Environment and classical channels in categorical quantum mechanics
Bob Coecke,Simon Perdrix +1 more
- Vol. 6247, pp 230-244
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TLDR
A both simple and comprehensive graphical calculus for quantum computing is presented, which axiomatize the notion of an environment, which together with the axiomatic notion of classical structure enables to define classical channels, quantum measurements and classical control.Abstract:
We present a both simple and comprehensive graphical calculus for quantum computing. We axiomatize the notion of an environment, which together with the axiomatic notion of classical structure enables us to define classical channels, quantum measurements and classical control. If we moreover adjoin the axiomatic notion of complementarity, we obtain sufficient structural power for constructive representation and correctness derivation of typical quantum informatic protocols.read more
Citations
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MonographDOI
Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning
Bob Coecke,Aleks Kissinger +1 more
TL;DR: This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations.
Journal ArticleDOI
Interacting quantum observables: Categorical algebra and diagrammatics
Bob Coecke,Ross Duncan +1 more
TL;DR: The ZX-calculus is introduced, an intuitive and universal graphical calculus for multi-qubit systems, which greatly simplifies derivations in the area of quantum computation and information and axiomatize phase shifts within this framework.
Posted Content
The compositional structure of multipartite quantum entanglement
Bob Coecke,Aleks Kissinger +1 more
TL;DR: In this paper, the algebraic and graphical structure of the GHZ-state and the W-state, as well as a purely graphical distinction that characterises the behaviours of these states, are exposed.
Journal ArticleDOI
Categories of quantum and classical channels
TL;DR: In this paper, the authors introduce a construction that turns a category of pure state spaces and operators into a class of observable algebras and superoperators, which contains both quantum and classical channels, providing elegant abstract notions of preparation and measurement.
Book ChapterDOI
The compositional structure of multipartite quantum entanglement
Bob Coecke,Aleks Kissinger +1 more
TL;DR: It is shown that multipartite quantum entanglement admits a compositional structure, and hence is subject to modern computer science methods, and induces a generalised graph state paradigm for measurement-based quantum computing.
References
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Journal ArticleDOI
Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
Charles H. Bennett,Gilles Brassard,Claude Crépeau,Richard Jozsa,Asher Peres,William K. Wootters +5 more
TL;DR: An unknown quantum state \ensuremath{\Vert}\ensure Math{\varphi}〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations.
Journal ArticleDOI
Quantum cryptography based on Bell's theorem.
TL;DR: Practical application of the generalized Bells theorem in the so-called key distribution process in cryptography is reported, based on the Bohms version of the Einstein-Podolsky-Rosen gedanken experiment andBells theorem is used to test for eavesdropping.
Journal ArticleDOI
Communication via One- and Two-Particle Operators on Einstein-Podolsky-Rosen States
TL;DR: The set of states accessible from an initial EPR state by one-particle operations are characterized and it is shown that in a sense they allow two bits to be encoded reliably in one spin-1/2 particle.
Journal ArticleDOI
Decoherence and the transition from quantum to classical
TL;DR: In this paper, the authors argue that without quantum physics we could not explain the behavior of solids, the structure and function of DNA, the color of the stars, the action of lasers or the properties of superfluids.