# Materials

Below you can find some write-ups or projects I created. Mostly, they were prepared for courses that I completed. Their goal was to summarize an existing paper or to prove a selected theorem in a detailed, accessible way. Maybe someone will find them useful.

## Non-additivity of Channel Capacities in the Quantum Shannon Theory

In classical information theory channel capacities are additive. Is it the case in quantum information theory as well? Can we transmit any information by combining quantum channels which alone have no capacity? This project summarizes a paper *Quantum Communication With Zero-Capacity Channels* by Graeme Smith and Jon Yard that answers these questions.

Download my work __here__.

## Classical Machine Learning for Quantum Systems and Quantum Enhanced Machine Learning

What is *Quantum Machine Learning*? We may use classical machine learning to solve problems in quantum physics or we may use quantum algorithms to develop new, fully quantum machine learning techniques. I chose a paper from both categories and summarized them in my project. The first paper is *A Neural Decoder for Topological Codes* by Giacomo Torlai, Roger G. Melko which proposes a stochastic neural network to create decoders for topological quantum error-correction codes. The second paper is *Quantum Perceptron Models* by Nathan Wiebe, Ashish Kapoor, Krysta M Svore which shows how to quantumly represent and train a perceptron.

Download my work __here__.

## Hypercontractivity Via the Entropy Method

In this project I present a detailed proof of a hypercontractive inequality using basic entropic quantities and their properties. The proof comes from the paper *Hypercontractivity Via the Entropy Method* by Blais and Tan.

Download my work __here__.

## E91 Cryptographic Protocol

E91 protocol proposed by Ekert was one of the first practical applications of quantum entanglement. It achieves the task of quantum key distribution. In this short document I present a step by step proof of the protocol.

Download my work __here__.

## Lower bound on PPT distillable entanglement from isotropic states

Quantum entanglement is an essential resource in quantum information theory. What is the rate of distillation of entanglement from isotropic states using operations that are positive-partial-transpose-preserving? This project presents a detailed proof of a theorem from the paper *A semidefinite program for distillable entanglement* by Rains that shows a lower bound for this rate. The problem is equivalent to the rate of transmission through a quantum depolarizing channel assisted by PPTp codes.

Download my work __here__.