dorsal/arxiv
View SchemaUniversal Uncertainty Principle in the Measurement Operator Formalism
| Authors | Masanao Ozawa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510083 |
| URL | https://arxiv.org/abs/quant-ph/0510083 |
| DOI | 10.1088/1464-4266/7/12/033 |
| Journal | J. Opt. B: Quantum Semiclass. Opt. 7, S672-S681 (2005) |
Abstract
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation was found to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing in a unified treatment. This paper examines the above development on the noise-disturbance uncertainty principle in the model-independent approach based on the measurement operator formalism, which is widely accepted to describe a class of generalized measurements in the field of quantum information. We obtain explicit formulas for the noise and disturbance of measurements given by the measurement operators, and show that projective measurements do not satisfy the Heisenberg-type noise-disturbance relation that is typical in the gamma-ray microscope thought experiments. We also show that the disturbance on a Pauli operator of a projective measurement of another Pauli operator constantly equals the square root of 2, and examine how this measurement violates the Heisenberg-type relation but satisfies the new noise-disturbance relation.
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"abstract": "Heisenberg\u0027s uncertainty principle has been understood to set a limitation on\nmeasurements; however, the long-standing mathematical formulation established\nby Heisenberg, Kennard, and Robertson does not allow such an interpretation.\nRecently, a new relation was found to give a universally valid relation between\nnoise and disturbance in general quantum measurements, and it has become clear\nthat the new relation plays a role of the first principle to derive various\nquantum limits on measurement and information processing in a unified\ntreatment. This paper examines the above development on the noise-disturbance\nuncertainty principle in the model-independent approach based on the\nmeasurement operator formalism, which is widely accepted to describe a class of\ngeneralized measurements in the field of quantum information. We obtain\nexplicit formulas for the noise and disturbance of measurements given by the\nmeasurement operators, and show that projective measurements do not satisfy the\nHeisenberg-type noise-disturbance relation that is typical in the gamma-ray\nmicroscope thought experiments. We also show that the disturbance on a Pauli\noperator of a projective measurement of another Pauli operator constantly\nequals the square root of 2, and examine how this measurement violates the\nHeisenberg-type relation but satisfies the new noise-disturbance relation.",
"arxiv_id": "quant-ph/0510083",
"authors": [
"Masanao Ozawa"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1464-4266/7/12/033",
"journal_ref": "J. Opt. B: Quantum Semiclass. Opt. 7, S672-S681 (2005)",
"title": "Universal Uncertainty Principle in the Measurement Operator Formalism",
"url": "https://arxiv.org/abs/quant-ph/0510083"
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