Quantum information processing (QIP) studies the representation, manipulation, and transmission of information using quantum systems. By leveraging counterintuitive quantum phenomena such as superposition and entanglement, QIP enables new paradigms for computation, communication, and learning that can surpass classical limits in certain regimes. Foundational tasks in QIP include quantum data compression, quantum communication, and quantum learning and optimization, which together form the basis for scalable quantum technologies. This thesis develops new frameworks and algorithms at the intersection of quantum information theory, quantum learning, and quantum-inspired modeling. The thesis is organized into three parts. The first part studies quantum compression problems; the second addresses quantum communication; and the third develops quantum learning and optimization frameworks with applications to complex systems. In the first part, a new formulation for lossy quantum-classical source coding, termed rate-channel theory, is introduced, replacing the conventional distortion-based formulation with a posterior-channel-based framework under a block-error criterion. The framework is further generalized to incorporate quantum side information at the decoder. A connection between rate-channel theory and classical rate-distortion theory is also established, showing that optimal rate-distortion performance can be recovered under suitable conditions. These results provide a unified and flexible framework for data compression, which is essential for scalable quantum computing infrastructure, enabling efficient storage of quantum data, such as outputs from quantum sensors (e.g., MRI) and information encoded in photonic systems for satellite and optical communication. In the second part, the problem of computing functions of distributed sources over classical-quantum multiple access channels is studied. A new coding framework is developed that combines algebraic structured codes with unstructured random coding techniques, enabling efficient communication of functions without reconstructing individual sources. The resulting achievable conditions, expressed in terms of single-letter quantum information quantities, strictly enlarge the class of sources for which reliable computation is possible. These results contribute to the theoretical foundations of quantum network communication and are directly relevant to deep-space satellite-based quantum communication, distributed quantum computing, and the design of scalable quantum network infrastructures. In the final part, new approaches to quantum learning and optimization are developed. A geometry-aware quantum optimization framework is proposed based on a novel quantum information metric and an unbiased estimator constructed from single-shot measurements. This leads to an optimization method with constant sample complexity per iteration and provable exponential convergence under mild conditions, while avoiding saddle points and local minima. Such advances are particularly relevant for challenging optimization tasks in quantum sensing and quantum computational modeling of many-body systems. Building on this optimization framework, a Hamiltonian learning approach is introduced to infer interaction structures from time-resolved measurement data, with finite-sample guarantees and polynomial scaling with system size. This framework is further extended to develop a quantum-inspired generative model for gene regulatory network inference, where interactions are encoded as a parameterized Hamiltonian evolving over pseudotime. The proposed methods demonstrate strong performance on synthetic benchmarks and reveal biologically meaningful structures in real-world data, with applications to multi-omics integration, cancer genomics, and systems biology. Overall, this thesis advances the theoretical and algorithmic foundations of quantum information processing, with contributions spanning compression, communication, and learning. These developments support the design of resource-efficient and scalable quantum technologies, enabling applications in quantum sensing, quantum networks, distributed quantum computation, and the modeling of complex physical and biological systems.
Quantum information processing (QIP) studies the representation, manipulation, and transmission of information using quantum systems. By leveraging counterintuitive quantum phenomena such as superposition and entanglement, QIP enables new paradigms for computation, communication, and learning that can surpass classical limits in certain regimes. Foundational tasks in QIP include quantum data compression, quantum communication, and quantum learning and optimization, which together form the basis for scalable quantum technologies. This thesis develops new frameworks and algorithms at the intersection of quantum information theory, quantum learning, and quantum-inspired modeling. The thesis is organized into three parts. The first part studies quantum compression problems; the second addresses quantum communication; and the third develops quantum learning and optimization frameworks with applications to complex systems. In the first part, a new formulation for lossy quantum-classical source coding, termed rate-channel theory, is introduced, replacing the conventional distortion-based formulation with a posterior-channel-based framework under a block-error criterion. The framework is further generalized to incorporate quantum side information at the decoder. A connection between rate-channel theory and classical rate-distortion theory is also established, showing that optimal rate-distortion performance can be recovered under suitable conditions. These results provide a unified and flexible framework for data compression, which is essential for scalable quantum computing infrastructure, enabling efficient storage of quantum data, such as outputs from quantum sensors (e.g., MRI) and information encoded in photonic systems for satellite and optical communication. In the second part, the problem of computing functions of distributed sources over classical-quantum multiple access channels is studied. A new coding framework is developed that combines algebraic structured codes with unstructured random coding techniques, enabling efficient communication of functions without reconstructing individual sources. The resulting achievable conditions, expressed in terms of single-letter quantum information quantities, strictly enlarge the class of sources for which reliable computation is possible. These results contribute to the theoretical foundations of quantum network communication and are directly relevant to deep-space satellite-based quantum communication, distributed quantum computing, and the design of scalable quantum network infrastructures. In the final part, new approaches to quantum learning and optimization are developed. A geometry-aware quantum optimization framework is proposed based on a novel quantum information metric and an unbiased estimator constructed from single-shot measurements. This leads to an optimization method with constant sample complexity per iteration and provable exponential convergence under mild conditions, while avoiding saddle points and local minima. Such advances are particularly relevant for challenging optimization tasks in quantum sensing and quantum computational modeling of many-body systems. Building on this optimization framework, a Hamiltonian learning approach is introduced to infer interaction structures from time-resolved measurement data, with finite-sample guarantees and polynomial scaling with system size. This framework is further extended to develop a quantum-inspired generative model for gene regulatory network inference, where interactions are encoded as a parameterized Hamiltonian evolving over pseudotime. The proposed methods demonstrate strong performance on synthetic benchmarks and reveal biologically meaningful structures in real-world data, with applications to multi-omics integration, cancer genomics, and systems biology. Overall, this thesis advances the theoretical and algorithmic foundations of quantum information processing, with contributions spanning compression, communication, and learning. These developments support the design of resource-efficient and scalable quantum technologies, enabling applications in quantum sensing, quantum networks, distributed quantum computation, and the modeling of complex physical and biological systems.
