dorsal/arxiv
View SchemaChannel kets, entangled states, and the location of quantum information
| Authors | Robert B. Griffiths |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409106 |
| URL | https://arxiv.org/abs/quant-ph/0409106 |
| DOI | 10.1103/PhysRevA.71.042337 |
| Journal | Phys. Rev. A 71 (2005) 042337 |
Abstract
The well-known duality relating entangled states and noisy quantum channels is expressed in terms of a channel ket, a pure state on a suitable tripartite system, which functions as a pre-probability allowing the calculation of statistical correlations between, for example, the entrance and exit of a channel, once a framework has been chosen so as to allow a consistent set of probabilities. In each framework the standard notions of ordinary (classical) information theory apply, and it makes sense to ask whether information of a particular sort about one system is or is not present in another system. Quantum effects arise when a single pre-probability is used to compute statistical correlations in different incompatible frameworks, and various constraints on the presence and absence of different kinds of information are expressed in a set of all-or-nothing theorems which generalize or give a precise meaning to the concept of ``no-cloning.'' These theorems are used to discuss: the location of information in quantum channels modeled using a mixed-state environment; the $CQ$ (classical-quantum) channels introduced by Holevo; and the location of information in the physical carriers of a quantum code. It is proposed that both channel and entanglement problems be classified in terms of pure states (functioning as pre-probabilities) on systems of $p\geq 2$ parts, with mixed bipartite entanglement and simple noisy channels belonging to the category $p=3$, a five-qubit code to the category $p=6$, etc.; then by the dimensions of the Hilbert spaces of the component parts, along with other criteria yet to be determined.
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"abstract": "The well-known duality relating entangled states and noisy quantum channels\nis expressed in terms of a channel ket, a pure state on a suitable tripartite\nsystem, which functions as a pre-probability allowing the calculation of\nstatistical correlations between, for example, the entrance and exit of a\nchannel, once a framework has been chosen so as to allow a consistent set of\nprobabilities. In each framework the standard notions of ordinary (classical)\ninformation theory apply, and it makes sense to ask whether information of a\nparticular sort about one system is or is not present in another system.\nQuantum effects arise when a single pre-probability is used to compute\nstatistical correlations in different incompatible frameworks, and various\nconstraints on the presence and absence of different kinds of information are\nexpressed in a set of all-or-nothing theorems which generalize or give a\nprecise meaning to the concept of ``no-cloning.\u0027\u0027 These theorems are used to\ndiscuss: the location of information in quantum channels modeled using a\nmixed-state environment; the $CQ$ (classical-quantum) channels introduced by\nHolevo; and the location of information in the physical carriers of a quantum\ncode. It is proposed that both channel and entanglement problems be classified\nin terms of pure states (functioning as pre-probabilities) on systems of $p\\geq\n2$ parts, with mixed bipartite entanglement and simple noisy channels belonging\nto the category $p=3$, a five-qubit code to the category $p=6$, etc.; then by\nthe dimensions of the Hilbert spaces of the component parts, along with other\ncriteria yet to be determined.",
"arxiv_id": "quant-ph/0409106",
"authors": [
"Robert B. Griffiths"
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"doi": "10.1103/PhysRevA.71.042337",
"journal_ref": "Phys. Rev. A 71 (2005) 042337",
"title": "Channel kets, entangled states, and the location of quantum information",
"url": "https://arxiv.org/abs/quant-ph/0409106"
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