Quantum Schr\"odinger bridge constructions establish the existence of a conditioned process under a positivity hypothesis on the endpoint data, and three independent ones adopt it. We show that hypothesis fails on a definite locus once the conditioned object is the two-state amplitude $\phi^*\psi$ of a pre- and post-se...
Chon-Fai Kam, Kai-Wen Wong Università degli Studi di Palermo, I. U et al.· 0 citations
Under the contraction of $SU(1,1)$ to the Heisenberg-Weyl group, the zeros of the Husimi function of a state redistribute according to a single scale, and we determine which of them survive. The stellar rank of a single-mode bosonic pure state, the number of these zeros, characterises the Gaussian states on the plane t...
A system between a preparation and a post-selection has had no agreed state since 1964. With positivity as the criterion, a post-selection admits an interval of orderings around the symmetric one exactly when the subspace it forbids is spanned by eigenvectors of a full-rank filtered state. Otherwise it certifies contex...
Chon-Fai Kam, Kai-Wen Wong Università degli Studi di Palermo, I. U et al.· 0 citations
Hudson's theorem states that a pure state of a bosonic mode has a non-negative Wigner function if and only if it is Gaussian. It underwrites the reading of Wigner negativity as a faithful signature of pure-state non-classicality. We show the statement has no analogue on curved phase space. For the positive discrete ser...
The standard geometric derivation of neural scaling exponents takes the intrinsic dimension of a data manifold as its input. On modular addition in $\mathbb{Z}_p$ that derivation has no input. The exact algebraic solution is an orbit of $\mathbb{Z}_p$ acting by isometries. Transitivity alone makes the ratio statistic u...
Chon-Fai Kam, M. Bessafi, Frédéric Cadet· 0 citations
Xu, Vardi and Safran (ICML 2026) prove that over-parameterized ridge regression over an unstructured random Gaussian feature map groks, with the delay between memorization and generalization growing as $1/\lambda$ in the weight decay. We show that on a structured feature map the same delay does not appear. For a band-l...
Chon-Fai Kam, M. Bessafi, Frédéric Cadet· 0 citations
It is proved that the local ZX simplification layer (spider fusion and identity removal) computes exactly the free-product normal form of Z_2 * Z_8, giving exact per-instance compression and, under a calibrated ergodicity hypothesis, a depth-independent limit law confirmed on two independently constructed nets.
Chon-Fai Kam, A. Mahasinghe, Kaushika De Silva et al.· 0 citations
Boson sampling demonstrates quantum advantage through the interference of indistinguishable particles, with output probabilities governed by matrix permanents. Realizing it on deterministic, matter-based platforms requires encoding the bosonic modes in finite-dimensional local Hilbert spaces, which introduces a leakage...
A measurement of what diagrammatic post-processing recovers from structural redundancy in the Solovay-Kitaev algorithm, which optimizes for numerical convergence rather than circuit economy, and its output carries structural redundancy that a gate-level compiler cannot see.
Dulari De Silva, A. Mahasinghe, Chon-Fai Kam et al.· 0 citations
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