Correlations from joint measurements in boxworld and applications to information processing

Abstract

Quantum measurements have been a central topic of research in quantum theory for many years. In the context of causal structures and communication over networks, we are often particularly interested in local measurements of subsystems of a multi-partite system and classical processing of their inputs and outcomes. Formally, this processing can often be described by means of maps that are known as wirings. These wirings are furthermore interesting for the analysis of generalized probabilistic theories, as they are shared by all of them. In this work, we explicitly characterise all possible mulitpartite measurements in the generalised probabilistic theory box-world for various numbers of parties n with systems characterised by n_i fiducial measurements (which can be thought of as inputs here) and n_o outcomes, for small n, n_i, n_o. This includes all n-party n_i-input, n_o-outcome wirings. For n > 2, we further classify these measurements into three classes: wirings, deterministic non-wiring type and non-deterministic non-wiring type measurements. We explore advantages of these different types of measurements over previous protocols in the context of non-locality distillation and state-distingishability. We further find examples of non-locality without entanglement (contrary to previous claims) and a relation of these measurements to classical process matrices.