2017/07/31 by Cristina Cirstoiu, David Jennings, Cirstoiu, Cristina +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph) #cond-mat.other #hep-lat #quant-ph
paper · pdf · doi:10.48550/arxiv.1707.09826
Main Text: 13 pages, 13 figures; Supplementary Material: 32 pages; Comments welcome!
arxiv created 2018/08/28 · arxiv updated 2018/08/29
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.