Quantum parameter estimation with general dynamics

Yuan, Haidong; Fung, Chi-Hang Fred

doi:10.1038/s41534-017-0014-6

Cited by 61 publications

(42 citation statements)

References 55 publications

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“…as previously defined, and the inequality holds for any W with W 1    (see appendix C). In the asymptotical limit, N N I K 1 = + , then equation (25) provides bounds on the scalings in quantum parameter estimation, which is consistent with the studies in quantum metrology [32,33,35,38,39] but here it has a more general context (see also [24]).…”

Section: A Unified Framework For Quantum Metrology and Perfect Channesupporting

confidence: 81%

“…This can be seen as the counterpart of Uhlmann's purification theorem on quantum channels [23] (however the proof does not use Uhlmann's purification theorem [24]…”

Section: Fidelity Function For Quantum Channelsmentioning

confidence: 99%

“…This equality can be shown by using a result from the supplementary material of [24] which showed that…”

Section: Fidelity Function For Quantum Channelsmentioning

confidence: 99%

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Fidelity and Fisher information on quantum channels

Yuan

Fung

2017

New J. Phys.

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The fidelity function for quantum states has been widely used in quantum information science and frequently arises in the quantification of optimal performances for the estimation and distinguishing of quantum states. A fidelity function for quantum channels is expected to have the same wide applications in quantum information science. In this paper we propose a fidelity function for quantum channels and show that various distance measures on quantum channels can be obtained from this fidelity function; for example, the Bures angle and the Bures distance can be extended to quantum channels via this fidelity function. We then show that the distances between quantum channels lead naturally to a quantum channel Fisher information which quantifies the ultimate precision limit in quantum metrology; the ultimate precision limit can thus be seen as a manifestation of the distances between quantum channels. We also show that the fidelity of quantum channels provides a unified framework for perfect quantum channel discrimination and quantum metrology. In particular, we show that the minimum number of uses needed for perfect channel discrimination is exactly the counterpart of the precision limit in quantum metrology, and various useful lower bounds for the minimum number of uses needed for perfect channel discrimination can be obtained via this connection.

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Section: A Unified Framework For Quantum Metrology and Perfect Channesupporting

confidence: 81%

“…This can be seen as the counterpart of Uhlmann's purification theorem on quantum channels [23] (however the proof does not use Uhlmann's purification theorem [24]…”

Section: Fidelity Function For Quantum Channelsmentioning

confidence: 99%

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Fidelity and Fisher information on quantum channels

Yuan

Fung

2017

New J. Phys.

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“…where generalised Bures angle approach to quantum channels 212 , and through the geometry of quantum channels, which has been used to explore the effects depolarisation, dephasing, spontaneous emission and photon loss channels 44,213 .…”

Section: A Metrology In Noisy Quantum Channelsmentioning

confidence: 99%

Geometric perspective on quantum parameter estimation

Sidhu

Kok

2020

AVS Quantum Science

177

132

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Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this review, we collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. We give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. We address the question how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation. CONTENTS

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“…Without noise, entangling the measurement system with ancillary quantum degrees of freedom provides no advantage to scaling of measurement precision with number of particles [15,16]. Contrariwise, in the presence of noise, which deleteriously affects measurement precision, entangling with ancillae is suggested to deliver higher precision than not using entanglement with ancillae [17][18][19][20].…”

mentioning

confidence: 99%

Entanglement-enhanced quantum metrology in a noisy environment

Wang

Zhan

et al. 2018

Phys. Rev. A

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Quantum metrology overcomes standard precision limits and plays a central role in science and technology. Practically it is vulnerable to imperfections such as decoherence. Here, we demonstrate quantum metrology for noisy channels such that entanglement with ancillary qubits enhances the quantum Fisher information for phase estimation but not otherwise. Our photonic experiment covers a range of noise for various types of channels, including for two randomly alternating channels such that assisted entanglement fails for each noisy channel individually. We have simulated noisy channels by implementing space-multiplexed dual interferometers with quantum photonic inputs. We have demonstrated the advantage of entanglement-assisted protocols in phase estimation experiment run with either single-probe or multi-probe approach. These results establish that entanglement with ancillae is a valuable approach for delivering quantum-enhanced metrology. Our new approach to entanglement-assisted quantum metrology via a simple linear-optical interferometric network with easy-to-prepare photonic inputs provides a path towards practical quantum metrology.arXiv:1707.08790v2 [quant-ph]

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Quantum parameter estimation with general dynamics

Cited by 61 publications

References 55 publications

Fidelity and Fisher information on quantum channels

Fidelity and Fisher information on quantum channels

Geometric perspective on quantum parameter estimation

Entanglement-enhanced quantum metrology in a noisy environment

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