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Cited by 525Quantum Information and CryptographyQuantum Mechanics and ApplicationsQuantum Computing Algorithms and Architecture

Geometry of Quantum States: An Introduction to Quantum Entanglement

Bengtsson, Ingemar, Życzkowski, Karol·2017·Cambridge University Press eBooks
DOI 10.1017/9781139207010
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Abstract

Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.

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  • For any single qubit quantum channel E, over all single qubit unitary channels {U_i}, u(E) = max_{U_i,U_j} (1/3) Σ_{k=1}^3 |λ_k(U_i•E•U_j)^2|.

    “Lemma C.2.For any single qubit quantum channel E, over all single qubit unitary channels {U i } we have”

    From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [84]

  • For any single qubit channel E, there exist two specific unitaries U1 and U2 such that T_{U1•E•U2} is diagonal, so its eigenvalues and singular values coincide.

    “However, for any single qubit channel E, we can always find [84] two specific unitaries U 1 and U 2 such that T U 1 •E•U 2 is a diagonal matrix, and therefore for which the eigenvalues and singular values coincide”

    From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [84]

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Sorted by citations

Authors
Bengtsson, I., & Życzkowski, K.
Affiliations
  • Stockholm University (SE)
  • Jagiellonian University (PL)
ORCID
Venue
Cambridge University Press eBooks
Publisher
Cambridge University Press
Published
2017-08-30
DOI
10.1017/9781139207010
OpenAlex
W4249726483
Cited by
525
References
0
Citations by year
2026: 59 · 2025: 72 · 2024: 73 · 2023: 75 · 2022: 57 · 2021: 64 · 2020: 58 · 2019: 39 · 2018: 22 · 2017: 4 · 2015: 1 · 2013: 1
FWCI
15.16
Type
book
Language
en
Open access
closed
Licence
www.cambridge.org/core/terms (unspecified)
Locations
Cambridge University Press eBooks (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Keywords
quantum information, quantum states, quantum entanglement, multipartite entanglement, mutually unbiased bases, discrete Wigner function, unitary designs, Gleason's theorem, Kochen-Specker theorem, concentration measurement, quantum probability

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