Recent content by rsg

From linear algebra point of view, a bounded operator A acting on a Hilbert space H is said to be positive (P), if for all |x\rangle\in H, \langle x|A|x\rangle\geq0. An operator E which maps density operators of a space H_1 to H_2 is called completely positive (CP). (Now you understand why...

Let O(n,F_q) be the orthogonal group over finite field F_q. The question is how to calculate the order of the group. The answer is given in http://en.wikipedia.org/wiki/Orthogonal_group#Over_finite_fields". This seems to be a standard result, but I could not find a proof for this in the basic...

These groups are known in literature as Heisenberg group over a finite field. It is generally written in the upper triangular matrix form. But that does not make any difference. So let me define a typical element of this field as A=\langle a,b,c\rangle where a, b, c have the same meaning and...

Let x^2_1+x^2_2=1 be an unit circle upon a finite field Z_{p} where p is a prime. Is there any algorithm (other than the brute force algorithm) which can give all the possible solutions (x_1,x_2)\in Z_{p}\times Z_{p} as well as the total number of such solutions? If exists, what is the...