Zobrazeno 1 - 10
of 46
pro vyhledávání: '"Carette, Titouan"'
We give generators and relations for the hypergraph props of Gaussian relations and positive affine Lagrangian relations. The former extends Gaussian probabilistic processes by completely-uninformative priors, and the latter extends Gaussian quantum
Externí odkaz:
http://arxiv.org/abs/2403.10479
We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical systems, as w
Externí odkaz:
http://arxiv.org/abs/2401.07914
Publikováno v:
EPTCS 384, 2023, pp. 220-264
We present a smorgasbord of results on the stabiliser ZX-calculus for odd prime-dimensional qudits (i.e. qupits). We derive a simplified rule set that closely resembles the original rules of qubit ZX-calculus. Using these rules, we demonstrate analog
Externí odkaz:
http://arxiv.org/abs/2306.05204
Quantum reference frames are needed in quantum theory for much the same reasons that reference frames are in classical theories: to manifest invariance in line with fundamental relativity principles and to provide a basis for the definition of observ
Externí odkaz:
http://arxiv.org/abs/2303.14002
We exhibit a strong connection between the matchgate formalism introduced by Valiant and the ZW-calculus of Coecke and Kissinger. This connection provides a natural compositional framework for matchgate theory as well as a direct combinatorial interp
Externí odkaz:
http://arxiv.org/abs/2302.08767
Autor:
Carette, Titouan, Moutot, Etienne
By reformulating Wang tiles with tensors, we propose a natural generalization to the probabilistic and quantum setting. In this new framework, we introduce notions of tilings and periodicity directly extending their classical counterparts. In the one
Externí odkaz:
http://arxiv.org/abs/2302.04503
Universal and complete graphical languages have been successfully designed for pure state quantum mechanics, corresponding to linear maps between Hilbert spaces, and mixed states quantum mechanics, corresponding to completely positive superoperators.
Externí odkaz:
http://arxiv.org/abs/2302.04212
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally "centrality", i.e. the property for an effect to commute with all othe
Externí odkaz:
http://arxiv.org/abs/2207.09190
Autor:
Carette, Titouan
String diagrams can nicely express numerous computations in symmetric strict monoidal categories (SSMC). To be entirely exact, this is only true for props: the SSMCs whose monoid of objects are free. In this paper, we show a propification theorem ass
Externí odkaz:
http://arxiv.org/abs/2205.07760
Autor:
Booth, Robert I., Carette, Titouan
Publikováno v:
MFCS 2022, 24:1-24:15
We introduce a family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions. These calculi recover many of the nice features of the qubit ZX-calculus which were lost in previous proposals for higher-dimensio
Externí odkaz:
http://arxiv.org/abs/2204.12531