Quantum communication and information technologies are poised to transform secure data transmission, distributed quantum computing, and scalable networking by leveraging fundamental principles such as superposition, entanglement, and the no-cloning theorem. This survey presents a structured overview of the quantum information processing (QIP) landscape, spanning theoretical foundations to system-level architectures. We cover quantum states, unitary evolution, gates, and channels, leading to the mathematical framework of quantum operations and the effects of decoherence. Quantum error correction (QEC) is examined through block codes and fault-tolerant operations, along with its integration with entanglement purification to address challenges of noisy intermediate-scale quantum (NISQ) devices. Physical platforms, including gate-based, continuousvariable and measurement-based models, are analyzed with an emphasis on error mitigation strategies to preserve coherence. We also discuss advancements in quantum sensing, particularly phase estimation, and evaluate communication protocols such as quantum key distribution (QKD) and teleportation in terms of fidelity, efficiency, and resilience. At the system level, components such as quantum networks, repeaters, and routers are reviewed with attention to scalability and security. Each section concludes with lessons learned, reflecting on challenges, trade-offs, and open questions. The survey culminates in outlining future directions in hybrid QEC-sensing integration, AI-enhanced error correction, and topological architectures, offering a forward-looking perspective on the co-evolution of quantum technologies. By bridging theory, protocols, physical systems, and architectures, this work charts a comprehensive roadmap toward secure, scalable, and high-fidelity quantum communication.
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make difficult problems more accessible. A demonstration of how to efficiently implement such an algorithm, avoiding interfacial bottlenecks, is provided, finding optimal protocols to establish entanglement through a lossy channel. The central software package developed addresses polynomial optimization problems. Many problems naturally involve only a polynomial objective and constraint polynomials. Such problems can automatically be cast into semidefinite programs that provide a hierarchy of outer approximations. The resulting problems are often so large and scale so unfavorably with respect to the variable number and degree involved that the boundary of the doable is reached quickly. However, technical progress both in hardware and algorithms has pushed this boundary - but software frameworks for polynomial optimization have not followed in the same manner, often now making them the bottleneck that before was the solver. The package PolynomialOptimization.jl developed during this thesis aims to fill the gap and provide a very resource-efficient intermediate layer together with a wide number of algorithms to reduce the problem size, and naturally supporting complex numbers and semidefinite constraints ubiquitous in quantum information problems. Its application on an entanglement distribution problem is demonstrated, showing that even relaxations with semidefinite matrices of three- and four-digit size can be solved conveniently. Finally, a new way to calculate interior-point barriers for the cone of sums-of-squares matrices in a nearly time-optimal way is developed, whose efficient implementation has the potential of further reducing resource consumption.
This thesis consists of two parts: quantum compression and quantum learning theory. A common theme between these problems is that we study them through the lens of information theory. \n \nWe first study the task of visible compression of an ensemble of quantum states with entanglement assistance in the one-shot setting. The protocols achieving the best compression use many more qubits of shared entanglement than the number of qubits in the states in the ensemble. Other compression protocols, with potentially higher communication cost, have entanglement cost bounded by the number of qubits in the given states. This motivates the question as to whether entanglement is truly necessary for compression, and if so, how much of it is needed. We show that an ensemble given by Jain, Radhakrishnan, and Sen (ICALP'03) cannot be compressed by more than a constant number of qubits without shared entanglement, while in the presence of shared entanglement, the communication cost of compression can be arbitrarily smaller than the entanglement cost. \n \nNext, we study the task of quantum state redistribution, the most general version of compression of quantum states. We design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined in terms of quantum max-relative entropy and quantum hypothesis testing entropy. Our result is the first to connect quantum state redistribution and Markov chains and gives an operational interpretation for a possible one-shot analogue of quantum conditional mutual information. The communication cost of our protocol is lower than all previously known ones and asymptotically achieves the well-known rate of quantum conditional mutual information. \n \nIn the last part, we focus on quantum algorithms for learning Boolean functions using quantum examples. We consider two commonly studied models of learning, namely, quantum PAC learning and quantum agnostic learning. We reproduce the optimal lower bounds by Arunachalam and de Wolf (JMLR’18) for the sample complexity of either of these models using information theory and spectral analysis. Our proofs are simpler than the previous ones and the techniques can be possibly extended to similar scenarios.
