Detection of non-classicality in Quantum Theory: Insights from Quantum Networks and Stabilizer States
Non-classicality, Quantum Networks, Bell-Non locality, Quantum correlations, Magic states, Stabilizer polytope,
Universal computation
Non-classicality is a fundamental feature of quantum mechanics, manifesting in diverse forms such as non-local correlations in quantum networks and the computational advantage provided by magic states. In quantum networks, non-classicality enables the realization of tasks beyond classical capabilities, playing a crucial role in secure communication and cryptography. Concurrently, in the domain of quantum computation, non-classicality emerges through magic states, which provide the essential resources for universal quantum computation that cannot be achieved by stabilizer operations alone. This thesis presents results on the characterization and detection of non-classicality within these different scenarios. The work is organized along two primary research lines. First, we explore the use of interventions—a tool from causal inference—to detect quantum correlations in quantum networks. We construct an interventional-observational polytope for the instrumental scenario and show stronger non-classicality certification. Subsequently, we generalize the concept of interventions from observable variables to latent variables, specifically in the quantum case where one has partial access to quantum states. We apply this generalization to demonstrate non-classicality in the challenging triangle scenario. Second, addressing the resource theory of magic, we introduce a semi-device-independent framework to detect magic in both Bell and prepare-and-measure scenarios. We derive inequalities that act as witnesses of non-stabilizerness (or magic), such that a violation of these inequalities certifies the presence of magic in the underlying states without relying on full characterization of the devices. Through these contributions, we aim to establish a new research direction where tools from causal inference, Bell non-locality, and quantum networks are synergized to enable the device-independent detection of various quantum resources, including magic states.