Device-independent tests of time-like correlations

We develop a device-independent framework for testing quantum channels. That is, we falsify a hypothesis about a quantum channel based only on an observed set of input-output correlations. Formally, the problem consists of characterizing the set of input-output correlations compatible with any arbitrary given quantum channel. For binary (i.e., two input symbols, two output symbols) correlations, we show that extremal correlations are always achieved by orthogonal encodings and measurements, irrespective of whether or not the channel preserves commutativity. We further provide a full, closed-form characterization of the sets of binary correlations in the case of: i) any dihedrally-covariant qubit channel (such as any Pauli and amplitude-damping channels), and ii) any universally-covariant commutativity-preserving channel in an arbitrary dimension (such as any erasure, depolarizing, universal cloning, and universal transposition channels).