Related papers: Zero-error communication via quantum channels, non…
We study the effects of quantum entanglement on the performance of two classical zero-error communication tasks among multiple parties. Both tasks are generalizations of the two-party zero-error channel-coding problem, where a sender and a…
In this paper, we present a condition for the zero-error capacity of quantum channels. To achieve this result we first prove that the eigenvectors (or eigenstates) common to the Kraus operators representing the quantum channel are fixed…
The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this approach, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse…
The zero-error capacity of channels with a countably infinite input alphabet formally generalises Shannon's classical problem about the capacity of discrete memoryless channels. We solve the problem for three particular channels. Our…
We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits…
A fundamental quantity of interest in Shannon theory, classical or quantum, is the error exponent of a given channel $W$ and rate $R$: the constant $E(W,R)$ which governs the exponential decay of decoding error when using ever larger…
We study zero-error entanglement assisted source-channel coding (communication in the presence of side information). Adapting a technique of Beigi, we show that such coding requires existence of a set of vectors satisfying orthogonality…
In this thesis, we are interested in the limits of quantum communication with and without entanglement, and with and without noise assumptions on the communication setup. When a sender and a receiver are connected by a communication line…
Permutation channels model communication and storage scenarios in which the positional identity of the physical carriers is partially or completely lost, so that the transmitted information is only accessible up to an unknown reordering.…
For classical point-to-point channels, it has been shown by Bennett et al. that quantum entanglement assistance cannot improve their capacity, and by Cubitt et al. that entanglement assistance cannot activate (increase from zero to…
Coding theorems in quantum Shannon theory express the ultimate rates at which a sender can transmit information over a noisy quantum channel. More often than not, the known formulas expressing these transmission rates are intractable,…
We study quantum versions of the Shannon capacity of graphs and non-commutative graphs. We introduce the asymptotic spectrum of graphs with respect to quantum and entanglement-assisted homomorphisms, and we introduce the asymptotic spectrum…
The Shannon capacity of a graph is an important graph invariant in information theory that is extremely difficult to compute. The Lovasz number, which is based on semidefinite programming relaxation, is a well-known upper bound for the…
Shannon's channel coding theorem describes the maximum possible rate of reliable information transfer through a classical noisy communication channel. It, together with the source coding theorem, characterizes lossless channel communication…
Quantum communication theory focuses on the study of quantum channels for transmitting quantum information, where the transmission rate is measured by quantum channel capacity. This quantity exhibits several intriguing properties, such as…
The Shannon capacity of a graph G is the maximum asymptotic rate at which messages can be sent with zero probability of error through a noisy channel with confusability graph G. This extensively studied graph parameter disregards the fact…
We demonstrate superadditivity of one-shot zero-error classical capacity in an asymmetric communication setting where a noisy classical channel is used in parallel with a perfect quantum channel. Each channel individually supports only a…
Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of…
We begin with a detailed description of a low dimensional quantum channel ($d_A=4, d_E=3$) demonstrating the symmetric form of superactivation of one-shot zero-error quantum capacity. This means appearance of a noiseless (perfectly…
We analyze the problem of zero-error communication through timing channels that can be interpreted as discrete-time queues with bounded waiting times. The channel model includes the following assumptions: 1) Time is slotted, 2) at most $ N…