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.

We propose an extension of the classical Rényi divergences to quantum states through an optimization over probability distributions induced by restricted sets of measurements. In particular, we define the notion of locally-measured Rényi divergences, where the set of allowed measurements originates from variants of locality constraints between (distant) partiesAandB. We then derive variational bounds on the locally-measured Rényi divergences and systematically discuss when these bounds become exact characterizations. As an application, we evaluate the locally-measured Rényi divergences on variants of highly symmetric data-hiding states, showcasing the reduced distinguishing power of locality-constrained measurements. For n-fold tensor powers, we further employ our variational formulae to derive corresponding additivity results, which gives the locally-measured Rényi divergences operational meaning as optimal rate exponents in asymptotic locally-measured hypothesis testing.

We propose an extension of the classical Rényi divergences to quantum states through an optimization over probability distributions induced by restricted sets of measurements. In particular, we define the notion of locally-measured Rényi divergences, where the set of allowed measurements orig-inates from locality constraints between (distant) parties$A$and$B$. As our main result, we derive variational characterizations of these locally-measured Rényi divergences. We then evaluate them for variants of data-hiding states, showcasing the reduced distinguishing power of locality-constrained measurements, and give corresponding applications in locally-measured hypothesis testing.