What is the structure of general quantum processes on composite systems that respect a global or local symmetry principle? How does the irreversible use of quantum resources behave under such symmetry principles? Here we employ an information-theoretic framework to address these questions and show that every symmetric quantum process on a system has a highly rigid decomposition in terms of the flow of symmetry-breaking degrees of freedom between each subsystem and its environment. The decomposition has a natural causal structure that can be represented diagrammatically and makes explicit gauge degrees of freedom between subsystems. The framework also provides a novel quantum information perspective on lattice gauge theories and a method to gauge general quantum processes beyond Lagrangian formulations. This procedure admits a simple resource-theoretic interpretation, and thus offers a natural context in which features such as information flow and entanglement in gauge theories and quantum thermodynamics could be studied. The framework also provides a flexible toolkit with which to analyse the structure of general quantum processes. As an application, we make use of a `polar decomposition' for quantum processes to discuss the repeatable use of quantum resources and to provide a novel perspective in terms of the coordinates induced on the orbit of a local process under a symmetry action.
What is the structure of general quantum processes on composite systems that respect a global or local symmetry principle? How does the irreversible use of quantum resources behave under such symmetry principles? Here we employ an information-theoretic framework to address these questions and show that every symmetric quantum process on a system has a highly rigid decomposition in terms of the flow of symmetry-breaking degrees of freedom between each subsystem and its environment. The decomposition has a natural causal structure that can be represented diagrammatically and makes explicit gauge degrees of freedom between subsystems. The framework also provides a novel quantum information perspective on lattice gauge theories and a method to gauge general quantum processes beyond Lagrangian formulations. This procedure admits a simple resource-theoretic interpretation, and thus offers a natural context in which features such as information flow and entanglement in gauge theories and quantum thermodynamics could be studied. The framework also provides a flexible toolkit with which to analyse the structure of general quantum processes. As an application, we make use of a `polar decomposition' for quantum processes to discuss the repeatable use of quantum resources and to provide a novel perspective in terms of the coordinates induced on the orbit of a local process under a symmetry action.
Quantum information has become a powerful tool for probing the structure of quantum field theories, yet its application to gauge theories remains subtle. On the one hand, quantum information theory assumes subsystem locality, i.e.~the factorization of the total Hilbert space into subsystems. On the other hand, gauge constraints prevent the total Hilbert space to decompose into a spacetime-local tensor product structure. Because the Hilbert space structure of gauge theories does not accommodate the subsystem decomposition used in quantum information theory, standard information-theoretic results, such as the Local Operations and Classical Communication (LOCC) theorem, cannot be used straightforwardly in the context of gauge theories. In this work, we bridge this gap in the case of a two-dimensional lattice gauge model that captures key features of electromagnetism. In particular, we construct gauge-invariant local algebras and derive a physically meaningful decomposition of the Hilbert space, providing an operationally consistent notion of locality in the absence of a local tensor-product structure. We apply this framework to field-mediated entanglement protocols relevant to proposed tests of the quantum nature of gravity. We show that the discretized version of electromagnetism satisfies an analogue of the LOCC theorem: entanglement cannot be generated without genuine quantum field interactions, even in the absence of a spacetime-local tensor product factorization of the Hilbert space. This may point towards an operational way to define a subsystem structure for gauge theories.
Symmetry principles have played a crucial role in the development of modern physics and underpin our most fundamental theories of nature. The present thesis is concerned with the analysis of symmetries in the context of quantum information theory. Whenever a quantum mechanical system interacts with its environment it is subjected to decoherence, a process that is typically irreversible and most generally treated abstractly using the concept of quantum operations. If there is an underlying symmetry principle, additional structures emerge. The central question we address is, What are the consequences of global or local gauge symmetry on the structure of many-body quantum processes?This leads us to a diagrammatic framework of decomposing quantum operations into terms that respond to the symmetry principle in particular ways and respect the causal structures involved. We present two core applications. First, we address the interplay between irreversibility and repeatable use of coherent resources under symmetry constraints. Second, we give an information-theoretic perspective on gauging globally symmetric dynamics to a local symmetry applicable even in the presence of irreversibility and thus it goes beyond the usual Lagrangian formulation. Finally, we analyse the departure from conservation laws under symmetric dynamics subject to decoherence.
Quantum information has become a powerful tool for probing the structure of quantum field theories, yet its application to gauge theories remains subtle. On the one hand, quantum information theory assumes subsystem locality, i.e.~the factorization of the total Hilbert space into subsystems. On the other hand, gauge constraints prevent the total Hilbert space to decompose into a spacetime-local tensor product structure. Because the Hilbert space structure of gauge theories does not accommodate the subsystem decomposition used in quantum information theory, standard information-theoretic results, such as the Local Operations and Classical Communication (LOCC) theorem, cannot be used straightforwardly in the context of gauge theories. In this work, we bridge this gap in the case of a two-dimensional lattice gauge model that captures key features of electromagnetism. In particular, we construct gauge-invariant local algebras and derive a physically meaningful decomposition of the Hilbert space, providing an operationally consistent notion of locality in the absence of a local tensor-product structure. We apply this framework to field-mediated entanglement protocols relevant to proposed tests of the quantum nature of gravity. We show that the discretized version of electromagnetism satisfies an analogue of the LOCC theorem: entanglement cannot be generated without genuine quantum field interactions, even in the absence of a spacetime-local tensor product factorization of the Hilbert space. This may point towards an operational way to define a subsystem structure for gauge theories.
How far can we take the resource theoretic approach to explore physics? Resource theories like LOCC, reference frames and quantum thermodynamics have proven a powerful tool to study how agents who are subject to certain constraints can act on physical systems. This approach has advanced our understanding of fundamental physical principles, such as the second law of thermodynamics, and provided operational measures to quantify resources such as entanglement or information content. In this work, we significantly extend the approach and range of applicability of resource theories. Firstly we generalize the notion of resource theories to include any description or knowledge that agents may have of a physical state, beyond the density operator formalism. We show how to relate theories that differ in the language used to describe resources, like micro and macroscopic thermodynamics. Finally, we take a top-down approach to locality, in which a subsystem structure is derived from a global theory rather than assumed. The extended framework introduced here enables us to formalize new tasks in the language of resource theories, ranging from tomography, cryptography, thermodynamics and foundational questions, both within and beyond quantum theory.
Quantum entanglement is conventionally characterized as a structural property of tensor-product Hilbert spaces, with limited emphasis on its geometric or gauge-theoretic organization. Within standard quantum field theory on a fixed classical spacetime background, we show that entanglement can be represented as a global compatibility constraint acting on internal degrees of freedom in the gauge-bundle formulation of the Standard Model. This representation is encoded by a vacuum-level internal gauge structure Ξ(x) that is locally pure gauge, dynamically inert, and acts exclusively on internal fibers, leaving all local dynamics and the Standard Model Lagrangian unchanged. We formalize this perspective as a vacuum internal gauge structure (VIGS) and prove a corresponding structural result—the Vacuum Internal Gauge Theorem—which establishes that global compatibility relations associated with Ξ act only on internal Hilbert-space factors and preserve locality and no-signaling within the regime considered here. The framework complements standard Hilbert-space and algebraic descriptions of entanglement by making explicit how global internal correlations can be organized geometrically without invoking nonlocal dynamics. Finally, we identify an experimentally accessible operational signature, based on correlated versus independent internal-frame scrambling, that distinguishes this geometric representation within existing entanglement platforms.