Reduction of a state of a quantum system to a subsystem gives partial quantum information about the true state of the total system. In connection with optimal state determination for two qubits, the question was raised about the maximum number of pairwise complementary reductions. The main result of the paper tells that the maximum number is 4, that is, if A,A, . . . ,A are pairwise complementa...

Reduction of a state of a quantum system to a subsystem gives partial quantum information about the true state of the total system. In connection with optimal state determination for two qubits, the question was raised about the maximum number of pairwise complementary reductions. The main result of the paper tells that the maximum number is 4, that is, if A,A, . . . ,A are pairwise complementa...

let g be a group. a subset x of g is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in x. if |x| ≥ |y | for any other set of pairwise non-commuting elements y in g, then x is said to be a maximal subset of pairwise non-commuting elements. in this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

Reduction of a state of a quantum system to a subsystem gives partial quantum information about the true state of the total system. In connection with optimal state determination for two qubits, the question was raised about the maximum number of pairwise complementary reductions. The main result of the paper tells that the maximum number is 4, that is, if A;A; : : : ;A are pairwise complementa...

Analytic formulas are developed for various types of power and error rates of some closed testing procedures. The formulas involve non-convex regions that may be integrated with high, pre-specified accuracy using available software. The non-convex regions are represented as a union of hyper-rectangles. These regions are transformed to the unit hypercube, then summed, to create an expression for...

A classic result of Johnson and Lindenstrauss asserts that any set of n points in d-dimensional Euclidean space can be embedded into k-dimensional Euclidean space—where k is logarithmic in n and independent of d—so that all pairwise distances are maintained within an arbitrarily small factor. All known constructions of such embeddings involve projecting the n points onto a spherically random k-...

We compute the radiative ro-vibrational emission spectrum of H2 involving quasibound states via a simple numerical method resolution Schr\"odinger equation by introducing modifed effective molecular potential. The comparison eigenvalues obtained with our approximation and other theoretical methods based on scattering resonance properties is excellent. Electric quadrupole magnetic dipole contrib...