Research output: Contribution to journal › Review article

Journal | Journal of Physics A: Mathematical and Theoretical |
---|---|

Date | Submitted - Jan 2018 |

Date | Accepted/In press - 23 May 2018 |

Date | E-pub ahead of print - 7 Jun 2018 |

Date | Published (current) - 13 Jul 2018 |

Issue number | 28 |

Volume | 51 |

Number of pages | 34 |

Early online date | 7/06/18 |

Original language | English |

In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be measured jointly. The pioneers of quantum mechanics were acutely aware and puzzled by this fact, and it motivated Heisenberg to seek a mitigation, which he formulated in his seminal paper of 1927. He provided intuitive arguments to show that the values of, say, the position and momentum of a particle can at least be unsharply defined, and they can be measured together provided some approximation errors are allowed. Only now, nine decades later, a working theory of approximate joint measurements is taking shape, leading to rigorous and experimentally testable formulations of associated error tradeoff relations. Here we briefly review this new development, explaining the concepts and steps taken in the construction of optimal joint approximations of pairs of incompatible observables. As a case study, we deduce measurement uncertainty relations for qubit observables using two distinct error measures. We provide an operational interpretation of the error bounds and discuss some of the first experimental tests of such relations.

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- QUANTUM THEORY, quantum uncertainty, quantum measurement

## Department of Physics and Turku Centre for Quantum Physics, University of Turku

Activity: Visiting an external institution › Academic

## Quantum Measurement Uncertainty in Quantum Metrology and Estimation

Project: Research

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