8 papers
Comment on "The polarization hierarchy for polynomial optimization over convex bodies, with applications to nonnegative matrix rank"
Julius A. Zeiss
We revisit the feasibility and convergence claims for the polarization hierarchy of Plávala, Ligthart and Gross [Linear Algebra Appl.\ 723 (2025) 15--32]. Counterexamples show that…
A counterexample to the quantum Hedetniemi conjecture
Julius A. Zeiss
Godsil, Roberson, Šámal and Severini conjectured that the quantum chromatic number of the categorical product of two graphs equals the minimum of the quantum chromatic numbers of t…
Optimal entanglement-assisted source coding under a balanced-difference promise
Julius A. Zeiss
Entanglement can reduce the communication required for coding tasks, but establishing the minimum achievable cost is essential to understanding its limits. We address this question…
Sharp continuity of quantum conditional entropy
Mario Berta, Pablo Costa Rico, Gereon Kossmann +2
We prove the sharp uniform continuity bound for quantum conditional entropy. If two bipartite states are at trace distance at most and , the optimal dimension-only mo…
Fixed points in de Finetti hierarchies
Gereon Kossmann, Julius A. Zeiss
De Finetti theorems convert permutation symmetry into approximate mixtures of product states and thereby justify a wide range of reductions in classical and quantum statistics. In…
Finite de Finetti for convex bodies and Polynomial Optimization
Julius A. Zeiss, Gereon Koßmann, René Schwonnek +1
Leveraging a recently proposed notion of relative entropy in general probabilistic theories (GPT), we prove a finite de Finetti representation theorem for general convex bodies. We…
On approximate quantum error correction for symmetric noise
Gereon Koßmann, Julius A. Zeiss, Omar Fawzi +1
We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds…
Approximating fixed size quantum correlations in polynomial time
Julius A. Zeiss, Gereon Koßmann, Omar Fawzi +1
We show that -additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $…