Degenerate four-wave mixing ͑FWM͒ from individual localized excitonic transitions is measured using a dual-polarization extension of heterodyne spectral interferometry. A fine-structure splitting ͑FSS͒ of the localized excitons of 20-80 eV is observed, revealing a spatially anisotropic localization in the quantum well plane, preferentially oriented along the ͓110͔ direction. The ratio of the transition dipole moments of the FSS transitions is in the range 0.7-1.4, with no significant correlation to the FSS. Retrieving both polarization components of the FWM in amplitude and phase we measure the time-resolved polarization state of the exciton after pulsed excitation, showing a coherent evolution oscillating between linear and virtually circular polarization. The polarization of the created FWM state is a result of the initial polarization state created by the first excitation pulse, its free evolution up to the arrival of the second pulse, and its conversion into the FWM controlled by the polarization of the second pulse. DOI: 10.1103/PhysRevB.78.041103 PACS number͑s͒: 78.47.Fg, 78.47.jj, 78.47.jm, 78.47.nj With the recent development of the heterodyne spectral interferometry ͑HSI͒ technique, 1 the measurement of the nonlinear coherent response, e.g., four-wave mixing ͑FWM͒, of individual localized two-level systems has become feasible. Standard FWM experiments 2,3 rely on directional selection of the nonlinear optical response and therefore are not suited for emitters localized to subwavelength regions, like excitons confined in quantum dots. HSI overcomes this limitation by taking advantage of an effective frequency selection of the FWM signal, relying only on the time invariance of the system investigated. HSI has been used to determine broadening mechanisms and measure microscopic dephasing time within finite, inhomogenously broadened ensembles of excitons 4 or transitions experiencing spectral wandering. 5 By applying spectral interferometry, 6 the FWM is retrieved both in amplitude and phase. This permits not only to obtain complete information about the state vector on the Bloch sphere, but also allows the resonant observation of coherent control of excitons on ultrafast time scales.7 By performing delaytime dependent HSI and transforming-in analog to NMR techniques 8,9 -the data into a two-frequency representation R −1,2 ͑ , 1 ͒, one can observe and classify coherent coupling between individual localized excitons. 1 Similar twodimensional techniques are used to investigate many-body interactions in quantum wells 10 and vibrational and electronic coupling in molecules.11 HSI is therefore a powerful tool for coherent characterization, ultrafast coherent control, and manipulation of excitonic qbits.In this work we extend the HSI technique to a dualpolarization scheme ͑DHSI͒, which allows us to simultaneously measure both polarization components of the field in phase and amplitude, completely determining the time or spectrally resolved polarization state of the FWM. A similar technique has been introduced...