dorsal/arxiv
View SchemaCausal and localizable quantum operations
| Authors | David Beckman, Daniel Gottesman, M. A. Nielsen, John Preskill |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0102043 |
| URL | https://arxiv.org/abs/quant-ph/0102043 |
| DOI | 10.1103/PhysRevA.64.052309 |
| Journal | Phys.Rev. A64 (2001) 052309 |
Abstract
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.
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"abstract": "We examine constraints on quantum operations imposed by relativistic\ncausality. A bipartite superoperator is said to be localizable if it can be\nimplemented by two parties (Alice and Bob) who share entanglement but do not\ncommunicate; it is causal if the superoperator does not convey information from\nAlice to Bob or from Bob to Alice. We characterize the general structure of\ncausal complete measurement superoperators, and exhibit examples that are\ncausal but not localizable. We construct another class of causal bipartite\nsuperoperators that are not localizable by invoking bounds on the strength of\ncorrelations among the parts of a quantum system. A bipartite superoperator is\nsaid to be semilocalizable if it can be implemented with one-way quantum\ncommunication from Alice to Bob, and it is semicausal if it conveys no\ninformation from Bob to Alice. We show that all semicausal complete measurement\nsuperoperators are semilocalizable, and we establish a general criterion for\nsemicausality. In the multipartite case, we observe that a measurement\nsuperoperator that projects onto the eigenspaces of a stabilizer code is\nlocalizable.",
"arxiv_id": "quant-ph/0102043",
"authors": [
"David Beckman",
"Daniel Gottesman",
"M. A. Nielsen",
"John Preskill"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th"
],
"doi": "10.1103/PhysRevA.64.052309",
"journal_ref": "Phys.Rev. A64 (2001) 052309",
"title": "Causal and localizable quantum operations",
"url": "https://arxiv.org/abs/quant-ph/0102043"
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