Quantum communication and information networks offer unprecedented processing efficiency and security for data transfers. Technologies like quantum key distribution (QKD), quantum repeaters, quantum memory, and quantum entanglement sources are enabling technologies that ensure secure communication. QKD methods use quantum physics concepts to establish cryptographic keys, while quantum repeaters compensate for signal loss in fiber optic cables. Quantum memory enables storage and retrieval of quantum information, while quantum entanglement generators generate entangled photon pairs. Artificial intelligence and machine learning have significantly improved the efficacy and security of quantum communication. These methods can facilitate ultra-secure, reliable, large-scale communication and even a future quantum internet by analyzing quantum protocols and mitigating noise-induced errors. QKD protocols ensure secure communication channels, while quantum repeaters establish secure long-distance communication lines by mitigating signal loss. Traditional Internet technology is susceptible to surveillance due to Shannon's information theory and mathematics. The quantum internet (QI) uses satellite-based quantum communication and quantum cryptographic protocols for physical QI. Quantum entanglement sources fortify secure communication protocols, improving resistance to attacks. Quantum information networks (QINs) enhance computing, sensing, and security capabilities over extended distances. The development of reliable, robust communication systems depends on these technologies. Quantum-secured networks enhance urban security, smart management, and infrastructure protection by providing data privacy and facilitating secure data transmission, thereby facilitating robust infrastructure and technological development.
Quantum algorithms require quantum computers performing logical operations on a sufficiently large number of entangled qubits. Unfortunately, state-of-the-art quantum computers can only operate on tens of qubits. A solution to this scalability challenge is to employ the distributed paradigm, where a network of small-scale quantum computers are used in a distributed manner. It is the aim of my work to study the fundamental limits of distributed quantum problems and to further enhance their performance by exploiting the structure inherent to these problems employing asymptotically good Algebraic codes. This thesis consists of two parts. The first part studies the task of faithfully simulating a distributed quantum measurement, wherein we provide a protocol for the three parties, Alice, Bob and {Charlie}, to simulate a repeated action of a distributed quantum measurement using a pair of non-product approximating measurements by Alice and Bob, followed by a stochastic mapping at {Charlie}. The objective of the protocol is to utilize minimum resources, in terms of classical bits needed by Alice and Bob to communicate their measurement outcomes to {Charlie}, and the common randomness shared among the three parties, while faithfully simulating independent repeated instances of the original measurement. We characterize a set of sufficient communication and common randomness rates required for asymptotic simulatability in terms of single-letter quantum information quantities. We further improve the results obtained in the above by exploiting the structure present in the Charlie's stochastic bivariate mapping using random structured POVMs based on asymptotically good algebraic codes. The algebraic structure of these codes is matched to that of the bivariate function that models the action of Charlie. This leads to the computation being performed on the fly, thus obviating the need to reconstruct individual measurement outcomes at Charlie. We provide examples to illustrate the information-theoretic gains attained by endowing POVMs with algebraic structure. As an application of the distributed measurement compression problem, we also demonstrate a multi-party purity distillation protocol. Concluding this part, we consider the lossy quantum source coding problem where the objective is to compress a given quantum source below its von Neumann entropy. Inspired by the duality connections between the rate-distortion and channel coding problems in the classical setting, we propose a new formulation for the lossy quantum source coding problem. We require that the reconstruction of the compressed quantum source fulfill a global error constraint and employ the notion of a ``posterior reference map'' to measure the reconstruction error. Using these, we characterize the asymptotic performance limit of this problem in terms of single-letter coherent information of the given posterior reference map. In the second part of this thesis, we study the advantage algebraic structured codes can provide, to the class of the classical-quantum network problems. In particular, we investigate two problems. Firstly, we consider the problem of communicating a general bivariate function of two classical sources observed at the encoders of a classical-quantum multiple access channel. We propose and analyze a coding scheme based on algebraic structured coset codes that enables the decoder to recover the desired function without recovering the sources themselves. We derive a new set of sufficient conditions that are weaker than the current known for identified examples. In addition, we analyze the performance of these algebraic codes toward studying the capacity of a special class of 3-user classical-quantum interference channel.
Quantum information theory represents a revolutionary paradigm that merges quantum mechanics with information science, fundamentally transforming our understanding of computation, communication, and information processing. This chapter provides a comprehensive examination of quantum information theory, exploring its theoretical foundations, practical applications, and transformative potential across multiple domains. We investigate the core principles including quantum bits (qubits), superposition, entanglement, and quantum interference, while analyzing their implications for quantum computing, cryptography, and communication protocols. Through systematic literature review and methodological analysis, we present current research trends, breakthrough developments, and emerging applications. The chapter addresses significant challenges including decoherence, error correction, and scalability issues that currently limit practical implementation. Our discussion encompasses quantum algorithms, quantum error correction codes, and the evolving landscape of quantum technologies. We conclude by identifying future research directions and the potential societal impact of quantum information systems, emphasizing both the unprecedented opportunities and the technical obstacles that define this rapidly advancing field.