Measurement uncertainty: the problem of characterising optimal error bounds

Paul Busch; Thomas Joseph Bullock

Measurement uncertainty: the problem of characterising optimal error bounds

Paul Busch, Thomas Joseph Bullock

Mathematics

Research output: Working paper › Preprint

Abstract

We consider the task of characterizing optimal protocols for approximating incompatible observables via jointly measurable observables. This amounts to jointly minimizing the approximation errors (suitably quantified), subject to the compatibility constraint. We review two distinct ways of conceptualizing the joint measurement problem and elucidate their connection. As a case study we consider the approximation of two-valued qubit observables and scrutinize two recent approaches that are based on different ways of quantifying errors, each giving rise to a form of tradeoff relation for the error measures used. For the first of these approaches we exhibit a formulation of the trade-off in operational terms as a measurement uncertainty relation. Furthermore we find a disparity between the respective optimal approximators singled out by the two approaches, which underlines the operational shortcomings of the second type of error measures.

Original language	English
Number of pages	14
Volume	arXiv:1512.00104v2
Publication status	In preparation - May 2016

Keywords

quantum mechanics
uncertainty relations
quantum measurement

Access to Document

https://arxiv.org/abs/1512.00104

Cite this

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title = "Measurement uncertainty: the problem of characterising optimal error bounds",

abstract = "We consider the task of characterizing optimal protocols for approximating incompatible observables via jointly measurable observables. This amounts to jointly minimizing the approximation errors (suitably quantified), subject to the compatibility constraint. We review two distinct ways of conceptualizing the joint measurement problem and elucidate their connection. As a case study we consider the approximation of two-valued qubit observables and scrutinize two recent approaches that are based on different ways of quantifying errors, each giving rise to a form of tradeoff relation for the error measures used. For the first of these approaches we exhibit a formulation of the trade-off in operational terms as a measurement uncertainty relation. Furthermore we find a disparity between the respective optimal approximators singled out by the two approaches, which underlines the operational shortcomings of the second type of error measures.",

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AB - We consider the task of characterizing optimal protocols for approximating incompatible observables via jointly measurable observables. This amounts to jointly minimizing the approximation errors (suitably quantified), subject to the compatibility constraint. We review two distinct ways of conceptualizing the joint measurement problem and elucidate their connection. As a case study we consider the approximation of two-valued qubit observables and scrutinize two recent approaches that are based on different ways of quantifying errors, each giving rise to a form of tradeoff relation for the error measures used. For the first of these approaches we exhibit a formulation of the trade-off in operational terms as a measurement uncertainty relation. Furthermore we find a disparity between the respective optimal approximators singled out by the two approaches, which underlines the operational shortcomings of the second type of error measures.

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KW - quantum measurement

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BT - Measurement uncertainty: the problem of characterising optimal error bounds

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