Related papers: A random-coding based proof for the quantum coding…
In this paper the quantum source coding theorem is obtained for a completely ergodic source. This results extends Shannon's classical theorem as well as Schumacher's quantum noiseless coding theorem for memoryless sources. The control of…
We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a…
Quantum secret-sharing and quantum error-correction schemes rely on multipartite decoding protocols, yet the non-local operations involved are challenging and sometimes infeasible. Here we construct a quantum secret-sharing protocol with a…
In this paper we consider the transmission of classical information through a class of quantum channels with long-term memory, which are given by convex combinations of product channels. Hence, the memory of such channels is given by a…
The present work continues investigation of the capacities of measurement (quantum-classical) channels in the most general setting, initiated in~\cite{HCT}. The proof of coding theorems is given for the classical capacity and…
Shared entanglement is a resource available to parties communicating over a quantum channel, much akin to public coins in classical communication protocols. Whereas shared randomness does not help in the transmission of information, or…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
We define a large class of quantum sources and prove a quantum analog of the asymptotic equipartition property. Our proof relies on using local measurements on the quantum source to obtain an associated classical source. The classical…
Recent years have seen rapid development in the subject of quantum coding theory, with breakthroughs on many exciting classes of codes, including quantum LDPC codes, quantum locally testable codes, and quantum codes with interesting…
We give trade-offs between classical communication, quantum communication, and entanglement for processing information in the Shannon-theoretic setting. We first prove a unit-resource capacity theorem that applies to the scenario where only…
Starting from Shannon's celebrated 1948 channel coding theorem, we trace the evolution of channel coding from Hamming codes to capacity-approaching codes. We focus on the contributions that have led to the most significant improvements in…
Probabilistic quantum error correction is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this work, we deeply analyze probabilistic version of the…
It is well known that quantum theory forbids the exact copying of an unknown quantum state. Therefore in broadcasting of classical information by a quantum channel an additional contribution to the error in the decoding is expected. We…
We extend quantum rate distortion theory by considering auxiliary resources that might be available to a sender and receiver performing lossy quantum data compression. The first setting we consider is that of quantum rate distortion coding…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…
In the first part of this thesis, we discuss the algebraic approach to classical and quantum physics and develop information theoretic concepts within this setup. In the second part, we discuss the uncertainty principle in quantum…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
Turbo coding is a powerful class of forward error correcting codes, which can achieve performances close to the Shannon limit. The turbo principle can be applied to the problem of side-information source coding, and we investigate here its…
Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…