Theoretical Tools for Quantum Sensor Optimization and Entanglement Quantification
Theoretical Tools for Quantum Sensor Optimization and Entanglement Quantification
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151104
- ISBN
- 9798382717173
- DDC
- 530.1
- 저자명
- Beckey, Jacob L.
- 서명/저자
- Theoretical Tools for Quantum Sensor Optimization and Entanglement Quantification
- 발행사항
- [Sl] : University of Colorado at Boulder, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 198 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-11, Section: B.
- 주기사항
- Advisor: Smith, Graeme.
- 학위논문주기
- Thesis (Ph.D.)--University of Colorado at Boulder, 2024.
- 초록/해제
- 요약In this thesis, we develop theoretical tools aimed at facilitating the development of more useful quantum sensors and more efficient methods of multipartite entanglement quantification. In the first half, we study the quantum Fisher information (QFI) -- a canonical quantity in quantum metrology which captures the amount of information about unknown parameter(s) one can extract by measuring a quantum state that depends on those parameters. While the QFI can be computed easily in some simple cases, computing it for a generic quantum state whose dynamics might not be well-understood, is often intractable. We derive analytical, dynamics-agnostic bounds on the QFI that are computable on a quantum computer, allow one to estimate the QFI, and enable the variational preparation of the state that is approximately optimal for a given sensing task. We carefully prove their properties and point out relations to other quantities often used in quantum estimation theory.The second half of the thesis is dedicated to the study of a general family of multipartite entanglement measures, called the concentratable entanglements (CEs). We define the measures, show that many well-known measures are recovered as special cases, and then prove their essential mathematical properties. We then construct statistical estimators for these measures that utilize only one- and two-copy measurements, which are implementable using today's technologies. Moreover, we provide analytical performance guarantees in the form of upper bounds on the number of copies needed to estimate these measures to a desired precision, and provide upper bounds on the classical computation cost required to process the data from these protocols. Our work elucidates the various trade-offs for experimentalists striving to probe entanglement in quantum systems of many tens of qubits, and contributes to the quantum learning theory community aiming to quantify the hardness of estimating various properties of quantum states.
- 일반주제명
- Quantum physics
- 일반주제명
- Theoretical physics
- 일반주제명
- Physics
- 기타저자
- University of Colorado at Boulder Physics
- 기본자료저록
- Dissertations Abstracts International. 85-11B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530.1
■1001 ▼aBeckey, Jacob L.▼0(orcid)0000-0002-2009-8661
■24510▼aTheoretical Tools for Quantum Sensor Optimization and Entanglement Quantification
■260 ▼a[Sl]▼bUniversity of Colorado at Boulder▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a198 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-11, Section: B.
■500 ▼aAdvisor: Smith, Graeme.
■5021 ▼aThesis (Ph.D.)--University of Colorado at Boulder, 2024.
■520 ▼aIn this thesis, we develop theoretical tools aimed at facilitating the development of more useful quantum sensors and more efficient methods of multipartite entanglement quantification. In the first half, we study the quantum Fisher information (QFI) -- a canonical quantity in quantum metrology which captures the amount of information about unknown parameter(s) one can extract by measuring a quantum state that depends on those parameters. While the QFI can be computed easily in some simple cases, computing it for a generic quantum state whose dynamics might not be well-understood, is often intractable. We derive analytical, dynamics-agnostic bounds on the QFI that are computable on a quantum computer, allow one to estimate the QFI, and enable the variational preparation of the state that is approximately optimal for a given sensing task. We carefully prove their properties and point out relations to other quantities often used in quantum estimation theory.The second half of the thesis is dedicated to the study of a general family of multipartite entanglement measures, called the concentratable entanglements (CEs). We define the measures, show that many well-known measures are recovered as special cases, and then prove their essential mathematical properties. We then construct statistical estimators for these measures that utilize only one- and two-copy measurements, which are implementable using today's technologies. Moreover, we provide analytical performance guarantees in the form of upper bounds on the number of copies needed to estimate these measures to a desired precision, and provide upper bounds on the classical computation cost required to process the data from these protocols. Our work elucidates the various trade-offs for experimentalists striving to probe entanglement in quantum systems of many tens of qubits, and contributes to the quantum learning theory community aiming to quantify the hardness of estimating various properties of quantum states.
■590 ▼aSchool code: 0051.
■650 4▼aQuantum physics
■650 4▼aTheoretical physics
■650 4▼aPhysics
■653 ▼aQuantum computing
■653 ▼aQuantum entanglement
■653 ▼aQuantum learning theory
■653 ▼aQuantum metrology
■690 ▼a0599
■690 ▼a0753
■690 ▼a0605
■71020▼aUniversity of Colorado at Boulder▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g85-11B.
■790 ▼a0051
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17160711▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
