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Scientist


Nov
24
comment Hilbert-Schmidt basis for many qubits - reference
Maybe the discrete Wigner function is a bit other story, because they need to use trace on $GF(2^n)$ and exchange components in Hilbert-Schmidt scalar product.
Nov
24
comment Is this a simple Lie algebra?
It is rather $so(4,{\mathbb C}) \approx sl(2,{\mathbb C}) \oplus sl(2,{\mathbb C})$, because OP defines it as a complex algebra.
Nov
24
comment Is this a simple Lie algebra?
@Luboš Motl: any Pauli matrix meets two last equations and after all ${\rm diag}(+1,-1)$ is also Pauli matrix $\sigma_z$.
Nov
23
comment Hilbert-Schmidt basis for many qubits - reference
I guess, but I never heard about simple expressions for constrains
Nov
23
comment Hilbert-Schmidt basis for many qubits - reference
I supposed the decomposition itself is rather standard consequence of axioms of quantum mechanics and linear algebra, e.g. section 5.3 in my e-print arxiv.org/abs/quant-ph/0104126v1
Nov
22
comment Hilbert-Schmidt basis for many qubits - reference
So the term due to Hilbert-Schmidt inner product for matrices?
Nov
22
comment Hilbert-Schmidt basis for many qubits - reference
It is simply decomposition of $4^n$ dimensional “vector” with an orthogonal basis. Vector space is space of $2^n \times 2^n$ Hermitian matrices with respect to norm $(A,B) =Tr(AB) = Tr(AB^*)$. But I doubt, it could be called Hilbert-Schmidt decomposition because it is defined for any $n$ and for $n=2$ produces up to 16 terms instead of 4.
Nov
22
comment What proof techniques have failed for solving the SIC-POVM problem and what new insights have been gleaned from them?
Just mentioned related question on MO mathoverflow.net/questions/2897/…
Nov
3
answered Twistors in Curved Spacetime
Oct
30
comment What proof techniques have failed for solving the SIC-POVM problem and what new insights have been gleaned from them?
Constructions of SIC for consequent $d$ too different to hope on induction, e.g. see TABLE I in e-print you cited: for $d=3$ there are infinite number of SIC, but for other $d$ only finite number (and the numbers of SIC have rather unpredictable behavior).
Oct
30
comment What proof techniques have failed for solving the SIC-POVM problem and what new insights have been gleaned from them?
There is an item devoted to the problem here
Oct
30
comment Relevance of SIC-POVMs to quantum information
May be some examples are needed for clarification of the question, how suitably chosen set of random projectors are using instead of SIC-POVM-like objects for dimensions there SIC or MUB may be introduced? If SIC is analogue of orthonormal basis (see cite in my answer), it may be compared with using sets of random vectors instead of the orthonormal base.
Oct
27
answered Relevance of SIC-POVMs to quantum information
Oct
23
answered Gauge invariance for electromagnetic potential observables in test function form
Oct
11
answered Negative probabilities in quantum physics
Oct
10
comment What is the use of a Universal-NOT gate?
Likely yes. I see. It is "the second reference in Nature" I mentioned instead.
Oct
7
answered What is the use of a Universal-NOT gate?
Jul
22
comment Direction of Time on Event Horizon
Event horizon is just a boundary inside that any timelike direction points inside and so it is not possible to escape along any "axis of time". It is not possible to write a metric in diagonal form on the event horizon and it is neccesarry to use something like Eddington-Finkelstein coordinates.
Jul
21
comment What conservation law corresponds to Lorentz boosts?
@Marek: Center of mass is $\mathbf R$ and so it is better to say, that (correct) expression you wrote is not center mass, but specific conserved vector, ensuring center mass to move with constant speed, it is really discussed in Landau & Lifshitz yet without notion about Noether theorem.
Jul
20
answered What software programs are used to draw physics diagrams, and what are their relative merits?