Related papers: The Data Compression Theorem for Ergodic Quantum I…
This work introduces the Schmidt quantum compressor, an innovative approach to quantum data compression that leverages the principles of Schmidt decomposition to encode quantum information efficiently. In contrast to traditional variational…
In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the…
We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of…
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion…
We introduce a protocol called ENCORE which simultaneously compresses and encrypts data in a one-pass process that can be implemented efficiently and possesses a number of desirable features as a streaming encoder/decoder. Motivated by the…
The data processing inequality (DPI) is a fundamental feature of information theory. Informally it states that you cannot increase the information content of a quantum system by acting on it with a local physical operation. When the smooth…
Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: $(i)$ Estimate latent variables…
We propose a series of quantum algorithms for computing a wide range of quantum entropies and distances, including the von Neumann entropy, quantum R\'{e}nyi entropy, trace distance, and fidelity. The proposed algorithms significantly…
Practical quantum key distribution (QKD) protocols require a finite-size security proof. The phase error correction (PEC) approach is one of the general strategies for security analyses that has successfully proved finite-size security for…
In this paper we discuss a novel data compression technique for binary symmetric sources based on the cavity method over a Galois Field of order q (GF(q)). We present a scheme of low complexity and near optimal empirical performance. The…
We consider the computational aspects of lossy data compression problem, where the compression error is determined by a cover of the data space. We propose an algorithm which reduces the number of partitions needed to find the entropy with…
We perform a quantum information analysis for multi-mode Gaussian approximate position measurements, underlying noisy homodyning in quantum optics. The "Gaussian maximizer" property is established for the entropy reduction of these…
The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on…
Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic…
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We begin by establishing…
A key tenet of the Transactional Interpretation of Quantum Mechanics is the idea that photon absorption localizes the absorbing material system. In doing so, it measures the location of the absorber and hence reduces information entropy,…
Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally suitable, possibilities. Following Jaynes'…
We present herein a scheme by which to accurately evaluate the error exponents of a lossy data compression problem, which characterize average probabilities over a code ensemble of compression failure and success above or below a critical…
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of…