A Software Approach to the PPT2 ConjectureNovšak, Noah (Avtor) Zalar, Aljaž (Mentor) Klep, Igor (Komentor) PPT2 conjecturequantum entanglementpositive mapssemidefinite programmingbound entanglementThe PPT2 conjecture asserts that the composition of any two PPT maps is entanglement breaking. It is proven for maps on matrices of size up to $3 times 3$ and for several structured families, but the general case remains open; the smallest open case, $4 times 4$, is the one this thesis attacks computationally. We build a reproducible Julia pipeline that (i) mass-produces provably indecomposable entanglement witnesses via the Klep--McCullough--Šivic--Zalar construction of positive but not completely positive maps, rationalizing each certificate after the semidefinite program is solved so that every stored witness is exact -- 10,000 witnesses in under an hour, orders of magnitude faster than comparable implementations; (ii) generates bound entangled PPT candidates by generic random sampling, partial-transpose-invariant sampling, and witness-guided extraction; and (iii) tests the conjecture both by screening tens of thousands of composed channels with witness and DPS criteria, and by a see-saw SDP that searches the manifold of composed PPT maps directly. No counterexample is found. The witness library proves to be a collection of single-state detectors: each witness detects essentially only the state extracted from it. The central finding is a sharp contrast: every one of the 10,000 witnesses attains a negative optimum somewhere on the PPT cone, yet not one fires on the composition manifold -- precisely the signature expected if the conjecture holds in dimension four. This indicates that a counterexample, if one exists at all, must inhabit a measure-zero subset of the composition manifold that a random search cannot reach. As a by-product, the construction yields explicit biquadratic $4 times 4$-forms that are positive but not sums of squares, which is a notoriously difficult problem in real algebraic geometry.20262026-07-10 12:30:03Magistrsko delo/naloga184600VisID: 38589sl