Multivariate Trace Inequalities, p-Fidelity, and Universal Recovery Beyond Tracial von Neumann Algebras

Abstract: Trace inequalities are powerful in quantum information theory, often replacing classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivate entropy inequalities in von Neumann algebras that lack a useful notion of a trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki-Lieb-Thirring and Golden-Thompson inequalities from (Sutter, Berta & Tomamichel 2017). Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of the recovery map tightening of the data processing inequality for relative entropy. We also generalize via subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that non-decrease of relative entropy is equivalent to existence of an L1-isometry implementing the channel on both input states.

HEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

Purdue HET

Series comments: The recorded talks will be available on YouTube here: www.youtube.com/playlist?list=PLxU3vHZccQj64m9zsQR74D5WP1z1g4t1J