We present a bouquet of continuity bounds for quantum entropies, falling broadly into two
classes: first, a tight analysis of the Alicki–Fannes continuity bounds for the conditional von …

The quantum steering ellipsoid of a two-qubit state is the set of Bloch vectors that Bob can
collapse Alice's qubit to, considering all possible measurements on his qubit. We provide an …

Evaluating capacities of quantum channels is the first purpose of quantum Shannon theory,
but in most cases the task proves to be very hard. Here, we introduce the set of Multi-level …

Degradable quantum channels are an important class of completely positive trace-
preserving maps. Among other properties, they offer a single-letter formula for the quantum …

We present upper bounds on the quantum and private capacity of single-mode, phase-
insensitive bosonic Gaussian channels based on degradable extensions. Our findings are …

A new upper bound for the quantum capacity of the d-dimensional depolarizing channels is
presented. Our derivation makes use of a flagged extension of the map where the receiver …

We determine both the quantum and the private capacities of low-noise quantum channels
to leading orders in the channel's distance to the perfect channel. It has been an open …

Interest in the Werner-Holevo channel Λ 1 (ρ)= 1 2 [tr (ρ) I− ρ T] has been mainly due to its
abstract mathematical properties. We show that in three dimensions and with a slight …

We study four well-known capacities of a two-parameter family of qubit Pauli channels.
These are the channels that are covariant under the SO (2) group and contain the …

As the title indicates, this chapter presents a brief, self-contained introduction to five
fundamental problems in quantum information science (QIS) that are especially well suited …