dorsal/arxiv
View SchemaThe Nature and Location of Quantum Information
| Authors | Robert B. Griffiths |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0203058 |
| URL | https://arxiv.org/abs/quant-ph/0203058 |
| DOI | 10.1103/PhysRevA.66.012311 |
| Journal | Phys. Rev. A 66 (2002) 012311. |
Abstract
Quantum information is defined by applying the concepts of ordinary (Shannon) information theory to a quantum sample space consisting of a single framework or consistent family. A classical analogy for a spin-half particle and other arguments show that the infinite amount of information needed to specify a precise vector in its Hilbert space is not a measure of the information carried by a quantum entity with a $d$-dimensional Hilbert space; the latter is, instead, bounded by log d bits (1 bit per qubit). The two bits of information transmitted in dense coding are located not in one but in the correlation between two qubits, consistent with this bound. A quantum channel can be thought of as a "structure" or collection of frameworks, and the physical location of the information in the individual frameworks can be used to identify the location of the channel. Analysis of a quantum circuit used as a model of teleportation shows that the location of the channel depends upon which structure is employed; for ordinary teleportation it is not (contrary to Deutsch and Hayden) present in the two bits resulting from the Bell-basis measurement, but in correlations of these with a distant qubit. In neither teleportation nor dense coding does information travel backwards in time, nor is it transmitted by nonlocal (superluminal) influences. It is (tentatively) proposed that all aspects of quantum information can in principle be understood in terms of the (basically classical) behavior of information in a particular framework, along with the framework dependence of this information.
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"abstract": "Quantum information is defined by applying the concepts of ordinary (Shannon)\ninformation theory to a quantum sample space consisting of a single framework\nor consistent family. A classical analogy for a spin-half particle and other\narguments show that the infinite amount of information needed to specify a\nprecise vector in its Hilbert space is not a measure of the information carried\nby a quantum entity with a $d$-dimensional Hilbert space; the latter is,\ninstead, bounded by log d bits (1 bit per qubit). The two bits of information\ntransmitted in dense coding are located not in one but in the correlation\nbetween two qubits, consistent with this bound. A quantum channel can be\nthought of as a \"structure\" or collection of frameworks, and the physical\nlocation of the information in the individual frameworks can be used to\nidentify the location of the channel. Analysis of a quantum circuit used as a\nmodel of teleportation shows that the location of the channel depends upon\nwhich structure is employed; for ordinary teleportation it is not (contrary to\nDeutsch and Hayden) present in the two bits resulting from the Bell-basis\nmeasurement, but in correlations of these with a distant qubit. In neither\nteleportation nor dense coding does information travel backwards in time, nor\nis it transmitted by nonlocal (superluminal) influences. It is (tentatively)\nproposed that all aspects of quantum information can in principle be understood\nin terms of the (basically classical) behavior of information in a particular\nframework, along with the framework dependence of this information.",
"arxiv_id": "quant-ph/0203058",
"authors": [
"Robert B. Griffiths"
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"doi": "10.1103/PhysRevA.66.012311",
"journal_ref": "Phys. Rev. A 66 (2002) 012311.",
"title": "The Nature and Location of Quantum Information",
"url": "https://arxiv.org/abs/quant-ph/0203058"
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