{"id":"palomar/PALOMAR-2026-10-13-000001","url":"https://github.com/JD-Jones-ASES/qubit-cloning-lean/tree/f619a52e67849f80205127e3ba7877f7f7658e50","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-13-000001-v1.json","repo":"https://github.com/JD-Jones-ASES/qubit-cloning-lean","tags":["quant-ph","msc:81P45","msc:81P47","msc:15A45","quantum-information","quantum-cloning","lean"],"score":0,"title":"Optimal universal 1 → 2 qubit cloning at fidelity 5/6, the universal-NOT, and asymmetric cloning","trust":"high","domain":"quant-ph","source":"palomar","authors":["JD Jones"],"reviews":0,"subject":"quant-ph","summary":"A Lean 4 development of the optimal universal 1 -> 2 cloning of a qubit, with every figure of merit finite: a channel from one qubit to two is a finite Kraus family K_i : C^2 -> C^2 (x) C^2 with sum K_i^* K_i = 1 (the blank qubit is fixed, so this is a 1 -> 2 map; the Choi-Kraus theorem is not proved), the two clone fidelities of a pure input psi are Re and Re , and F1-bar, F2-bar are their averages over the six Pauli eigenstates (1 +- sigma)/2, Gaussian-rational density matrices (the six states form a 2-design, the octahedron being a spherical 3-design, so these equal the Bloch-sphere…","category":"research","comments":0,"disputed":false,"division":"physics","mentions":0,"verified":true,"discussed":0,"published":"2026-10-13","reactions":{},"formalized":true,"formalizes":[{"title":"Quantum copying: Beyond the no-cloning theorem","identifier":"doi:10.1103/PhysRevA.54.1844","relationship":"formalizes"},{"title":"Optimal quantum cloning machines","identifier":"doi:10.1103/PhysRevLett.79.2153","relationship":"formalizes"},{"title":"Optimal cloning of pure states","identifier":"doi:10.1103/PhysRevA.58.1827","relationship":"formalizes"},{"title":"Optimal copying of one quantum bit","identifier":"doi:10.1103/PhysRevA.58.4377","relationship":"formalizes"},{"title":"Highly asymmetric quantum cloning in arbitrary dimension","identifier":"arXiv:quant-ph/0505212","relationship":"formalizes"}]}