Counterexamples to the Maximal p-Norm Multiplicativity Conjecture for all p > 1

• Published in: Communications in mathematical physics Vol. 284; no. 1; pp. 263 - 280
• Main Authors: Hayden, Patrick, Winter, Andreas
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.11.2008; Springer
• Subjects: Classical and Quantum Gravitation; Complex Systems; Exact sciences and technology; Mathematical and Computational Physics; Mathematical methods in physics; Mathematical Physics; Other topics in mathematical methods in physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Theoretical; Entangle State; Entropy; Quantum Information Theory; Quantum Channel; Classical Capacity; Quantum information; Mathematical physics; Quantum theory; Information theory

For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p -norms. Equivalently, for all p  > 1, the minimum output Rényi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, the minimum output Rény...