Uncertainty Reconciles Complementarity with Joint Measurability

P Busch; Chris Shilladay

doi:10.1103/PhysRevA.68.034102

Uncertainty Reconciles Complementarity with Joint Measurability

P Busch, Chris Shilladay

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary observables is proposed. The measured observables are represented as positive operator valued measures (POVMs), whose intrinsic fuzziness parameters are found to satisfy an intriguing pay-off relation reflecting the complementarity. At the same time, this relation represents an instance of a Heisenberg uncertainty relation for measurement imprecisions. A model-independent consideration show that this uncertainty relation is logically connected with the joint measurability of the POVMs in question.

Original language	English
Article number	034102/1-4
Journal	Phys. Rev. A
Volume	68
DOIs	https://doi.org/10.1103/PhysRevA.68.034102
Publication status	Published - 2003

Keywords

Mathematical Physics

Access to Document

10.1103/PhysRevA.68.034102

http://arxiv.org/abs/quant-ph/0207081

Cite this

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abstract = "The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary observables is proposed. The measured observables are represented as positive operator valued measures (POVMs), whose intrinsic fuzziness parameters are found to satisfy an intriguing pay-off relation reflecting the complementarity. At the same time, this relation represents an instance of a Heisenberg uncertainty relation for measurement imprecisions. A model-independent consideration show that this uncertainty relation is logically connected with the joint measurability of the POVMs in question.",

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