No abstract

We perform a reconstruction of the polarization sector of the density matrix of an intense polarization squeezed beam starting from a complete set of Stokes measurements. By using an appropriate quasidistribution, we map this onto the Poincaré space providing a full quantum mechanical characterization of the measured polarization state.

No abstract

We study the physical implementation of a qutrit quantum computer in the context of trapped ions. Qutrits are defined in terms of electronic levels of trapped ions. We concentrate our attention on a universal two-qutrit gate, which corresponds to a controlled-NOT gate between qutrits. Using this gate and a general gate of an individual qutrit, any gate can be decomposed into a sequence of these gates. In particular, we show how this works for performing the quantum Fourier transform for n qutrits.

The problem of electromagnetic-field quantization in time-dependent nonuniform linear nondispersive media is investigated. The explicit formulas for the number of photons generated from the initial vacuum state due to the change in time of dielectric permeability of the medium are obtained in the case when the spatial and temporal dependences are factorized. The concrete time dependences include adiabatic and sudden changes of permeability, the parametric resonance at twice the eigenfrequency of the mode, Epstein's symmetric and transition profiles, "temporal Fabry-Perot resonator, " and some others.The upper and lower bounds for the squeezing and correlation coefficients of the field in the final state are given in terms of the reAection coefficient from an equivilent potential barrier or the number of created quanta. The problem of impulse propagation in a spatially uniform but time-dependent dielectric medium is discussed.PACS number(s): 42.50.Dv

A complete set of d + 1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d − 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.

For a system of N qubits, spanning a Hilbert space of dimension d = 2 N , it is known that there exists d + 1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases with different properties as far as separability is concerned. Here we derive the four sets of nine bases for three qubits, and show how they are unitarily related. We also briefly discuss the four-qubit case, give the entanglement structure of sixteen sets of bases,and show some of them, and their interrelations, as examples. The extension of the method to the general case of N qubits is outlined.

We derive an exact (differential) evolution equation for a class of SU(2) quasiprobability distribution functions. Linear and quadratic cases are considered as well as the quasiclassical limit of the large dimension of representation, S≫1.