24 citations · 56 across the 12 of their papers we have counts for
14 papers
Operator Algebra Generalization of a Theorem of Watrous and Mixed Unitary Quantum Channels
David W Kribs, Jeremy Levick, Rajesh Pereira +1
We establish an operator algebra generalization of Watrous' theorem \cite{watrous2009} on mixing unital quantum channels (completely positive trace-preserving maps) with the comple…
Entanglement Breaking Rank via Complementary Channels and Multiplicative Domains
David W. Kribs, Jeremy Levick, Rajesh Pereira +1
Quantum entanglement can be studied through the theory of completely positive maps in a number of ways, including by making use of the Choi-Jamilkowski isomorphism, which identifie…
Entanglement Breaking Channels, Stochastic Matrices, and Primitivity
Jennifer Ahiable, David W. Kribs, Jeremy Levick +2
We consider the important class of quantum operations (completely positive trace-preserving maps) called entanglement breaking channels. We show how every such channel induces stoc…
An extension of Bravyi-Smolin's construction for UMEBs
Jeremy Levick, Mizanur Rahaman
We extend Bravyi and Smolin's construction for obtaining unextendible maximally entangled bases (UMEBs) from equiangular lines. We show that equiangular real projections of rank mo…
Positively Factorizable Maps
Jeremy Levick, Mizanur Rahaman
We initiate a study of linear maps on that have the property that they factor through a tracial von Neumann algebra via operators $Z\in M_n(\mat…
Nullspaces of Entanglement Breaking Channels and Applications
D. W. Kribs, J. Levick, K. Olfert +2
We investigate the nullspace structures of entanglement breaking channels, and related applications. We show that every operator space of trace zero matrices is the nullspace of an…
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…
Approximate Quasiorthogonality of Operator Algebras and Relative Quantum Privacy
David W. Kribs, Jeremy Levick, Mike Nelson +2
We show that the approximate quasiorthogonality of two operator algebras is equivalent to the algebras being approximately private relative to their conditional expectation quantum…
Factorizations of Quantum Channels
Jeremy Levick
We find a connection between the existence of a factorization of a quantum channel and the existence of low-rank solutions to certain linear matrix equations. Using this, we show t…
Matrix N-dilations of quantum channels
Jeremy Levick, Robert T. W. Martin
We study unital quantum channels which are obtained via partial trace of a -automorphism of a finite unital matrix -algebra. We prove that any such channel, , on a unital…
Quantum Privacy and Schur Product Channels
Jeremy Levick, David W. Kribs, Rajesh Pereira
We investigate the quantum privacy properties of an important class of quantum chan-nels, by making use of a connection with Schur product matrix operations and associated correlat…
An Uncertainty Principle For Completely Positive Maps
Jeremy Levick
We present an "uncertainty principle" for quantum channels, showing a relationship between the dimensions of the range of a channel and the range of its complement. We examine some…
Private Quantum Subsystems and Quasiorthogonal Operator Algebras
Jeremy Levick, Tomas Jochym-O'Connor, David Kribs +2
We generalize a recently discovered example of a private quantum subsystem to find private subsystems for Abelian subgroups of the -qubit Pauli group, which exist in the absence…