We prove that all states (mixed or pure) of qubit–qutrit ( $$2\times 3$$ ) systems have entanglement-preserving unitary (EPU) equivalence to a compact subset true-generalized X (TGX) called EPU-minimal TGX which we give explicitly. Thus, for any spectrum–entanglement combination achievable by general states, there exists an state the same spectrum and entanglement. use I-concurrence measure ent...

Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common mechanical constraints such as, e.g., orthogonality of isometric unitary matrices, CPTP property channels, conditions on density seen quotient or embedded Riemannian manifolds. This allows to use techniques for solving quantum-mechanical In the present work, we i...

We consider the normwise condition number and backward error of eigenvalues of matrix polynomials having ⋆-palindromic/antipalindromic and ⋆-even/odd structure with respect to structure preserving perturbations. Here ⋆ denotes either the transpose T or the conjugate transpose ∗. We show that when the polynomials are complex and ⋆ denotes complex conjugate, then to each of the structures there c...

background and objective: vesicoureteral reflux (vur) is one of the most common urinary tract abnormalities in patients with urinary tract infection. nowadays noninvasive diagnostic methods are suggested to recognize vur and its severity. methods: we measured urinary and serum fibronectin in 51 children with vur. results: the mean serum fibronectin was 318.3±112.1 in children with low grade vur...

The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum control, especially in control of quantum information processing. Motivated by this problem, we develop a measure for evaluating the distance between unitar...

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

We consider a probability measure m on a Hilbert space X and a bounded linear transformation on X that preserves the measure. We characterize the linear dynamical systems (X, m, T) for the cases where either X is finite dimensional or T is unitary and we give an example where T is a weighted shift operator. We apply the results to the limit identification problem for a vector-valued ergodic the...

In quantum cryptography, a one-way permutation is a bounded unitary operator U : H → H on a Hilbert space H that is easy to compute on every input, but hard to invert given the image of a random input. Levin [Probl. Inf. Transm., vol. 39 (1): 92-103 (2003)] has conjectured that the unitary transformation g(a, x) = (a, f(x) + ax), where f is any length-preserving function and a, x ∈ GF2‖x‖ , is ...

A topological group G is called extremely amenable if every continuous action of G on a compact space has a fixed point. This concept is linked with geometry of high dimensions (concentration of measure). We show that a von Neumann algebra is approximately finite-dimensional if and only if its unitary group with the strong topology is the product of an extremely amenable group with a compact gr...