We propose a method for calculating Coulomb matrix elements between exciton and biexciton states in semiconductor nanocrystals based on the envelope function formalism. We show that such a calculation requires proper treatment of the Bloch parts of the carrier wave functions which, in the leading order, leads to spin selection rules identical to those holding for optical interband transitions. Compared to the usual (intraband) Coulomb couplings, the resulting matrix elements are additionally scaled by the ratio of the lattice constant to the nanocrystal radius. As a result, the Coulomb coupling between exciton and biexciton states scale as 1/R 2 . We present also some statistical estimates of the distribution of the coupling magnitudes and energies of the coupled states The number of biexciton states coupled to exciton states form a certain energy range shows a power-law scaling with the ratio of the coupling magnitude to the energy separation. We estimate also the degree of mixing between exciton and biexciton states. The amount of biexciton admixture to exciton states at least 1 eV above the multiple exciton generation threshold can reach 80% but varies strongly with the nanocrystal size.

We study the influence of phonon scattering on the noise characteristics of a quantum point contact coupled to a two-electron system in a double quantum dot, as proposed for a singlet-triplet measurement scheme in a double-dot system. We point out that at low temperatures phonon-induced relaxation to the ground state suppresses transitions to doubly occupied singlet states which are the source of detectable current fluctuations in this measurement scheme. Thus, for a relatively strong electron-phonon interaction present in the system, the two configurations display the same noise characteristics. In this way, coupling to phonons reduces the distinguishability between the singlet and triplet configurations. Under such conditions, the proposed measurement scheme is no longer valid even though the times of the measurement-induced decoherence of an initial singlettriplet superposition and of the localization into the singlet or triplet subspace remain essentially unchanged.

We study the effect of decoherence on a quantum von Neumann measurement process. We discuss the effect of phonon noise on the direct measurement of two-electron spin states in a double quantum dot achieved by monitoring the noise of the current flowing through a quantum point contact coupled to one of the dots. We show that although the decoherence is damaging to the procedure at the extremely low temperatures characteristic of spin-in-quantum-dots experiments, and may even be fatal, increasing the temperature leads to a revival of the usefulness of the protocol: At higher temperatures, when the reservoir becomes an effective source of energy, it can enhance system fluctuations, and under such conditions the decoherence becomes advantageous to the measurement scheme and leads to the enhancement of the distinguishability between the measured states. Hence, the uncontrollable interaction of the measured system with the environment can be either an advantage or a disadvantage for a quantum measurement, depending on the characteristics of the decoherence process.