Cyril Branciard

We construct and classify entangled measurements with tetrahedral symmetry as group-covariant orbits of a fiducial state. For this class, localizability follows from the Clifford level of a diagonal phase in the fiducial, yielding an explicit hierarchy and efficient constructions. The framework recovers the two-qubit Elegant Joint Measurement (EJM) uniquely and extends it to multiqubit EJMs with identical local geometry but inequivalent global entanglement classes for n\ge3. A continuous family interpolating between the Bell measurement and the EJM realizes an infinite set of localizable tetrahedral bases.

Quantum theory is in principle compatible with scenarios where physical processes occur in an indefinite order, potentially yielding advantages in a broad range of information processing tasks. However, advantages in communication, the most basic form of information processing, have so far remained controversial and hard to prove. Here we provide a framework for assessing the role of causal order in communication, by comparing different causal structures under the constraint that the allowed operations must not generate signaling from signaling-incapable devices. Using this framework, we establish a clear-cut advantage of indefinite causal order, and, at the same time, we identify a series of fundamental limits to the communication power of causal structures in quantum mechanics. Notably, we find that a special form of indefinite causal order, obtained by coherently controlling the order of two processes, enhances the transmission of classical messages in a one-shot scenario, but no quantum operation with indefinite order can offer advantages over shared entanglement when asymptotically many uses of the same communication device are employed. Overall, our results unveil non-trivial relations between communication, causal order, entanglement, and no-signaling quantum processes.