Optimal Protocols for Quantum Metrology with Noisy Measurements

Measurement noise is a major source of noise in quantum metrology. Here, we explore preprocessing protocols that apply quantum controls to the quantum sensor state prior to the final noisy measurement (but after the unknown parameter has been imparted), aiming to maximize the estimation precision. W...
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Autor*in:	Sisi Zhou [verfasserIn] Spyridon Michalakis [verfasserIn] Tuvia Gefen [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Übergeordnetes Werk:	In: PRX Quantum - American Physical Society, 2021, 4(2023), 4, p 040305
Übergeordnetes Werk:	volume:4 ; year:2023 ; number:4, p 040305

Links:	Link aufrufen Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1103/PRXQuantum.4.040305

Katalog-ID:	DOAJ091857074

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callnumber-first	Q - Science
author	Sisi Zhou
spellingShingle	Sisi Zhou misc QC1-999 misc QA76.75-76.765 misc Physics misc Computer software Optimal Protocols for Quantum Metrology with Noisy Measurements
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topic_title	QC1-999 QA76.75-76.765 Optimal Protocols for Quantum Metrology with Noisy Measurements
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title	Optimal Protocols for Quantum Metrology with Noisy Measurements
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title_full	Optimal Protocols for Quantum Metrology with Noisy Measurements
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title_sort	optimal protocols for quantum metrology with noisy measurements
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title_auth	Optimal Protocols for Quantum Metrology with Noisy Measurements
abstract	Measurement noise is a major source of noise in quantum metrology. Here, we explore preprocessing protocols that apply quantum controls to the quantum sensor state prior to the final noisy measurement (but after the unknown parameter has been imparted), aiming to maximize the estimation precision. We define the quantum preprocessing-optimized Fisher information, which determines the ultimate precision limit for quantum sensors under measurement noise, and conduct a thorough investigation into optimal preprocessing protocols. First, we formulate the preprocessing optimization problem as a biconvex optimization using the error observable formalism, based on which we prove that unitary controls are optimal for pure states and derive analytical solutions of the optimal controls in several practically relevant cases. Then we prove that for classically mixed states (whose eigenvalues encode the unknown parameter) under commuting-operator measurements, coarse-graining controls are optimal, while unitary controls are suboptimal in certain cases. Finally, we demonstrate that in multiprobe systems where noisy measurements act independently on each probe, the noiseless precision limit can be asymptotically recovered using global controls for a wide range of quantum states and measurements. Applications to noisy Ramsey interferometry and thermometry are presented, as well as explicit circuit constructions of optimal controls.
abstractGer	Measurement noise is a major source of noise in quantum metrology. Here, we explore preprocessing protocols that apply quantum controls to the quantum sensor state prior to the final noisy measurement (but after the unknown parameter has been imparted), aiming to maximize the estimation precision. We define the quantum preprocessing-optimized Fisher information, which determines the ultimate precision limit for quantum sensors under measurement noise, and conduct a thorough investigation into optimal preprocessing protocols. First, we formulate the preprocessing optimization problem as a biconvex optimization using the error observable formalism, based on which we prove that unitary controls are optimal for pure states and derive analytical solutions of the optimal controls in several practically relevant cases. Then we prove that for classically mixed states (whose eigenvalues encode the unknown parameter) under commuting-operator measurements, coarse-graining controls are optimal, while unitary controls are suboptimal in certain cases. Finally, we demonstrate that in multiprobe systems where noisy measurements act independently on each probe, the noiseless precision limit can be asymptotically recovered using global controls for a wide range of quantum states and measurements. Applications to noisy Ramsey interferometry and thermometry are presented, as well as explicit circuit constructions of optimal controls.
abstract_unstemmed	Measurement noise is a major source of noise in quantum metrology. Here, we explore preprocessing protocols that apply quantum controls to the quantum sensor state prior to the final noisy measurement (but after the unknown parameter has been imparted), aiming to maximize the estimation precision. We define the quantum preprocessing-optimized Fisher information, which determines the ultimate precision limit for quantum sensors under measurement noise, and conduct a thorough investigation into optimal preprocessing protocols. First, we formulate the preprocessing optimization problem as a biconvex optimization using the error observable formalism, based on which we prove that unitary controls are optimal for pure states and derive analytical solutions of the optimal controls in several practically relevant cases. Then we prove that for classically mixed states (whose eigenvalues encode the unknown parameter) under commuting-operator measurements, coarse-graining controls are optimal, while unitary controls are suboptimal in certain cases. Finally, we demonstrate that in multiprobe systems where noisy measurements act independently on each probe, the noiseless precision limit can be asymptotically recovered using global controls for a wide range of quantum states and measurements. Applications to noisy Ramsey interferometry and thermometry are presented, as well as explicit circuit constructions of optimal controls.
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title_short	Optimal Protocols for Quantum Metrology with Noisy Measurements
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Optimal Protocols for Quantum Metrology with Noisy Measurements

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