arXiv:1301.5401v3 [math.PR] 3 Jul 2013 Weingarten calculus for matrix ensembles associated
with compact symmetric spaces Page 1 arXiv:1301.5401v3 [math.PR] 3 Jul 2013 Weingarten …

We argue that one of the following statements must be true:(a) extensive violations of
quantum information theory's additivity conjectures exist or (b) there exists a set …

In a previous paper, we proved that, in the appropriate asymptotic regime, the limit of the
collection of possible eigenvalues of output states of a random quantum channel is a …

It is known that random quantum channels exhibit significant violations of multiplicativity of
maximum output p-norms for any p> 1. In this work, we show that a weaker variant of …

We prove additivity violation of minimum output entropy of quantum channels by
straightforward application of ϵ ϵ-net argument and Lévy's lemma. The additivity conjecture …

It is now well-known that, with high probability, the additivity of minimum output entropy does
not hold for pairs of the random quantum channel and its complex conjugate. We investigate …

The free contraction norm (or the (t)-norm) was introduced by Belinschi, Collins and Nechita
as a tool to compute the typical location of the collection of singular values associated to a …

Inspired by Montanaro's work, we introduce the concept of additivity rates of a quantum
channel L, which give the first order (linear) term of the minimum output p-Rényi entropies of …

We address the local spectral behavior of the random matrix $\Pi_1 U^{\otimes k}\Pi_2
U^{\otimes k*}\Pi_1 $, where $ U $ is a Haar distributed unitary matrix of size $ n\times n …

In this paper, we study the behavior of the output of pure entangled states after being
transformed by a product of conjugate random unitary channels. This study is motivated by …