Related papers: The Data Compression Theorem for Ergodic Quantum I…
A system of interacting qubits can be viewed as a non-i.i.d quantum information source. A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each…
Suppose that a quantum source is known to have von Neumann entropy less than or equal to S but is otherwise completely unspecified. We describe a method of universal quantum data compression which will faithfully compress the quantum…
The quantum entropy-typical subspace theory is specified. It is shown that any mixed state with von Neumann entropy less than h can be preserved approximately by the entropy-typical subspace with entropy= h. This result implies an universal…
For a real number $r>0$, let $F(r)$ be the family of all stationary ergodic quantum sources with von Neumann entropy rates less than $r$. We prove that, for any $r>0$, there exists a blind, source-independent block compression scheme which…
B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…
This thesis addresses problems in the field of quantum information theory. The first part of the thesis is opened with concrete definitions of general quantum source models and their compression, and each subsequent chapter addresses the…
The emerging field of quantum machine learning has the potential of revolutionizing our perspectives of quantum computing and artificial intelligence. In the predominantly empirical realm of quantum machine learning, a theoretical void…
We prove that the average smooth Renyi entropy rate will approach the entropy rate of a stationary, ergodic information source, which is equal to the Shannon entropy rate for a classical information source and the von Neumann entropy rate…
Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum R\'enyi entropies. In order to do this, we appeal to a very general quantum encoding scheme that…
A model of a quantum information source is proposed, based on the Gibbs ensemble of ideal (free) particles (bosons or fermions). We identify the (thermodynamic) von Neumann entropy as the information rate and establish the classical…
The information spectrum approach gives general formulae for optimal rates of various information theoretic protocols, under minimal assumptions on the nature of the sources, channels and entanglement resources involved. This paper…
We describe a universal information compression scheme that compresses any pure quantum i.i.d. source asymptotically to its von Neumann entropy, with no prior knowledge of the structure of the source. We introduce a diagonalisation…
The general scheme of data compression using the quantum noiseless coding theorem of Schumacher is dicussed for general quantum sources. When the Hilbert space of the quantum source is decomposable into orthogonal subspaces, one can first…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
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…
We consider the most general (finite-dimensional) quantum mechanical information source, which is given by a quantum system $A$ that is correlated with a reference system $R$. The task is to compress $A$ in such a way as to reproduce 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…
A generic approach for compiling any classical block compression algorithm into a quantum block compression algorithm is presented. Using this technique, compression asymptoticaly approaching the von Neumann entropy of a qubit source can be…
We present a formula that determines the optimal number of qubits per message that allows asymptotically faithful compression of the quantum information carried by an ensemble of mixed states. The set of mixed states determines a…
In this article we study lossless compression of strings of pure quantum states of indeterminate-length quantum codes which were introduced by Schumacher and Westmoreland. Past work has assumed that the strings of quantum data are prepared…