Concepedia

Hilbert Space Representations

Hilbert Space Representations is a formal framework in functional analysis that represents states of a quantum system as vectors in a complete inner product space, distinguished by its adherence to the axioms of Hilbert spaces and its application in modeling superposition and orthogonality in quantum mechanics.

2.4K

Publications

135.5K

Citations

3.7K

Authors

1.3K

Institutions

Publications per year

2017–2026

415

Parents

Publications

2.4K

<i>The Principles of Quantum Mechanics</i>

P. A. M. Dirac, J. C. Polkinghorne · Physics Today · 1958 · 5.3K citations

, , +10

Hamiltonian Systems and Transformation in Hilbert Space

B. O. Koopman · Proceedings of the National Academy of Sciences · 1931 · 2.3K citations · Full text

, , +14

Hilbert space representation of the minimal length uncertainty relation

Achim Kempf, G. Mangano, Robert B. Mann · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 1995 · 2K citations · Full text

, , +15

Quantum Machine Learning in Feature Hilbert Spaces

Maria Schuld, Nathan Killoran · Physical Review Letters · 2019 · 1.7K citations · Full text

, , +15

Security of Quantum Key Distribution Using<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">d</mml:mi></mml:math>-Level Systems

Nicolas J. Cerf, Mohamed Bourennane, Anders Karlsson et al. · Physical Review Letters · 2002 · 1.3K citations · Full text

, , +14

1–5 of 2.4K

Authors

3.7K

  1. AG
    Arthur Gretton

    University College London, United Kingdom

    11 publications · 369 citations

    11

    h-index

  2. PE
    Palle E. T. Jørgensen

    University of Iowa, United States

    12 publications · 265 citations

    11

    h-index

  3. GM
    G. Marmo

    Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Italy

    10 publications · 520 citations

    10

    h-index

  4. VI
    V. I. Manʹko

    P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Russia

    10 publications · 478 citations

    10

    h-index

  5. DA
    Diederik Aerts

    Vrije Universiteit Brussel, Belgium

    9 publications · 577 citations

    9

    h-index

1–5 of 3.7K

Institutions

1.3K

  1. Centre National de la Recherche Scientifique

    Paris, France

    27 h-index

    73 publications

    4.5K citations

  2. University of California, Berkeley

    Berkeley, United States

    21 h-index

    41 publications

    2.1K citations

  3. Massachusetts Institute of Technology

    Cambridge, United States

    21 h-index

    44 publications

    4.2K citations

  4. Princeton University

    Princeton, United States

    20 h-index

    40 publications

    5.1K citations

  5. Perimeter Institute

    Waterloo, Canada

    18 h-index

    34 publications

    2.3K citations

  6. University of Waterloo

    Waterloo, Canada

    17 h-index

    49 publications

    3.1K citations

  7. The University of Texas at Austin

    Austin, United States

    17 h-index

    35 publications

    1.2K citations

  8. Stanford University

    Stanford, United States

    16 h-index

    28 publications

    1.8K citations

1–8 of 1.3K

Venues

  1. Physical Review A

    PRA · 96 publications · 7.1K citations

    43

    h-index

  2. Journal of Mathematical Physics

    165 publications · 8.3K citations

    40

    h-index

  3. Physical Review Letters

    PRL · 42 publications · 7.1K citations

    31

    h-index

  4. Journal of Physics A Mathematical and General

    70 publications · 2.3K citations

    27

    h-index

  5. The Journal of Chemical Physics

    36 publications · 1.9K citations

    23

    h-index

1–5