dorsal/arxiv
View SchemaInformation Tradeoff Relations for Finite-Strength Quantum Measurements
| Authors | Christopher A. Fuchs, Kurt Jacobs |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0009101 |
| URL | https://arxiv.org/abs/quant-ph/0009101 |
| DOI | 10.1103/PhysRevA.63.062305 |
| Journal | Phys. Rev. A 63, 062305 (2001) |
Abstract
In this paper we give a new way to quantify the folklore notion that quantum measurements bring a disturbance to the system being measured. We consider two observers who initially assign identical mixed-state density operators to a two-state quantum system. The question we address is to what extent one observer can, by measurement, increase the purity of his density operator without affecting the purity of the other observer's. If there were no restrictions on the first observer's measurements, then he could carry this out trivially by measuring the initial density operator's eigenbasis. If, however, the allowed measurements are those of finite strength---i.e., those measurements strictly within the interior of the convex set of all measurements---then the issue becomes significantly more complex. We find that for a large class of such measurements the first observer's purity increases the most precisely when there is some loss of purity for the second observer. More generally the tradeoff between the two purities, when it exists, forms a monotonic relation. This tradeoff has potential application to quantum state control and feedback.
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"abstract": "In this paper we give a new way to quantify the folklore notion that quantum\nmeasurements bring a disturbance to the system being measured. We consider two\nobservers who initially assign identical mixed-state density operators to a\ntwo-state quantum system. The question we address is to what extent one\nobserver can, by measurement, increase the purity of his density operator\nwithout affecting the purity of the other observer\u0027s. If there were no\nrestrictions on the first observer\u0027s measurements, then he could carry this out\ntrivially by measuring the initial density operator\u0027s eigenbasis. If, however,\nthe allowed measurements are those of finite strength---i.e., those\nmeasurements strictly within the interior of the convex set of all\nmeasurements---then the issue becomes significantly more complex. We find that\nfor a large class of such measurements the first observer\u0027s purity increases\nthe most precisely when there is some loss of purity for the second observer.\nMore generally the tradeoff between the two purities, when it exists, forms a\nmonotonic relation. This tradeoff has potential application to quantum state\ncontrol and feedback.",
"arxiv_id": "quant-ph/0009101",
"authors": [
"Christopher A. Fuchs",
"Kurt Jacobs"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.63.062305",
"journal_ref": "Phys. Rev. A 63, 062305 (2001)",
"title": "Information Tradeoff Relations for Finite-Strength Quantum Measurements",
"url": "https://arxiv.org/abs/quant-ph/0009101"
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