Closed-Form Arbitrary-Gap Rényi Nonadditivity Above Any Positive Order via Direct Products of Free Groups and High-Girth Graphs
Year: 2026
Type: preprint
Abstract: We give a closed-form finite-dimensional construction of quantum channels with real algebraic entries exhibiting arbitrarily large violations of minimum-output Rényi entropy additivity uniformly above any prescribed positive Rényi order, using a different finite realization based on direct products of free groups and fixed-field high-girth graphs. More precisely, for every $p_0>0$ and $g>0$, we construct one channel and one Bell input for which the additivity gap is greater than $g$ simultaneously for all $p\in[p_0,\infty]$. With $r=\lceil2g\rceil$, the construction uses $15r$ output qubits and $O(r2^{30r}+r^2(1+p_0^{-1}))$ input qubits. Compared with the stated parameters of Shou and Gorshkov \cite{ShouGorshkov2026}, our construction uses fewer output qubits for every target gap and has a smaller asymptotic input-qubit bound as the gap grows with the positive cutoff fixed. At the von Neumann order, a separate specialization gives an explicit channel with gap greater than $1/1024$ using $37608898$ input qubits and $8$ output qubits.
Source: arXiv (Cornell University)
Authors: Zhen, Guocheng, Chen, Ranyiliu, Wang, Xin
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G2052179644, G8274973648
OpenAlex ID: W7220705461