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Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics: Knot Theory, Categorical Quantum Mechanics, and Logic and Computation.
The logic of quantum mechanics
G. Birkhoff and J. von Neumann · 1936
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On algebras which are connected with the semisimple continuous groups
R. Brauer · 1937
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The Calculi of Lambda Conversion
A. Church · 1941
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The Principles of Quantum Mechanics (third edition)
P. A. M. Dirac · 1947
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The mathematics of sentence structure
J. Lambek · 1958
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Relations between the ‘percolation’ and ‘coloring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
H. N. V. Temperley and E. H. Lieb · 1971
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Fully abstract models of typed lambda-calculus
R. Milner · 1977
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Coherence for compact closed categories
G. M. Kelly and M. L. Laplaza · 1980
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The Lambda Calculus, volume 103 of Studies in Logic
H. P. Barendregt · 1984
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A polynomial invariant for links via von Neumann algebras
V. F. R. Jones · 1985
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Linear Logic
J.-Y. Girard · 1987
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Topological quantum field theory
E. Witten · 1988
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Braided compact closed categories with applications to low-dimensional topology
P. Freyd and D. Yetter · 1989
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Geometry of Interaction I: Interpretation of System F
J.-Y. Girard · 1989
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An invariant of regular isotopy
L. H. Kauffman · 1990
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Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
C. H. Bennet, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wooters · 1993
Cited alongside, same era.
‘Event-ready-detectors’ Bell experiment via entanglement swapping
M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert · 1993
Cited alongside, same era.
New foundations for the geometry of interaction
S. Abramsky and R. Jagadeesan · 1994
Cited alongside, same era.
Knots in Physics
L. H. Kauffman · 1994
Cited alongside, same era.
Quantum Groups
C. Kassel · 1995
Cited alongside, same era.
Knot Logic
L. H. Kauffman · 1995
Cited alongside, same era.
Retracing some paths in process algebra
Self-adjunctions and matrices
K. Dosen and Z. Petric · 2003
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Measurement-based quantum computation on cluster states
R. Raussendorf, D. Browne, and H.-J. Briegel · 2003
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High-level methods for quantum computation and information
S. Abramsky · 2004
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A categorical semantics of quantum protocols
S. Abramsky and B. Coecke · 2004
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Biologic II
L. H. Kauffman · 2004
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Abstract scalars, loops, and free traced and strongly compact closed categories
S. Abramsky · 2005
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Abstract physical traces
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S. Abramsky · 1996
Cited alongside, same era.
Traced monoidal categories
A. Joyal, R. Street, and D. Verity · 1996
Cited alongside, same era.
Mathematical linguistics and proof theory
W. Buszkowski · 1997
Cited alongside, same era.
Graph Theory
J. Diestel · 1997
Cited alongside, same era.
Categorial type logic
M. Moortgat · 1997
Cited alongside, same era.
Why John von Neumann did not like the Hilbert space formalism of quantum mechanics (and what he liked instead)
M. Rédei · 1997
Cited alongside, same era.
S. Abramsky and B. Coecke · 2005
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Partition algebras
T. Halvorson and A. Ram · 2005
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Knot diagrammatics
L. H. Kauffman · 2005
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A categorical quantum logic
S. Abramsky and R. W. Duncan · 2006
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De-linearizing linearity: projective quantum axiomatics from strong compact closure
B. Coecke · 2006
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Generalized measurements and Naimark’s theorem without sums
B. Coecke and E. O. Paquette · 2006
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Quantum measurements without sums
B. Coecke and D. Pavlovic · 2006
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Dagger compact closed categories and completely positive maps
P. Selinger · 2006
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