17 citations · 55 across the 18 of their papers we have counts for
26 papers
Actions of quantum groups on dual operator spaces and their crossed products
Jason Crann, Joeri De Ro, Jacek Krajczok
We study the category of dual operator spaces equipped with an action of a locally compact quantum group . The Fubini crossed product functor $-\rtimes^\mathcal{F} \mat…
A Banach algebra encoding quantum group duality
Jason Crann, Matthias Neufang
We introduce and study a new Banach algebra structure on the trace-zero subspace of trace class operators for any locally compact quantum group $\m…
An operator system approach to self-testing
Jason Crann, Ivan G. Todorov, Lyudmila Turowska
We develop a general framework for self-testing, in which bipartite correlations are described by states on the commuting tensor product of a pair of operator systems. We propose a…
Fejér representations for discrete quantum groups and applications
Jason Crann, Soroush Kazemi, Matthias Neufang
We prove that a discrete quantum group has the approximation property if and only if a Fejér-type representation holds for its -algebraic or von Neumann algebraic…
Algebraic approach to spacetime bulk reconstruction
Jason Crann, Monica Jinwoo Kang
Motivated by the theory of holographic quantum error correction in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, together with the kink transform conjecture o…
Values of cooperative quantum games
Jason Crann, Rupert H. Levene, Ivan G. Todorov +1
We develop a resource-theoretical approach that allows us to quantify values of two-player, one-round cooperative games with quantum inputs and outputs, as well as values of quantu…
Orthogonal Unitary Bases and a Subfactor Conjecture
Jason Crann, David W. Kribs, Rajesh Pereira
We show that any finite dimensional von Neumann algebra admits an orthonormal unitary basis with respect to its standard trace. We also show that a finite dimensional von Neumann s…
Quantum teleportation in the commuting operator framework
Alexandre Conlon, Jason Crann, David W. Kribs +1
We introduce a notion of teleportation scheme between subalgebras of semi-finite von Neumann algebras in the commuting operator model of locality. Using techniques from subfactor t…
Gaussian quantum information over general quantum kinematical systems I: Gaussian states
Cedric Beny, Jason Crann, Hun Hee Lee +2
We develop a theory of Gaussian states over general quantum kinematical systems with finitely many degrees of freedom. The underlying phase space is described by a locally compact…
A weak expectation property for operator modules, injectivity and amenable actions
Alex Bearden, Jason Crann
We introduce an equivariant version of the weak expectation property (WEP) at the level of operator modules over completely contractive Banach algebras . We prove a number of ge…
Finite presentation, the local lifting property, and local approximation properties of operator modules
Jason Crann
We introduce notions of finite presentation and co-exactness which serve as qualitative and quantitative analogues of finite-dimensionality for operator modules over completely con…
Amenable dynamical systems over locally compact groups
Alex Bearden, Jason Crann
We establish several new characterizations of amenable - and -dynamical systems over arbitrary locally compact groups. In the -setting we show that amenability is eq…
State convertibility in the von Neumann algebra framework
Jason Crann, David W. Kribs, Rupert H. Levene +1
We establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi-finite v…
A non-commutative Fejér theorem for crossed products, the approximation property, and applications
Jason Crann, Matthias Neufang
We prove that a locally compact group has the approximation property (AP), introduced by Haagerup-Kraus, if and only if a non-commutative Fejér theorem holds for the associated $C^…
A new duality via the Haagerup tensor product
Mahmood Alaghmandan, Jason Crann, Matthias Neufang
We initiate the study of a new notion of duality defined with respect to the module Haagerup tensor product. This notion not only recovers the standard operator space dual for Hilb…
Mapping ideals of quantum group multipliers
Mahmood Alaghmandan, Jason Crann, Matthias Neufang
We study the dual relationship between quantum group convolution maps and completely bounded multipliers of $\widehat{\mathbb{G}…
Inner amenability and approximation properties of locally compact quantum groups
Jason Crann
We introduce an appropriate notion of inner amenability for locally compact quantum groups, study its basic properties, related notions, and examples arising from the bicrossed pro…
Fourier algebras of hypergroups and central algebras on compact (quantum) groups
Mahmood Alaghmandan, Jason Crann
This paper concerns the study of regular Fourier hypergroups through multipliers of their associated Fourier algebras. We establish hypergroup analogues of well-known characterizat…
Character density in central subalgebras of compact quantum groups
Mahmood Alaghmandan, Jason Crann
We investigate quantum group generalizations of various density results from Fourier analysis on compact groups. In particular, we establish the density of characters in the space…
On hereditary properties of quantum group amenability
Jason Crann
Given a locally compact quantum group and a closed quantum subgroup , we show that is amenable if and only if is amenable and $\m…
On the operator homology of the Fourier algebra and its -multiplier completion
Jason Crann, Zsolt Tanko
We study various operator homological properties of the Fourier algebra of a locally compact group . Establishing the converse of two results of Ruan and Xu, we show that…
Private algebras in quantum information and infinite-dimensional complementarity
Jason Crann, David W. Kribs, Rupert H. Levene +1
We introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of compleme…
Amenability and covariant injectivity of locally compact quantum groups II
Jason Crann
Building on our previous work, we study the non-relative homology of quantum group convolution algebras. Our main result establishes the equivalence of amenability of a locally com…
An uncertainty principle for unimodular quantum groups
Jason Crann, Mehrdad Kalantar
We present a generalization of Hirschman's entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups. As a corollary, we streng…