相关论文: Universal quantum information compression and degr…
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…
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…
This paper considers the problem of data compression for dependent quantum systems. It is the second in a series under the same title. As in the previous paper, we are interested in Lempel--Ziv encoding for quantum Gibbs ensembles. Here, we…
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…
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…
We extend the data compression theorem to the case of ergodic quantum information sources. Moreover, we provide an asymptotically optimal compression scheme which is based on the concept of high probability subspaces. The rate of this…
The outcomes of projective measurements on a quantum many-body system in a chosen basis are inherently probabilistic. The Shannon entropy of this probability distribution (the "diagonal entropy") often reveals universal features, such as…
We define an algorithm that parses multidimensional arrays sequentially into mainly unrepeated but nested multidimensional sub-arrays of increasing size, and show that the resulting sub-block pointer encoder compresses almost every…
We simply construct a quantum universal variable-length source code in which, independent of information source, both of the average error and the probability that the coding rate is greater than the entropy rate $H(rho_p)$, tend to 0. If…
In order to compress quantum messages without loss of information it is necessary to allow the length of the encoded messages to vary. We develop a general framework for variable-length quantum messages in close analogy to the classical…
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…
We design a quantum method for classical information compression that exploits the hidden subgroup quantum algorithm. We consider sequence data in a database with a priori unknown symmetries of the hidden subgroup type. We prove that data…
In this paper, we consider the one-shot version of the classical Wyner-Ziv problem where a source is compressed in a lossy fashion when only the decoder has access to a correlated side information. Following the entropy-constrained…
Weakly almost i.i.d. quantum sources are sequences of multipartite states whose fixed-size marginals converge, on average, to tensor powers of a reference state, while allowing arbitrary global correlations and entanglement. We establish…
This paper presents conditional versions of Lempel-Ziv (LZ) algorithm for settings where compressor and decompressor have access to the same side information. We propose a fixed-length-parsing LZ algorithm with side information, motivated…
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…
Consider a source E of pure quantum states with von Neumann entropy S. By the quantum source coding theorem, arbitrarily long strings of signals may be encoded asymptotically into S qubits/signal (the Schumacher limit) in such a way that…
Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate…
The problem of classical data compression when the decoder has quantum side information at his disposal is considered. This is a quantum generalization of the classical Slepian-Wolf theorem. The optimal compression rate is found to be…
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…