Laneve, Lorenzo Wolf, Stefan 2025 Quantum signal processing (QSP) is a framework which was proven to unify and simplify a large number of known quantum algorithms, as well as discovering new ones. QSP allows one to transform a signal embedded in a given unitary using polynomials. Characterizing which polynomials can be achieved with QSP protocols is an important part of the power of this technique, and while such a characterization is well-understood in the case of univariate signals, it is unclear which multivariate polynomials can be constructed when the signal is a vector, rather than a scalar. This work uses a slightly different formalism than what is found in the literature, and uses it to find simpler necessary conditions for decomposability, as well as a sufficient condition – the first, to the best of our knowledge, proven for a (generally inhomogeneous) multivariate polynomial in the context of quantum signal processing. application/pdf https://susi.usi.ch/global/documents/335483 https://localhost:5000/ark:/12658/srd1335483 https://susi.usi.ch/documents/335483/files/q-2025-02-20-1641.pdf eng info:eu-repo/semantics/altIdentifier/issn/2521-327X info:eu-repo/semantics/altIdentifier/doi/10.22331/q-2025-02-20-1641 info:eu-repo/semantics/altIdentifier/ark/12658/srd1335483 info:eu-repo/semantics/openAccess CC BY Quantum. - 2025, vol. 9, p. 1641 info:eu-repo/classification/udc/004 On multivariate polynomials achievable with quantum signal processing http://purl.org/coar/resource_type/c_6501