A categorical semantics of quantum protocols

By Samson Abramsky, Bob Coecke. Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004., 2004

928 citations recorded by the source corpus.

Particular focus in this paper is on quantum information protocols, which exploit quantum-mechanical effects in an essential way. The particular examples we shall use to illustrate our approach will be teleportation (Benett et al., 1993), logic-gate teleportation (Gottesman and Chuang,1999), and entanglement swapping (Zukowski et al., 1993). The ideas illustrated in these protocols form the basis for novel and potentially very important applications to secure and fault-tolerant communication and computation (2001,1999,2000).

View Paper: https://www.semanticscholar.org/paper/75df2286a87813de189273a5d97b70afb5bed178

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Quantum picturalism (2009, methodology): “the space of functionals) then the Bell-states, trace and transpose are basis independent [36,40].”
Interacting Quantum Observables (2008, background): “2 A detailed categorical account on FdHilbwp is in [3]; in particular, neither FdHilbp nor FdHilbwp has biproducts, so the approach to measurements taken in [1] will not work here.”
Monads need not be endofunctors (2010, background): “, in quantum computing we are interested in dagger compact closed categories [2].”
Quantum measurements without sums (2006, background): “An important aspect of the †-compact semantics of quantum protocols proposed in [2, 7, 31] was the interplay of the multiplicative and additive structures of tensor products and direct sums, respectively.”
Category-theoretic quantitative compositional distributional models of natural language semantics (2013, background): “For those interested, this property is one of the central elements behind the diagrammatic proof of quantum teleportation [1, 16], the diagrammatic representation of which closely resembles that shown in Figure 3.”
The ZX-calculus is complete for stabilizer quantum mechanics (2013, background): “1 Categorical quantum mechanics In 2004, Abramsky and Coecke introduced a formalism for describing quantum mechanics using category theory [3].”
Categories for the practising physicist (2009, background): “[ 2 ]), or, we can study which structural features for example distinguish classical from quantum theories (e.g.”
Reformulating and Reconstructing Quantum Theory (2011, methodology): “We can append this set to o[1] to get a new maximal effect associated with the first of the distinguishable states.”
“What is a Thing?”: Topos Theory in the Foundations of Physics (2008, background): “For example, Baez’s advocation of n-categories [5, 6]; ‘categorial quantum theory’ [2, 73]; Takeuti’s theory(19) of ‘quantum sets’ [71]; and Crane’s work on categorial models of space-time [17].”
Theory-independent limits on correlations from generalized Bayesian networks (2014, methodology): “CDP use a graphical notation that builds upon that of Abramsky and Coecke [1].”
A Survey of Graphical Languages for Monoidal Categories (2009, unknown): “Deﬁnition ([1, 33]) .”
Quantum Theory and Beyond: Is Entanglement Special? (2009, background): “[53] f or investigating the same question in much more general framework of compact closed categories.”
A topos foundation for theories of physics: I. Formal languages for physics (2007, methodology): “A recent example of such an attempt is the work of Abramsky and Coecke who construct a categorical analogue of some of the critical parts of the Hilbert space formalism [5]; see also the work by Vicary [6].”
Dagger Compact Closed Categories and Completely Positive Maps: (Extended Abstract) (2007, background): “The respective axiomatics of [9] and [1] are at the outset quite different: the former attempts to capture von Neumann’s formulation of quantum mechanics in terms of mixed states, density matrices, and completely positive maps, while the latter formalizes the Hilbert space point of view centered on ”
Categories in Control (2014, unknown): “The operation sending each linear relation to its adjoint extends to a contravariant functor † : FinRelk → FinRelk, which obeys a list of properties that are summarized by saying that FinRelk is a ‘†-compact’ category [1, 18].”
Interacting quantum observables: categorical algebra and diagrammatics (2009, methodology): “This research programme was initiated by Abramsky and one of the authors in [1].”