dorsal/arxiv
View SchemaUncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
| Authors | Masanao Ozawa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307057 |
| URL | https://arxiv.org/abs/quant-ph/0307057 |
| DOI | 10.1016/j.aop.2003.12.012 |
| Journal | Ann. Phys. 311, 350-416 (2004). |
Abstract
Heisenberg's uncertainty relation for measurement noise and disturbance states that any position measurement with noise epsilon brings the momentum disturbance not less than hbar/2epsilon. This relation holds only for restricted class of measuring apparatuses. Here, Heisenberg's uncertainty relation is generalized to a relation that holds for all the possible quantum measurements, from which conditions are obtained for measuring apparatuses to satisfy Heisenberg's relation. In particular, every apparatus with the noise and the disturbance statistically independent from the measured object is proven to satisfy Heisenberg's relation. For this purpose, all the possible quantum measurements are characterized by naturally acceptable axioms. Then, a mathematical notion of the distance between probability operator valued measures and observables is introduced and the basic properties are explored. Based on this notion, the measurement noise and disturbance are naturally defined for any quantum measurements in a model independent formulation. Under this formulation, various uncertainty relations are also derived for apparatuses with independent noise, independent disturbance, unbiased noise, and unbiased disturbance as well as noiseless apparatuses and nondisturbing apparatuses. Two models of position measurements are discussed to show that Heisenberg's relation can be violated even by approximately repeatable position measurements.
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"abstract": "Heisenberg\u0027s uncertainty relation for measurement noise and disturbance\nstates that any position measurement with noise epsilon brings the momentum\ndisturbance not less than hbar/2epsilon. This relation holds only for\nrestricted class of measuring apparatuses. Here, Heisenberg\u0027s uncertainty\nrelation is generalized to a relation that holds for all the possible quantum\nmeasurements, from which conditions are obtained for measuring apparatuses to\nsatisfy Heisenberg\u0027s relation. In particular, every apparatus with the noise\nand the disturbance statistically independent from the measured object is\nproven to satisfy Heisenberg\u0027s relation. For this purpose, all the possible\nquantum measurements are characterized by naturally acceptable axioms. Then, a\nmathematical notion of the distance between probability operator valued\nmeasures and observables is introduced and the basic properties are explored.\nBased on this notion, the measurement noise and disturbance are naturally\ndefined for any quantum measurements in a model independent formulation. Under\nthis formulation, various uncertainty relations are also derived for\napparatuses with independent noise, independent disturbance, unbiased noise,\nand unbiased disturbance as well as noiseless apparatuses and nondisturbing\napparatuses. Two models of position measurements are discussed to show that\nHeisenberg\u0027s relation can be violated even by approximately repeatable position\nmeasurements.",
"arxiv_id": "quant-ph/0307057",
"authors": [
"Masanao Ozawa"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.aop.2003.12.012",
"journal_ref": "Ann. Phys. 311, 350-416 (2004).",
"title": "Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements",
"url": "https://arxiv.org/abs/quant-ph/0307057"
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