서브메뉴
검색
Discrete and Continuous Variable Systems: Properties, Protocols, and Applications
Discrete and Continuous Variable Systems: Properties, Protocols, and Applications
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202104822
- ISBN
- 9798293835614
- DDC
- 530.1
- 서명/저자
- Discrete and Continuous Variable Systems: Properties, Protocols, and Applications
- 발행사항
- [Sl] : University of Maryland, College Park, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 359 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-03, Section: B.
- 주기사항
- Advisor: Gorshkov, Alexey V.;Albert, Victor V.;Schine, Nathan.
- 학위논문주기
- Thesis (Ph.D.)--University of Maryland, College Park, 2025.
- 초록/해제
- 요약Quantum information science is a promising, interdisciplinary field focusing on both understanding and utilizing quantum systems. Two major paradigms of quantum mechanics are discrete variable (finite dimensional) systems, such as qubits and qudits, and continuous variable (infinite dimensional) systems, such as bosonic modes. In this dissertation, we explore the properties, protocols, and applications of both discrete and continuous variable systems.In the first part of this dissertation, we study Hilbert space structures called quantum state designs, which are small ensembles of quantum states that mimic properties of the full space. While such designs are well-studied in the discrete variable setting, we show that they can also be defined and constructed in the continuous variable setting. Using specific multimode ensembles, we demonstrate continuous variable shadow tomography protocols which allow for efficient estimation of expectation values of many observables. Additionally, we use these ensembles to define notions of average and entanglement fidelities of continuous variable quantum channels, and we derive an explicit relationship between them that resembles the analogous relationship in the discrete variable setting.Meanwhile, on the discrete variable side, we construct a theory of designs on the torus and find general methods for constructing them in arbitrary dimensions. Using these toric designs and their relationship to quantum state designs, we construct many new and explicit families of quantum state designs. Furthermore, we use toric designs to prove various structure theorems about complete sets of mutually unbiased bases.In the second part of this dissertation, we examine entanglement in continuous variable systems. Specifically, we analytically derive average and typical entanglement properties, as measured by all integer Renyi-α entropies, of random ensembles of Gaussian states outputted from a Gaussian boson sampling device.Finally, in the third part of this dissertation, we examine the use of qubit systems for resolving frequency spectrums in signal processing applications. Specifically, we show that a classical signal whose spectrum contains closely spaced frequencies can be resolved by coupling the signal to a qubit and performing a superresolution protocol. We find general conditions for a protocol to exhibit superresolution and show various analytic and numerically-optimized protocols that achieve superresolution.
- 일반주제명
- Quantum physics
- 일반주제명
- Theoretical physics
- 일반주제명
- Physics
- 일반주제명
- Mathematics
- 키워드
- Quantum sensing
- 키워드
- Superresolution
- 기타저자
- University of Maryland, College Park Physics
- 기본자료저록
- Dissertations Abstracts International. 87-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008260126s2025 us c eng d■001000017359019
■00520260202104822
■006m o d
■007cr#unu||||||||
■020 ▼a9798293835614
■035 ▼a(MiAaPQ)AAI32169430
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530.1
■1001 ▼aIosue, Joseph Thomas.▼0(orcid)0000-0003-3383-1946
■24510▼aDiscrete and Continuous Variable Systems: Properties, Protocols, and Applications
■260 ▼a[Sl]▼bUniversity of Maryland, College Park▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a359 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-03, Section: B.
■500 ▼aAdvisor: Gorshkov, Alexey V.;Albert, Victor V.;Schine, Nathan.
■5021 ▼aThesis (Ph.D.)--University of Maryland, College Park, 2025.
■520 ▼aQuantum information science is a promising, interdisciplinary field focusing on both understanding and utilizing quantum systems. Two major paradigms of quantum mechanics are discrete variable (finite dimensional) systems, such as qubits and qudits, and continuous variable (infinite dimensional) systems, such as bosonic modes. In this dissertation, we explore the properties, protocols, and applications of both discrete and continuous variable systems.In the first part of this dissertation, we study Hilbert space structures called quantum state designs, which are small ensembles of quantum states that mimic properties of the full space. While such designs are well-studied in the discrete variable setting, we show that they can also be defined and constructed in the continuous variable setting. Using specific multimode ensembles, we demonstrate continuous variable shadow tomography protocols which allow for efficient estimation of expectation values of many observables. Additionally, we use these ensembles to define notions of average and entanglement fidelities of continuous variable quantum channels, and we derive an explicit relationship between them that resembles the analogous relationship in the discrete variable setting.Meanwhile, on the discrete variable side, we construct a theory of designs on the torus and find general methods for constructing them in arbitrary dimensions. Using these toric designs and their relationship to quantum state designs, we construct many new and explicit families of quantum state designs. Furthermore, we use toric designs to prove various structure theorems about complete sets of mutually unbiased bases.In the second part of this dissertation, we examine entanglement in continuous variable systems. Specifically, we analytically derive average and typical entanglement properties, as measured by all integer Renyi-α entropies, of random ensembles of Gaussian states outputted from a Gaussian boson sampling device.Finally, in the third part of this dissertation, we examine the use of qubit systems for resolving frequency spectrums in signal processing applications. Specifically, we show that a classical signal whose spectrum contains closely spaced frequencies can be resolved by coupling the signal to a qubit and performing a superresolution protocol. We find general conditions for a protocol to exhibit superresolution and show various analytic and numerically-optimized protocols that achieve superresolution.
■590 ▼aSchool code: 0117.
■650 4▼aQuantum physics
■650 4▼aTheoretical physics
■650 4▼aPhysics
■650 4▼aMathematics
■653 ▼aGaussian boson sampling
■653 ▼aQuantum sensing
■653 ▼aQuantum state designs
■653 ▼aSuperresolution
■653 ▼aContinuous variable systems
■690 ▼a0599
■690 ▼a0753
■690 ▼a0605
■690 ▼a0405
■71020▼aUniversity of Maryland, College Park▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g87-03B.
■790 ▼a0117
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359019▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
