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Europhysics Letters (EPL)

Quantum data compression under localized features

Qi Han, Lijie Gou, Shuai Wang, Rong Zhang

Published Oct 1, 2024• 2 citations
Publisher

Abstract

Abstract In this paper, we first introduce the local quantum information processing task by compressing the density operator based on local quantum Bernoulli noises. Then, the local quantum compression theorem is given, that is, the local quantum entropy is the minimum achievable rate of local compression. Finally, we prove the theorem with the proof of the direct coding theorem and the inverse theorem. The direct coding theorem shows that a scheme with such a local compression rate exists, and that this local compression rate converges to the local quantum entropy. The inverse theorem shows that the compression scheme with the rate below the local entropy is unachievable. With the continuous development of quantum technology, local quantum data compression technology will have broad application prospects and development space.

DOI
10.1209/0295-5075/ad8514

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Abstract In this paper, we first introduce the local quantum information processing task by compressing the density operator based on local quantum Bernoulli noises. Then, the local quantum compression theorem is given, that is, the local quantum entropy is the minimum achievable rate of local compression. Finally, we prove the theorem with the proof of the direct coding theorem and the inverse theorem. The direct coding theorem shows that a scheme with such a local compression rate exists, and that this local compression rate converges to the local quantum entropy. The inverse theorem shows that the compression scheme with the rate below the local entropy is unachievable. With the continuous development of quantum technology, local quantum data compression technology will have broad application prospects and development space.
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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 perform classical data compression before performing the quantum data compression for individual subspaces. For minimizing the resource in quantum coding, a general parameterization of the dimensions in the Jozsa-Schumacher quantum data compression scheme is presented.
Abstract In the era of rapid development of quantum mechanics, some issues in the field of quantum information have become increasingly important. Local quantum Bernoulli noises (LQBNs) is a localized Bernoulli functional, and it is the localization of quantum Bernoulli noises (QBNs). The distinctive feature of LQBNs lies in its localization properties, which make it highly valuable in the field of quantum information. In this paper, we study three new types of quantum conditional entropy with localization characteristics from three dimensions: local quantum conditional entropy, local quantum conditional entropy at the same position, and classical-quantum conditional entropy. Based on the locality of LQBNs, we prove that the local quantum conditional entropy is concave and unitary invariant. Surprisingly, we find that the local quantum mutual information (entropy) corresponding to the same position is 0. The local quantum conditional entropy defined based on the local quantum state at a specific position, proposed in this paper, provides new insights into understanding the impact of local quantum noise on the information transmission in quantum channels. This discovery not only deepens our understanding of the internal structure of local quantum entropy, but also reveals its influence on the performance of quantum communication.
We provide a framework for one-shot quantum rate distortion coding, in which the goal is to determine the minimum number of qubits required to compress quantum information as a function of the probability that the distortion incurred upon decompression exceeds some specified level. We obtain a one-shot characterization of the minimum qubit compression size for an entanglement-assisted quantum rate-distortion code in terms of the smooth max-information, a quantity previously employed in the one-shot quantum reverse Shannon theorem. Next, we show how this characterization converges to the known expression for the entanglement-assisted quantum rate distortion function for asymptotically many copies of a memoryless quantum information source. Finally, we give a tight, finite blocklength characterization for the entanglement-assisted minimum qubit compression size of a memoryless isotropic qubit source subject to an average symbolwise distortion constraint.
Local Quantum Bernoulli Noises (LQBNs) is the localization of Quantum Bernoulli Noises (QBNs), which has high research value in the field of quantum information and has received widespread attention in recent years. In this paper, a new entropy exchange and coherent information with localization characteristics are studied. According to the quantum channel constructed by LQBNs, the relationship between coherent information and coherent mutual entropy with localization characteristics is proved. Finally, we also prove that the coherent information based on LQBNs may disappear.