26 citations · 124 across the 11 of their papers we have counts for
12 papers
Jordan products of quantum channels and their compatibility
Mark Girard, Martin Plávala, Jamie Sikora
Given two quantum channels, we examine the task of determining whether they are compatible - meaning that one can perform both channels simultaneously but, in the future, choose ex…
Twirling channels have minimal mixed-unitary rank
Mark Girard, Jeremy Levick
For a positive integer and a unitary representation of a compact group , the twirling channel for this representation is the linear mapping $Φ:…
On the mixed-unitary rank of quantum channels
Mark Girard, Debbie Leung, Jeremy Levick +4
In the theory of quantum information, the mixed-unitary quantum channels, for any positive integer dimension , are those linear maps that can be expressed as a convex combinatio…
Convex cones in mapping spaces between matrix algebras
Mark Girard, Seung-Hyeok Kye, Erling Størmer
We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by complete…
On directional derivatives of trace functionals of the form $A\mapsto\Tr(Pf(A))$
Mark W. Girard
Given a function $f:(0,\infty)\rightarrow\RR$ and a positive semidefinite matrix , one may define a trace functional on positive definite matrices as $A\…
Certifying optimality for convex quantum channel optimization problems
Bryan Coutts, Mark Girard, John Watrous
We identify necessary and sufficient conditions for a quantum channel to be optimal for any convex optimization problem in which the optimization is taken over the set of all quant…
Entanglement manipulation and distillability beyond LOCC
Eric Chitambar, Julio I. de Vicente, Mark W. Girard +1
When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classic…
The binegativity of two qubits
Mark W. Girard, Gilad Gour
We introduce an entanglement-related quantity that we call the binegativity. Based on numerical evidence, we conjecture that the binegativity is an entanglement measure for two-qub…
Entanglement monotones and transformations of symmetric bipartite states
Mark W. Girard, Gilad Gour
The primary goal in the study of entanglement as a resource theory is to find conditions that determine when one quantum state can or cannot be transformed into another via local o…
Computable entanglement conversion witness that is better than the negativity
Mark W. Girard, Gilad Gour
The primary goal of entanglement theory is to determine convertibility conditions for two quantum states. Up until now, this has always been done with the use of entanglement monot…
On convex optimization problems in quantum information theory
Mark W. Girard, Gilad Gour, Shmuel Friedland
Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices.…
Gradient-based stopping rules for maximum-likelihood quantum-state tomography
Scott Glancy, Emanuel Knill, Mark Girard
When performing maximum-likelihood quantum-state tomography, one must find the quantum state that maximizes the likelihood of the state given observed measurements on identically p…