53 citations · 128 across the 13 of their papers we have counts for
13 papers
Covariant quantum combinatorics with applications to zero-error communication
Dominic Verdon
We develop the theory of quantum (a.k.a. noncommutative) relations and quantum (a.k.a. noncommutative) graphs in the finite-dimensional covariant setting, where all systems (finite…
Testing quantum satisfiability
Ashley Montanaro, Changpeng Shao, Dominic Verdon
Quantum k-SAT (the problem of determining whether a k-local Hamiltonian is frustration-free) is known to be QMA_1-complete for k >= 3, and hence likely hard for quantum computers t…
Entanglement-invertible channels
Dominic Verdon
In a well-known result [Werner2001], Werner classified all tight quantum teleportation and dense coding schemes, showing that they correspond to unitary error bases. Here tightness…
A covariant Stinespring theorem
Dominic Verdon
We prove a finite-dimensional covariant Stinespring theorem for compact quantum groups. Let G be a compact quantum group, and let T:= Rep(G) be the rigid C*-tensor category of fini…
Entanglement-symmetries of covariant channels
Dominic Verdon
Let G and G' be monoidally equivalent compact quantum groups, and let H be a Hopf-Galois object realising a monoidal equivalence between these groups' representation categories. Th…
Unitary transformations of fibre functors
Dominic Verdon
We study unitary pseudonatural transformations (UPTs) between fibre functors Rep(G) -> Hilb, where G is a compact quantum group. For fibre functors F_1, F_2 we show that the catego…
Unitary pseudonatural transformations
Dominic Verdon
We suggest two approaches to a definition of unitarity for pseudonatural transformations between unitary pseudofunctors on pivotal dagger 2-categories. The first is to require that…
Quantum teleportation with infinite reference frame uncertainty and without prior alignment
Dominic Verdon, Jamie Vicary
We present two new schemes for quantum teleportation between parties whose local reference frames are misaligned by the action of a compact Lie group G. These schemes require no pr…
The Morita theory of quantum graph isomorphisms
Benjamin Musto, David Reutter, Dominic Verdon
We classify instances of quantum pseudo-telepathy in the graph isomorphism game, exploiting the recently discovered connection between quantum information and the theory of quantum…
A compositional approach to quantum functions
Benjamin Musto, David Reutter, Dominic Verdon
We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use t…
Perfect tight quantum teleportation without a shared reference frame
Dominic Verdon, Jamie Vicary
We present a new scheme for teleporting a quantum state between two parties whose local reference frames are misaligned by the action of a finite symmetry group. Unlike other propo…
Coherence for braided and symmetric pseudomonoids
Dominic Verdon
Presentations for unbraided, braided and symmetric pseudomonoids are defined. Biequivalences characterising the semistrict bicategories generated by these presentations are proven.…
Tight Reference Frame--Independent Quantum Teleportation
Dominic Verdon, Jamie Vicary
We give a tight scheme for teleporting a quantum state between two parties whose reference frames are misaligned by an action of a finite symmetry group. Unlike previously proposed…