The maximum output p-norm of quantum channels is not multiplicative for any p>2

2007/07/03 by Andreas Winter, Winter, Andreas · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Random Matrices and Applications #Stochastic processes and statistical mechanics #quant-ph

paper · pdf · doi:10.48550/arxiv.0707.0402

Superseded by arXiv:0807.4753! -- Old comment: Four pages only. If you write to me, please don't tell me how simple and obvious it is - I know that myself. I accept suggestions for journals to submit to, though; the obscurer the better. V2 has some corrections, and I removed one reference. Don't miss the more recent work arXiv:0707.3291

Abstract

We prove the claim made in the title by showing that approximately randomising maps of large dimension are counterexamples to the multiplicativity conjecture.

Cited by

• Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1

Related

• On the multiplicativity conjecture for quantum channels
• CB-norm estimates for maps between noncommutative L_p-spaces and quantum channel theory
• A quantum channel with additive minimum output entropy
• Additivity violation of quantum channels via strong convergence to semi-circular and circular elements
• A relation between completely bounded norms and conjugate channels