Quantum communication with side infromation

Quantum communication capacities refer to the maximum amount of quantum information that can be reliably transmitted through a noisy communication channel. However, evaluating these capacities for many quantum channels is challenging due to the superadditivity phenomenon. In this thesis, we tackle this problem by proposing the design of multiple degradable extensions for different important discrete and continuous variable channels. By introducing these extensions, we can establish upper bounds on the quantum and private capacities of the original channels. These extended channels often rely on a set of sufficient conditions that determine the degradability of flagged extensions, which are channels formed as convex combinations of other channels with some side information, commonly referred to as flags. Verifying these conditions is straightforward and greatly simplifies the process of constructing degradable extensions. This approach not only provides a practical solution for estimating the capacities of realistic channels but also enhances our understanding of their behavior in terms of degradability. We apply this technique to both discrete and continuous variable channels, expanding its applicability across different scenarios

Optimal Quantum Subtracting Machine

The impossibility of undoing a mixing process is analysed in the context of quantum information theory. The optimal machine to undo the mixing process is studied in the case of pure states, focusing on qubit systems. Exploiting the symmetry of the problem we parametrise the optimal machine in such a way that the number of parameters grows polynomially in the size of the problem. This simplification makes the numerical methods feasible. For simple but non-trivial cases we computed the analytical solution, comparing the performance of the optimal machine with other protocols.Comment: 13 pages, 2 figure

Bounding the quantum capacity with flagged extensions

In this article we consider flagged extensions of channels that can be written as convex combination of other channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate application is a bound on the quantum and private capacities of any channel being a mixture of a unitary operator and another channel, with the probability associated to the unitary operator being larger than $1/2$. We then specialize our sufficient conditions to flagged Pauli channels, obtaining a family of upper bounds on quantum and private capacities of Pauli channels. In particular, we establish new state-of-the-art upper bounds on the quantum and private capacities of the depolarizing channel, BB84 channel and generalized amplitude damping channel. Moreover, the flagged construction can be naturally applied to tensor powers of channels with less restricting degradability conditions, suggesting that better upper bounds could be found by considering a larger number of channel uses.Comment: 18 pages, 4 figure

Low-ground/High ground capacity regions analysis for Bosonic Gaussian Channels

We present a comprehensive characterization of the interconnections between single-mode, phaseinsensitive Gaussian Bosonic Channels resulting from channel concatenation. This characterization enables us to identify, in the parameter space of these maps, two distinct regions: low-ground and high-ground. In the low-ground region, the information capacities are smaller than a designated reference value, while in the high-ground region, they are provably greater. As a direct consequence, we systematically outline an explicit set of upper bounds for the quantum and private capacity of these maps, which combine known upper bounds and composition rules, improving upon existing results.Comment: 18 pages; 7 figure

Estimating Quantum and Private capacities of Gaussian channels via degradable extensions

We present upper bounds on the quantum and private capacity of single-mode, phase-insentitive Bosonic Gaussian Channels based on degradable extensions. Our findings are state-of-the-art in the following parameter regions: low temperature and high transmissivity for the thermal attenuator, low temperature for additive Gaussian noise, high temperature and intermediate amplification for the thermal amplifier.Comment: 5+4 pages, 3 figures. Typos corrected, improved presentatio