Related papers: Quantum rate distortion, reverse Shannon theorems,…
We study lossy compression of a finite statement source generated in a fixed deductive environment. The source symbols are statements in a knowledge base endowed with a shared proof system, and reconstruction fidelity is measured by…
We consider the lossy quantum source coding problem where the task is to compress a given quantum source below its von Neumann entropy. Inspired by the duality connections between the rate-distortion and channel coding problems in the…
Shannon proved that if we can transmit bits reliably at rates larger than the rate distortion function $R(D)$, then we can transmit this source to within a distortion $D$. We answer the converse question ``If we can transmit a source to…
The entanglement-assisted classical capacity of a noisy quantum channel is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have…
We establish a theory of quantum-to-classical rate distortion coding. In this setting, a sender Alice has many copies of a quantum information source. Her goal is to transmit classical information about the source, obtained by performing a…
The Quantum Reverse Shannon Theorem has been a milestone in quantum information theory. It states that asymptotically reliable simulation of a quantum channel, assisted by unlimited shared entanglement, requires a rate of classical…
Direct evaluation of the rate-distortion function has rarely been achieved when it is strictly greater than its Shannon lower bound. In this paper, we consider the rate-distortion function for the distortion measure defined by an…
Coded source compression, also known as source compression with helpers, has been a major variant of distributed source compression, but has hitherto received little attention in the quantum regime. This work treats and solves the…
In this work we investigate the behavior of the minimal rate needed in order to guarantee a given probability that the distortion exceeds a prescribed threshold, at some fixed finite quantization block length. We show that the excess coding…
A composite source, consisting of multiple subsources and a memoryless switch, outputs one symbol at a time from the subsource selected by the switch. If some data should be encoded more accurately than other data from an information…
The optimal rate of reliable communication over a quantum channel can be enhanced by pre-shared entanglement. Whereas the enhancement may be unbounded in infinite-dimensional settings even when the input power is constrained, a…
We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to…
This paper investigates a lossy source coding problem in which two decoders can access their side-information respectively. The correlated sources are a product of two component correlated sources, and we exclusively investigate the case…
Since the publication of Shannon's theory of one terminal source coding, a number of interesting extensions have been derived by researchers such as Slepian-Wolf, Wyner, Ahlswede-K\"{o}rner, Wyner-Ziv and Berger-Yeung. Specifically, the…
The Shannon lower bound is one of the few lower bounds on the rate-distortion function that holds for a large class of sources. In this paper, it is demonstrated that its gap to the rate-distortion function vanishes as the allowed…
The entanglement cost of a quantum channel is the minimal rate at which entanglement (between sender and receiver) is needed in order to simulate many copies of a quantum channel in the presence of free classical communication. In this…
Dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one, reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones, and more generally the…
Ask how the quantum compression of ensembles of pure states is affected by the availability of entanglement, and in settings where the encoder has access to side information. We find the optimal asymptotic quantum rate and the optimal…
We examine the structure of families of distortion balls from the perspective of Kolmogorov complexity. Special attention is paid to the canonical rate-distortion function of a source word which returns the minimal Kolmogorov complexity of…