Quantum processes without a causal order

Less than ten years ago it was realized that quantum theory permits the existence of processes which do not have a defined causal order. To date, several experiments have confirmed the existence of one such process, called the quantum SWITCH, in which it is impossible to say which of two parties acts first. This has since spawned a new field of research on quantum processes with an indefinite causal order. Building on a mathematical analogy to entanglement certification, various methods to quantify the lack of a causal order have been proposed and demonstrated. These characterization techniques range from playing specially designed games to the measurement of a so-called causal witness. Despite these promising strategies, there has not yet been a complete characterization of the quantum SWITCH and no measurement of its process fidelity. Here we present a new protocol to perform causal tomography which we carry out using a novel implementation of the quantum SWITCH, based on time-bin qubits in optical fiber. Our new implementation is readily scalable to more than two parties and, hence, could be used to observe the scaling advantages of certain quantum games. Using this platform, we perform the first measurement of the process fidelity of the quantum SWITCH.