A Realignment-Based Obstruction to Two-Superpositive Decompositions of PPT Operators: An Explicit Rational Certificate and Tensor-Power Construction
Year: 2026
Type: preprint
Abstract: We present an explicit rational certificate for a positive-partial-transpose (PPT) state on C^15625 tensor C^15625 outside the cone C2 + partial_transpose(C2), where C2 denotes the cone of positive semidefinite operators of Schmidt number at most two. A 5x5 grid-state seed has realignment norm bounded below by 1028/909, proved by a 25x25 integer matrix certificate. Six tensor copies amplify this to (1028/909)^6 > 2, while the realignment norm is at most twice the trace on C2 + partial_transpose(C2). An explicit Choi witness consequently defines a linear map that is simultaneously 2-positive and 2-copositive but nondecomposable. The accompanying archive contains the mathematical preprint, LaTeX source, exact-arithmetic verification programs, and computational checks. This is an unrefereed proof manuscript. Independent expert verification and exhaustive prior-art assessment remain outstanding. The construction does not resolve the PPT-cubed conjecture or establish an improved quantum teleportation protocol.
Author: Henry, Kias
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223821454