Quantum Entropy Prover

IEEE International Symposium on Information Theory (ISIT), pp. 1–6

Abstract

Information inequalities govern the ultimate limitations in information theory and as such play a pivotal role in characterizing what values the entropy of multipartite states can take. Proving an information inequality, however, quickly becomes arduous when the number of involved parties increases. For classical systems, [Yeung, IEEE Trans. Inf. Theory (1997)] proposed a framework to prove Shannon-type inequalities via linear programming. Here, we derive an analogous framework for quantum systems, based on the strong sub-additivity and weak monotonicity inequalities for the von-Neumann entropy. Importantly, this also allows us to handle constrained inequalities, which - in the classical case - served as a crucial tool in proving the existence of non-standard, so-called non-Shannon-type inequalities [Zhang & Yeung, IEEE Trans. Inf. Theory (1998)]. Our main contribution is the Python package qITIP, for which we present the theory and demonstrate its capabilities with several illustrative examples.

Authors 3

1. Shao‐Lun Huang Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Germany

2. Tobias Rippchen Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Germany

3. Mario Berta Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Germany