Quantum phenomena such as superposition and entanglement imbue quantum systems with information processing power in excess of their classical counterparts. These properties of quantum states are, however, highly fragile. As we enter the era of noisy intermediate-scale quantum (NISQ) devices, this vulnerability to noise is a major hurdle to the experimental realisation of quantum technologies. In this thesis we explore the role of noise in quantum information processing from two different perspectives. In Part I we consider noise from the perspective of quantum error correcting codes. Error correcting codes are often analysed with respect to simplified toy models of noise, such as iid depolarising noise. We consider generalising these techniques for analysing codes under more realistic noise models, including features such as biased or correlated errors. We also consider designing customised codes which not only take into account and exploit features of the underlying physical noise. Considering such tailored codes will be of particular importance for NISQ applications in which finite-size effects can be significant. In Part II we apply tools from information theory to study the finite-resource effects which arise in the trade-offs between resource costs and error rates for certain quantum information processing tasks. We start by considering classical communication over quantum channels, providing a refined analysis of the trade-off between communication rate and error in the regime of a finite number of channel uses. We then extend these techniques to the problem of resource interconversion in theories such as quantum entanglement and quantum thermodynamics, studying finite-size effects which arise in resource-error trade-offs. By studying this effect in detail, we also show how detrimental finite-size effects in devices such as thermal engines may be greatly suppressed by carefully engineering the underlying resource interconversion processes.
Quantum phenomena such as superposition and entanglement imbue quantum systems with information processing power in excess of their classical counterparts. These properties of quantum states are, however, highly fragile. As we enter the era of noisy intermediate-scale quantum (NISQ) devices, this vulnerability to noise is a major hurdle to the experimental realisation of quantum technologies. In this thesis we explore the role of noise in quantum information processing from two different perspectives. In Part I we consider noise from the perspective of quantum error correcting codes. Error correcting codes are often analysed with respect to simplified toy models of noise, such as iid depolarising noise. We consider generalising these techniques for analysing codes under more realistic noise models, including features such as biased or correlated errors. We also consider designing customised codes which not only take into account and exploit features of the underlying physical noise. Considering such tailored codes will be of particular importance for NISQ applications in which finite-size effects can be significant. In Part II we apply tools from information theory to study the finite-resource effects which arise in the trade-offs between resource costs and error rates for certain quantum information processing tasks. We start by considering classical communication over quantum channels, providing a refined analysis of the trade-off between communication rate and error in the regime of a finite number of channel uses. We then extend these techniques to the problem of resource interconversion in theories such as quantum entanglement and quantum thermodynamics, studying finite-size effects which arise in resource-error trade-offs. By studying this effect in detail, we also show how detrimental finite-size effects in devices such as thermal engines may be greatly suppressed by carefully engineering the underlying resource interconversion processes.
Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.
Distributed quantum information processing is a promising platform for scaling up quantum information processing, where small- and intermediate-scale quantum devices are connected by a network of quantum channels for communicating quantum information, so as to cooperate in achieving larger-scale information processing. In such distributed settings, entangled states shared among the multiple devices serve as a resource for achieving nonlocal information processing tasks by local operations and classical communication (LOCC), where transformations of multipartite entangled states play central roles. This thesis analyzes properties of quantum entanglement in these small- and intermediate-scale settings and multipartite settings. The first part of this thesis investigates a communication task, quantum state merging, on the small and intermediate scales. The second part of this thesis analyzes multipartite entanglement in distributed quantum information processing. These analyses clarify fundamental limitations and potential applications of distributed quantum information processing to characterize properties of quantum entanglement in the small- and intermediate-scale settings and multipartite settings, providing a paradigm for investigating multipartite entanglement in distributed quantum information processing over networks beyond the state convertibility under LOCC.
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 computers are highly sensitive to noise due to interactions with the environment, which severely limits the utility of near-term devices. Quantum error correction addresses this challenge by encoding logical information over multiple qubits in order to preserve information in the presence of noise. This facilitates the realization of the theoretical advantages of quantum computing such as exponential speed-up compared to classical computers for certain algorithms. Physical realizations of qubits may have different noise profiles, including biased noise, where phase-flip errors may be more likely than bit-flip errors. We propose a quantum error-correcting code, the XYZ² code, which is tailored to biased noise. The code has high error thresholds against biased noise, below which logical errors are exponentially suppressed with the linear dimension of the code. The important classical task of deriving corrections given partial information about errors is called decoding. We investigate several decoding strategies tailored to specific challenges, ranging from a novel maximum-likelihood sampling decoder, to a model-free, data-driven, neural-network-based decoder, to an efficient multi-step decoder for concatenated codes. We also study the link between quantum error-correcting codes and their statistical-mechanical counterparts by mapping to generalized random-bond Ising models and subsequently deriving the exact results for finite-size corrections under biased noise for moderate code sizes. Quantum error correction is still in its developing stages, and this work provides a useful contribution to the field by bridging a gap between theory and practice. By adapting well-studied topological codes to error models that are closer to reality, this work paves the way for the realization of a fault-tolerant quantum architecture.
Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects.
Abstract Quantum decoherence due to imperfect manipulation of quantum devices is a key issue in the noisy intermediate-scale quantum (NISQ) era. Standard analyses in quantum information and quantum computation use error rates to parameterize quantum noise channels. However, there is no explicit relation between the decoherence effect induced by a noise channel and its error rate. In this work, we propose to characterize the decoherence effect of a noise channel by the physical implementability of its inverse, which is a universal parameter quantifying the difficulty to simulate the noise inverse with accessible quantum channels. We establish two concise inequalities connecting the decrease of the state purity and logarithmic negativity after a noise channel to the physical implementability of the noise inverse, which is required to be decomposed as mutually orthogonal unitaries or product channels respectively. Our results are numerically demonstrated on several commonly adopted two-qubit noise models. We believe that these relations contribute to the theoretical research on the entanglement properties of noise channels and provide guiding principles for quantum circuit design.