Causal and localizable quantum operations

By David Beckman, Daniel Gottesman, Morten Nielsen, John Preskill. 2001

189 citations recorded by the source corpus.

We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate; it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-measurement superoperators are semilocalizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/b669a925af9215a9187cdaa824520c77da0a7dc6

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

A Postquantum Theory of Classical Gravity? (2018, unknown): “[75]), the behavior of the spin can differ depending on how one decomposes the Hamiltonian in terms of Lindblad operators.”
Quantum resource theories (2018, background): “This is a property belonging to a more general class of multi-instruments called semicausal (Beckman et al., 2001; Eggeling et al., 2002; Piani et al., 2006), and these can always be realized by replacing the classical communication and classical processing in Fig.”
The Theory of Quantum Information (2018, background): “5 is due to Eggeling, Schlingemann, and Werner [67], answering a question raised by Beckman, Gottesman, Nielsen, and Preskill [25] (who credit DiVincenzo for raising the question).”
Quantum channels and memory effects (2012, methodology): “H (Beckman et al., 2001; Eggeling, Schlingemann and Werner, 2001; Piani et al., 2006), they can be said non-signaling (or causal) channels, meaning that the output states of any subset 17 of the carriers cannot be influenced by the input state of the remaining carriers.”
Quantum Information and Relativity Theory (2002, background): “However, there are causal operations that are not localizable (Beckman et al., 2001).”
Index Theory of One Dimensional Quantum Walks and Cellular Automata (2009, unknown): “In quantum information it agrees with [2,4].”