Causal and localizable quantum operations - art. no. 052309

We examine constraints on quantum operations imposed by relativistic causal ity. A bipartite superoperator is said to be localizable if it can be imple mented by two parties (Alice and Bob) who share entanglement but do not com municate, it is causal if the superoperator does not convey information fro m Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that ar e causal but not localizable. We construct another class of causal bipartit e superoperators that are not localizable by invoking bounds on the strengt h of correlations among the parts of a quantum system. A bipartite superope rator is said to be semilocalizable if it can be implemented with one-way q uantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-meas urement superoperators are semi localizable, and we establish a general cri terion for semicausality. In the multipartite case, we observe that a measu rement superoperator that projects onto the eigenspaces of a stabilizer cod e is localizable.