A Categorical Semantics of Quantum Protocols
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Interacting Quantum Observables
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Graph States and the Necessity of Euler Decomposition
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Rewriting measurement-based quantum computations with generalised flow
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Environment and classical channels in categorical quantum mechanics
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Graphical Calculus for Quantum Key Distribution (Extended Abstract)
Electronic Notes in Theoretical Computer Science (ENTCS)
Phase Groups and the Origin of Non-locality for Qubits
Electronic Notes in Theoretical Computer Science (ENTCS)
The computational power of the W And GHZ States
Quantum Information & Computation
Environment and classical channels in categorical quantum mechanics
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
The search for structure in quantum computation
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Strong Complementarity and Non-locality in Categorical Quantum Mechanics
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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Multipartite quantum states constitute a (if not the) key resource for quantum computations and protocols. However obtaining a generic, structural understanding of entanglement in N-qubit systems is a long-standing open problem in quantum computer science. Here we show that multipartite quantum entanglement admits a compositional structure, and hence is subject to modern computer science methods. Recall that two N-qubit states are SLOCC-equivalent if they can be inter-converted by stochastic local (quantum) operations and classical communication. There are only two SLOCC-equivalence classes of genuinely entangled 3-qubit states, the GHZ-class and the W-class, and we show that these exactly correspond with two kinds of internal commutative Frobenius algebras on C2 in the symmetric monoidal category of Hilbert spaces and linear maps, namely 'special' ones and 'anti-special' ones. Within the graphical language of symmetric monoidal categories, the distinction between 'special' and 'anti-special' is purely topological, in terms of 'connected' vs. 'disconnected'. These GHZ and W Frobenius algebras form the primitives of a graphical calculus which is expressive enough to generate and reason about representatives of arbitrary N-qubit states. This calculus refines the graphical calculus of complementary observables in [5, ICALP'08], which has already shown itself to have many applications and admit automation. Our result also induces a generalised graph state paradigm for measurement-based quantum computing.