The purpose of this review is to present some of the latest developments using random
techniques, and in particular, random matrix techniques in quantum information theory. Our …

The quest to build a quantum computer is arguably one of the major scientific and
technological challenges of the twenty-first century, and quantum information theory (QIT) …

Given integers n ≥ mn≥ m, let Sep (n, m) Sep (n, m) be the set of separable states on the
Hilbert space C^ n ⊗ C^ m C n⊗ C m. It is well-known that for (n, m)=(3, 2)(n, m)=(3, 2) the …

Semidefinite programs (SDPs) are a framework for exact or approximate optimization with
widespread application in quantum information theory. We introduce a new method for using …

We study the problem of approximating the cone of positive semidefinite (PSD) matrices with
a cone that can be described by smaller-sized PSD constraints. Specifically, we ask the …

It is well known that state-of-the-art linear programming solvers are more efficient than their
semidefinite programming counterparts and can scale to much larger problem sizes. This …

The problem of determining whether a given quantum state is separable is known to be
computationally difficult. We develop an approach to this problem based on approximations …

A quantum channel whose image approximates the set of separable states is called a
disentangler, which plays a prominent role in the investigation of variants of the …

In this work we are interested in the problem of testing quantum entanglement. More
specifically, we study the separability problem in quantum property testing, where one is …

These are notes for five lectures given at the second School of pthe program “Operator
Algebras, Groups and Applications to Quantum Information” held in May 2019 at the ICMAT …