arXiv:quant-ph/9707014 · Physical Review Letters

Improvement of Frequency Standards with Quantum Entanglement

Susana F. Huelga, Chiara Macchiavello, Thomas Pellizzari, ARTUR K. EKERT, Martin Bodo Plenio, J. I. Cirac

Published Nov 17, 1997• 999 citations

Abstract

The optimal precision of frequency measurements in the presence of decoherence is discussed. We analyze different preparations of $n$ two-level systems as well as different measurement procedures. We show that standard Ramsey spectroscopy on uncorrelated atoms and optimal measurements on maximally entangled states provide the same resolution. The best resolution is achieved using partially entangled preparations with a high degree of symmetry.

DOI: 10.1103/physrevlett.79.3865

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arXiv:quant-ph/9707014 · Physical Review Letters

Improvement of Frequency Standards with Quantum Entanglement

Susana F. Huelga, Chiara Macchiavello, Thomas Pellizzari, ARTUR K. EKERT, Martin Bodo Plenio, J. I. Cirac

Published Nov 17, 1997• 999 citations

arXiv HTML PDF

Abstract

The optimal precision of frequency measurements in the presence of decoherence is discussed. We analyze different preparations of

n

two-level systems as well as different measurement procedures. We show that standard Ramsey spectroscopy on uncorrelated atoms and optimal measurements on maximally entangled states provide the same resolution. The best resolution is achieved using partially entangled preparations with a high degree of symmetry.

DOI: 10.1103/physrevlett.79.3865

Related papers

Decoherence and Quantum Error Correction in Frequency Standards

Chiara Macchiavello, Susana F. Huelga, J. I. Cirac +2 more

The precision of frequency measurements performed on trapped ions in the presence of decoherence is analysed. In particular, standard Ramsey spectroscopy on uucorrelated ions and optimal measurements on maximally entangled states are proved to lead to the same resolution, while the best precision is achieved using partially entangled preparations. The use of symrnetrisation procedures is proposed and it is shown how this allows to overcome even the optimal precision achievable when both the initial preparation and the final measurement are optimized. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.The precision of frequency measurements performed on trapped ions in the presence of decoherence is analysed. In particular, standard Ramsey spectroscopy on uucorrelated ions and optimal measurements on maximally entangled states are proved to lead to the same resolution, while the best precision is achieved using partially entangled preparations. The use of symrnetrisation procedures is proposed and it is shown how this allows to overcome even the optimal precision achievable when both the initial preparation and the final measurement are optimized. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Kluwer Academic Publishers eBooksDec 19, 200511 citations

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arXiv:2203.12656Physical Review XFeb 29, 20249 citations

The optimal precision of frequency measurements in the presence of decoherence is discussed. We analyze different preparations of

n

A quantum system can be prepared in an entangled state that is very sensitive to changes introduced to its dynamics and thus potentially can be utilized as a precise sensor of dynamics parameters.

N

entangled two-level atoms evolving unitarily can be used for frequency estimation with Heisenberg-limited precision which scales as ${N}^{\ensuremath{-}2}$, whereas uncorrelated states give only a standard-limited precision which scales as ${N}^{\ensuremath{-}1}$. As entangled states are also sensitive to disturbances introduced by interactions with external environments, quantum enhancement of the precision may be significantly limited for open quantum systems. This is the case when an interaction with an environment leads to local Markovian dephasing and the precision scales as ${N}^{\ensuremath{-}1}$ for all atom preparations. For local non-Markovian dephasing, however, Matsuzaki et al. [Phys. Rev. A 84, 012103 (2011)] and Chin et al. [Phys. Rev. Lett. 109, 233601 (2012)] showed that the atoms prepared in the maximally entangled state achieve Zeno scaling $\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}{N}^{\ensuremath{-}3/2}$ in precision and argued that this limit should hold for any entangled state. Here we prove that Zeno scaling is indeed the best possible scaling for all local non-Markovian dephasing models which feature initial Zeno dynamics. Moreover, Zeno scaling can hold only for experiments in the Zeno-dynamics regime, otherwise scaling of the precision is standard.