Efficient and robust estimation of non-classical effects in quantum devices

The ability to transfer quantum information between systems is a fundamental component of quantum technologies, and can generate correlations. However correlations in quantum channels are less well studied than those in quantum states. Motivated by recent techniques in randomized benchmarking (RB), we develop a range of results for efficient estimation of correlations in channels. We extend the notion of unitarity - an average figure of merit that captures the coherence of a quantum channel - to substructures within a bipartite quantum channel. We define a correlation unitarity and prove that it provides a witness of nonseparability -- a strictly non-classical effect. We find that this measure can be estimated with robustness to errors in state preparation and measurements (SPAM) for any separable or Pauli quantum channel, and we show that a benchmarking/tomography protocol with mid-circuit resets can reliably witness nonseparability for sufficiently small reset errors. Related experimental techniques, that we develop, can be used to study quantum incompatibility. Incompatibility is a feature of quantum theory that sets it apart from classical theory, and the inability to clone an unknown quantum state is one of the most fundamental instances. We extend the definition of unitarity to general physical theories. Then, we introduce the notion of compatible unitarity pair (CUP) sets, that correspond to the allowed values of unitarities for compatible channels in the theory. We show that a CUP-set constitutes a simple `fingerprint' of a physical theory, and that incompatibility can be studied through them. We analytically prove quantum CUP-sets encode both the no-cloning/broadcasting and no-hiding theorems of quantum theory. We then develop RB protocols that efficiently estimate quantum CUP-sets and provide simulations using IBMQ of the simplest instance. Finally, we discuss ways in which the above methods provide independent benchmarking information and test the limits of quantum theory on devices.