A Realignment-Based Obstruction to Two-Superpositive Decompositions of PPT Operators: An Explicit Rational Certificate and Tensor-Power Construction

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-28
DOI
https://doi.org/10.5281/zenodo.23696847
Primary Topic
Quantum Information and Cryptography
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

A Realignment-Based Obstruction to Two-Superpositive Decompositions of PPT Operators: An Explicit Rational Certificate and Tensor-Power Construction

Kias Henry
2 links
Zenodo (CERN European Organization for Nuclear Research)
Quantum Information and Cryptography
preprint

A Realignment-Based Obstruction to Two-Superpositive Decompositions of PPT Operators: An Explicit Rational Certificate and Tensor-Power Construction

Kias Henry
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Quantum Information and Cryptography
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon
A Realignment-Based Obstruction to Two-Superpositive Decompositions of PPT Operators: An Explicit Rational Certificate and Tensor-Power Construction — Kias Henry · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS