dorsal/arxiv
View SchemaOn bipartite pure-state entanglement structure in terms of disentanglement
| Authors | Fedor Herbut |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609073 |
| URL | https://arxiv.org/abs/quant-ph/0609073 |
| DOI | 10.1063/1.2375035 |
| Journal | J. Math. Phys. 47, 122103 (2006); Virtual Journal of Quantum Information 6(12), 2006 - Information Theory section |
Abstract
Schroedinger's disentanglement [E. Schroedinger, Proc. Cambridge Phil. Soc. 31, 555 (1935)], i. e., remote state decomposition, as a physical way to study entanglement, is carried one step further with respect to previous work in investigating the qualitative side of entanglement in any bipartite state vector. Remote measurement (or, equivalently, remote orthogonal state decomposition) from previous work is generalized to remote linearly-independent complete state decomposition both in the non-selective and the selective versions. The results are displayed in terms of commutative square diagrams, which show the power and beauty of the physical meaning of the (antiunitary) correlation operator inherent in the given bipartite state vector. This operator, together with the subsystem states (reduced density operators), constitutes the so-called correlated subsystem picture. It is the central part of the antilinear representation of a bipartite state vector, and it is a kind of core of its entanglement structure. The generalization of previously elaborated disentanglement expounded in this article is a synthesis of the antilinear representation of bipartite state vectors, which is reviewed, and the relevant results of Cassinelli et al. [J. Math. Analys. and Appl., 210, 472 (1997)] in mathematical analysis, which are summed up. Linearly-independent bases (finite or infinite) are shown to be almost as useful in some quantum mechanical studies as orthonormal ones. Finally, it is shown that linearly-independent remote pure-state preparation carries the highest probability of occurrence. This singles out linearly-independent remote influence from all possible ones.
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"abstract": "Schroedinger\u0027s disentanglement [E. Schroedinger, Proc. Cambridge Phil. Soc.\n31, 555 (1935)], i. e., remote state decomposition, as a physical way to study\nentanglement, is carried one step further with respect to previous work in\ninvestigating the qualitative side of entanglement in any bipartite state\nvector. Remote measurement (or, equivalently, remote orthogonal state\ndecomposition) from previous work is generalized to remote linearly-independent\ncomplete state decomposition both in the non-selective and the selective\nversions. The results are displayed in terms of commutative square diagrams,\nwhich show the power and beauty of the physical meaning of the (antiunitary)\ncorrelation operator inherent in the given bipartite state vector. This\noperator, together with the subsystem states (reduced density operators),\nconstitutes the so-called correlated subsystem picture. It is the central part\nof the antilinear representation of a bipartite state vector, and it is a kind\nof core of its entanglement structure. The generalization of previously\nelaborated disentanglement expounded in this article is a synthesis of the\nantilinear representation of bipartite state vectors, which is reviewed, and\nthe relevant results of Cassinelli et al. [J. Math. Analys. and Appl., 210, 472\n(1997)] in mathematical analysis, which are summed up. Linearly-independent\nbases (finite or infinite) are shown to be almost as useful in some quantum\nmechanical studies as orthonormal ones. Finally, it is shown that\nlinearly-independent remote pure-state preparation carries the highest\nprobability of occurrence. This singles out linearly-independent remote\ninfluence from all possible ones.",
"arxiv_id": "quant-ph/0609073",
"authors": [
"Fedor Herbut"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2375035",
"journal_ref": "J. Math. Phys. 47, 122103 (2006); Virtual Journal of Quantum\n Information 6(12), 2006 - Information Theory section",
"title": "On bipartite pure-state entanglement structure in terms of disentanglement",
"url": "https://arxiv.org/abs/quant-ph/0609073"
},
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