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arXiv:2206.03501 · Physical Review A

Rate reduction of blind quantum data compression with local approximations based on the unstable structure of quantum states

Kohdai Kuroiwa, Debbie Leung

Published May 26, 2023• 3 citations
arXivHTMLPDF

Abstract

In this paper we propose a protocol for a data compression task, blind quantum data compression, with finite local approximations. The rate of blind data compression is susceptible to approximations even when the approximations are diminutive. This instability originates from the sensitivity of a structure of quantum states against approximations, which makes the analysis of blind compression in the presence of approximations intractable. In this paper we construct a protocol that takes advantage of the instability to reduce the compression rate substantially. Our protocol shows a significant reduction in rate for specific examples we examine. Moreover, we apply our methods to diagonal states and propose two types of approximation methods in this special case. We perform numerical experiments and observe that one of these two approximation methods performs significantly better than the other. Thus, our analysis makes a step toward general investigation of blind quantum data compression with the allowance of approximations towards further investigation of approximation-rate trade-off of blind quantum data compression.

DOI
10.1103/physreva.107.052421

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In this paper we propose a protocol for a data compression task, blind quantum data compression, with finite local approximations. The rate of blind data compression is susceptible to approximations even when the approximations are diminutive. This instability originates from the sensitivity of a structure of quantum states against approximations, which makes the analysis of blind compression in the presence of approximations intractable. In this paper we construct a protocol that takes advantage of the instability to reduce the compression rate substantially. Our protocol shows a significant reduction in rate for specific examples we examine. Moreover, we apply our methods to diagonal states and propose two types of approximation methods in this special case. We perform numerical experiments and observe that one of these two approximation methods performs significantly better than the other. Thus, our analysis makes a step toward general investigation of blind quantum data compression with the allowance of approximations towards further investigation of approximation-rate trade-off of blind quantum data compression.
We establish exponential strong converse theorems for blind quantum data compression of finite-dimensional mixed-state sources, with and without entanglement assistance. Blind compression is a fundamental quantum information processing task in which the sender aims to transmit quantum states without direct access to the classical label. Strong converse is a notable aspect of data compression: the accuracy of the compression abruptly drops down to zero once the compression rate goes below a threshold. Strong converses for data compression have been established for pure-state sources; however, for mixed-state sources, the optimal compression rate is determined by a structural decomposition of quantum states and can change substantially under small perturbations. This sensitivity makes it difficult to quantitatively analyze the trade-off between compression rate and error. Despite recent progress, whether a strong converse holds at the optimal rate has remained unresolved in general. In this work, we resolve this question affirmatively. For unassisted compression, we show that at every rate below the optimum, the accuracy decays exponentially with the block length for general mixed-state sources without restrictions on protocols. We also prove exponential strong converse for blind compression with unlimited entanglement assistance at its optimal rate. Combining the two strong converse bounds yields exponential decay at every compression-entanglement rate pair outside the complete achievable rate region. Our proof introduces a new overlap quantity based on the structure of quantum states; this quantity connects preservation of the source information to the dimension of the transmitted system. We expect that this approach provides useful tools for converse analyses of other quantum information-processing tasks involving mixed states.
We provide a rate distortion interpretation of the problem of quantum data compression of ensembles of mixed states with commuting density operators. There are two versions of this problem. In the visible case the sequence of states is available to the encoder and in the blind or hidden case the encoder may access only a sequence of measurements. We find the exact optimal compression rates for both the visible and hidden cases. Our analysis includes the scenario in which asymptotic reconstruction is imperfect.
Designing a quantum data compression circuit with reasonable error using autoencoders can be time-consuming. Previous studies have explored qubit compression using specially designed circuits or autoencoders, with some attempts to apply it to small 16-bit black-and-white images using four qubits. However, analysis regarding the errors using general data is not discussed enough. This paper proposes a practical technique to optimize quantum compression for general data comprising hundreds of thousands of classical data points. We introduce Quantum State Error to investigate the potential for improving accuracy through qubit selection using degree reduction in quantum compression. By doing so, imperfect quantum autoencoder circuits may exhibit enhanced performance, offering improved lossy compression capabilities. Our experiments show promising results, where certain kind of circuits responds well to degree reduction by a factor of 3/4, reducing the number of faulty qubits up to 11.44%.
This paper explores a novel approach to data compression leveraging the principles of quantum entanglement. Traditional data compression methods rely on identifying and eliminating redundancy within data, often achieving limitations in compression ratios. We propose a system that utilizes entangled quantum states to represent data, achieving potentially higher compression rates and, crucially, lossless reconstruction. The core idea involves decomposing data into a set of entangled quantum subsystems. By exploiting the inherent correlations present within entangled states, we can effectively reduce redundancy without losing information. The paper details the mathematical framework underlying this approach, focusing on the key concepts of entanglement, quantum measurement, and the reconstruction process. We outline the theoretical advantages of this method compared to conventional techniques and discuss the challenges associated with its practical implementation. The primary goal is to demonstrate the potential of quantum entanglement for fundamentally transforming data compression, moving beyond the constraints of classical redundancy reduction. ---
This paper explores a novel approach to quantum data compression utilizing the principles of quantum state reordering. Traditional quantum data compression techniques often suffer from inefficiencies, primarily due to the inherent complexities of representing and manipulating quantum information. This work proposes a method that leverages quantum state reordering to achieve more effective data reduction. The core idea involves encoding quantum data into specific quantum states and subsequently applying reordering algorithms designed to exploit redundancies within the encoded states. This approach aligns with fundamental quantum information theory and provides a potentially more efficient pathway to compressing quantum data, reducing storage and transmission requirements. The theoretical framework presented outlines the key components, including state encoding, reordering algorithm design, and compression performance analysis. The ultimate goal is to demonstrate the feasibility and potential benefits of this technique for future quantum data management systems.
Quantum data compression aims to efficiently represent quantum states and information by exploiting the inherent fragility of quantum measurement processes. This paper explores a novel compression algorithm predicated on the principle of wavefunction collapse, hypothesizing that the collapse of a quantum wavefunction during compression provides a more efficient representation than traditional methods. We detail the core mechanism of this algorithm, outlining its design and the theoretical underpinning of its potential for near-lossless data compression. The paper presents a detailed explanation of the algorithm's components, including the analysis of the waveform, the collapse process, and the reconstruction process. We discuss the potential advantages and challenges associated with this approach, ultimately asserting that it represents a significant step towards a more robust and efficient data compression paradigm.