their eigenvectors, you can explicitly construct $D$.                                                                                                                                                                                                                                                                                           |
| Dec2  | comment | Examples of number theory showing up in physicsThat's weird, and certainly interesting. I'll give the paper a look.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |
| Dec2  | comment | Examples of number theory showing up in physicsThanks for taking the time to compose an answer. I don't really consider quantum algorithms as fundamental physics in the sense of this question, particularly given that the hidden subgroup stuff is driven by a generalization of problems from number theory (factoring/discrete logs). The graph state observation seems more related to the fact that you are looking at factoring a Hilbert space, which directly relates to primality of the dimesnionality, etc.                                                                                                                                                           |
| Dec2  | comment | Examples of number theory showing up in physics@Artem: It's true that you can arrive at above result via finite fields, but the structure of the partial results is governed by number theoretic properties. I don't really see the way of arriving at a given result as particularly fundamental, as there are often multiple paths to the result.                                                                                                                                                                                                                                                                                                                                |
| Dec2  | comment | What videos should everyone watch?You may want to expand the question with a bit more explanation as in the cstheory question. I've marked this CW.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |
| Dec1  | comment | Examples of number theory showing up in physicsThis seems more like engineering a physical system to embody certain number theoretic properties, rather than them occurring unexpectedly.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
| Dec1  | comment | What papers should everyone read?@TsuyoshiIto: I must admit I didn't check the claim that it was 4 pages.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
| Nov28 | comment | Quantum causal structure@lurscher: Good catch. I'm not really sure where things stand then. I've updated my answer to include the reference in your comment.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
| Nov27 | comment | Causality and operationalism: from sets and functions to monads"Of course, states don't exist, only processes do." - That's one hell of a statement. Perhaps we would be better sticking to physics than philosophy.                                                                                                                                                                                                                                                                                                                                                                                                                                                               |
| Nov25 | comment | Quantum causal structure@Peter: Sorry Peter, I was referring to the original question, not your comment. I don't dispute that the quantum gravity case is open, but we know so little about that area that it is hardly surprising that it is open. I know some of the results the question refers to, but can't make much sense of what the poster has in mind. I'll cast a virtual vote to close, but since my vote is binding, I won't actually close the question yet. I'd like to give the OP time to actually explain what they mean. If nothing happens in a few days, I'll kill the question.                                                                              |
| Nov25 | comment | Quantum causal structureI don't understand what you mean by quantum causal structure. Quantum mechanics is non-signalling so causal structure is the same as in the classical case.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |
| Nov25 | comment | Hilbert-Schmidt basis for many qubits - reference+1 from me. I use it a lot too, but couldn't think of anything interesting to say!                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |
| Nov24 | comment | What papers should everyone read?Four pages is hardly unusual in physics.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
| Nov21 | comment | CHSH violation and entanglement of quantum states@PiotrMigdal: Perhaps you should post that as an answer.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
| Nov16 | comment | Accurate quantum state estimation via “Keeping the experimentalist honest”@ChrisFerrie: Sorry, I meant if the measurements can depend on $\sigma$ not $\rho$. I've edited my above comments to reflect this.                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
| Nov15 | comment | Accurate quantum state estimation via “Keeping the experimentalist honest”And hence you need only measure in the $X$ basis, even though this does not have sufficiently many linearly independent outcomes to uniquely identify an arbitrary density matrix.                                                                                                                                                                                                                                                                                                                                                                                                                       |
| Nov15 | comment | Accurate quantum state estimation via “Keeping the experimentalist honest”This argument is for the case where the set of measurements is fixed and independent of $\sigma$. If the scheme need only work for certain classes of $\sigma$ then this imposes correlations between entries in the density matrix which reduces the number of linearly independent measurement operators required to uniquely identify it. An example of this is where $\sigma = |+\rangle\langle +|$, where purity implies that the state has expectation value 0 for $Z$ and $Y$ measurements, and if $\mbox{Tr}(\rho X) = \mbox{Tr}(\sigma X)$ then $\mbox{Tr}(\rho Y) = \mbox{Tr}(\sigma Y)$, etc. |
| Nov15 | comment | Accurate quantum state estimation via “Keeping the experimentalist honest”Also, if you take any complete or over-complete basis for tomography you can make the measurements and make them arbitrarily weak, you still satisfy the criterion (though Alice's expected loss tends towards zero as the measurement tends towards the identity).                                                                                                                                                                                                                                                                                                                                      |
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