dorsal/arxiv
View SchemaOn Quantum Operations as Quantum States
| Authors | Pablo Arrighi, Christophe Patricot |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307024 |
| URL | https://arxiv.org/abs/quant-ph/0307024 |
| DOI | 10.1016/j.aop.2003.11.005 |
| Journal | Annals Phys. 311 (2004) 26-52 |
Abstract
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely Positive-preserving linear maps; we go further and show that all of the important theorems concerning quantum operations can be derived directly from those concerning quantum states. As we do so the discussion first provides an elegant and original review of the main features of quantum operations. Next (in the second half of the paper) we find more results stemming from our formulation of the correspondence. Thus we provide a factorizability condition for quantum operations, and give two novel Schmidt-type decompositions of bipartite pure states. By translating the composition law of quantum operations, we define a group structure upon the set of totally entangled states. The question whether the correspondence is merely mathematical or can be given a physical interpretation is addressed throughout the text: we provide formulae which suggest quantum states inherently define a quantum operation between two of their subsystems, and which turn out to have applications in quantum cryptography. Keywords: Kraus, CP-maps, superoperators, extremality, trace-preserving, factorizable, triangular.
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"abstract": "We formalize the correspondence between quantum states and quantum operations\nisometrically, and harness its consequences. This correspondence was already\nimplicit in the various proofs of the operator sum representation of Completely\nPositive-preserving linear maps; we go further and show that all of the\nimportant theorems concerning quantum operations can be derived directly from\nthose concerning quantum states. As we do so the discussion first provides an\nelegant and original review of the main features of quantum operations. Next\n(in the second half of the paper) we find more results stemming from our\nformulation of the correspondence. Thus we provide a factorizability condition\nfor quantum operations, and give two novel Schmidt-type decompositions of\nbipartite pure states. By translating the composition law of quantum\noperations, we define a group structure upon the set of totally entangled\nstates. The question whether the correspondence is merely mathematical or can\nbe given a physical interpretation is addressed throughout the text: we provide\nformulae which suggest quantum states inherently define a quantum operation\nbetween two of their subsystems, and which turn out to have applications in\nquantum cryptography. Keywords: Kraus, CP-maps, superoperators, extremality,\ntrace-preserving, factorizable, triangular.",
"arxiv_id": "quant-ph/0307024",
"authors": [
"Pablo Arrighi",
"Christophe Patricot"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1016/j.aop.2003.11.005",
"journal_ref": "Annals Phys. 311 (2004) 26-52",
"title": "On Quantum Operations as Quantum States",
"url": "https://arxiv.org/abs/quant-ph/0307024"
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