All teleportation and dense coding schemes
Open accessAbstract
We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled vectors, (4) orthonormal bases of unitary operators with respect to the Hilbert–Schmidt scalar product and (5) depolarizing operations, whose Kraus operators can be chosen to be unitary. The teleportation and dense coding schemes are assumed to be `tight' in the sense that all Hilbert spaces involved have the same finite dimension d , and the classical channel involved distinguishes d 2 signals. A general construction procedure for orthonormal bases of unitaries, involving Latin squares and complex Hadamard matrices is also presented.
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While a full classification of N = 6 CHMs is unknown, it is currently conjectured that the set consists of an isolated matrix S6^(0) which does not belong to any family, and a newly discovered four-parameter generic family G6^(4).
“Whilst a full classification of N = 6 CHMs is unknown, it is currently conjectured that the set consists of an isolated matrix S (0) 6 which does not belong to any family [57], and a newly discovered four-parameter generic family G (4) 6 [58].”
From Universal linear optics (2015) · cites this paper as [57]
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References 6 · Cited by 270
Research works printed but not linked: 5
- Agaian S S Hadamard Matrices and Applications (Lecture Notes in Mathematics 1168) (Berlin: Springer)
- Braunstein S L, D'Ariano G M, Milburn G J and Sacchi M F 1999 Preprint quant-ph/9908036) · arXiv
- Haagerup U 1997 Orthogonal maximal abelian*-subalgebras of the n × n-matrices and cyclic n-roots Operator Algebras and Quantum Field Theory (Rome, 1996) (International Press) pp 296-322
- Knill E 1996 Group representations, error bases and quantum codes (preliminary report) Preprint quant- ph/9608049
- Vollbrecht K G H and Werner R F 1999 Preprint quant-ph/9910064) · arXiv
- Authors
- Werner, R. F.
- Affiliations
- Technische Universität Braunschweig (DE)
- Corresponding author
- Werner, R F
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 2001-08-24
- Volume
- 34
- Issue
- 35
- Pages
- 7081-7094
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2132641463
- Cited by
- 270
- References
- 6
- Citations by year
- 2026: 5 · 2025: 14 · 2024: 18 · 2023: 19 · 2022: 10 · 2021: 10 · 2020: 9 · 2019: 31 · 2018: 18 · 2017: 8 · 2016: 7 · 2015: 9 · 2014: 7 · 2013: 9 · 2012: 7
- FWCI
- 8.16
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- 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 teleportation, dense coding, Kraus operators, Latin squares, complex Hadamard matrices, bijections
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