Alex 'qubeat'

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Scientist

	541 reputation	bio	website		visits	member for	2 years
34 badges		location	Russia		seen	May 5 '12 at 20:03

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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?
Jul 20	comment	What software programs are used to draw physics diagrams, and what are their relative merits? I had problem with reduced quality in publication even with LaTeX "picture" procedure. Only safe way I found is a program with possibility of *.eps output and even in such a case may be problem due to fonts in some journals or conferences.