dorsal/arxiv
View SchemaGleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements
| Authors | Carlton M. Caves, Christopher A. Fuchs, Kiran Manne, Joseph M. Renes |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306179 |
| URL | https://arxiv.org/abs/quant-ph/0306179 |
| DOI | 10.1023/B:FOOP.0000019581.00318.a5 |
| Journal | Found. Phys. 34, 193 (2004) |
Abstract
We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures (POVMs), as opposed to the restricted class of orthogonal projection-valued measures used in the original theorem. The advantage of this method is that it works for two-dimensional quantum systems (qubits) and even for vector spaces over rational fields--settings where the standard theorem fails. Furthermore, unlike the method necessary for proving the original result, the present one is rather elementary. In the case of a qubit, we investigate similar results for frame functions defined upon various restricted classes of POVMs. For the so-called trine measurements, the standard quantum probability rule is again recovered.
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"abstract": "We prove a Gleason-type theorem for the quantum probability rule using frame\nfunctions defined on positive-operator-valued measures (POVMs), as opposed to\nthe restricted class of orthogonal projection-valued measures used in the\noriginal theorem. The advantage of this method is that it works for\ntwo-dimensional quantum systems (qubits) and even for vector spaces over\nrational fields--settings where the standard theorem fails. Furthermore, unlike\nthe method necessary for proving the original result, the present one is rather\nelementary. In the case of a qubit, we investigate similar results for frame\nfunctions defined upon various restricted classes of POVMs. For the so-called\ntrine measurements, the standard quantum probability rule is again recovered.",
"arxiv_id": "quant-ph/0306179",
"authors": [
"Carlton M. Caves",
"Christopher A. Fuchs",
"Kiran Manne",
"Joseph M. Renes"
],
"categories": [
"quant-ph"
],
"doi": "10.1023/B:FOOP.0000019581.00318.a5",
"journal_ref": "Found. Phys. 34, 193 (2004)",
"title": "Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements",
"url": "https://arxiv.org/abs/quant-ph/0306179"
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