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In multimode optical systems, the spectral covariance matrix encodes all the information about quantum correlations between the quadratures of Gaussian states. Recent research has revealed that, in scenarios that are more common than previously thought, part of these correlations remain inaccessible to standard homodyne detection scheme. Formally, this effect can be attributed to a non-real spectral covariance matrix. In this work, we provide a systematic framework and explicit criteria for identifying experimental configurations leading to such a behavior. This study will facilitate the proper exploitation and optimal engineering of CV quantum resources., Comment: 13 pages, 11 figures, submitted

The frequency comb of a multimode interferometer offers exceptional scalability potential for field-encoded quantum information. However, the staple field detection method, homodyne detection, cannot access quantum information in the whole comb because some spectral quadratures (and their asymmetries with respect to the LO) are out of reach. We present here the first general approach to make arbitrary, one-shot measurements of a multimode quantum optical source, something that is required for photonic quantum computing and is not possible when using homodyne detection with a pulse-shaped LO. This approach uses spectral mode-matching, which can be understood as interferometry with a memory effect. We derive a complete formalism and propose an implementation by microcavity arrays., Comment: 16 pages, 12 figures, submitted