{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/108418"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/108418","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the nature and decay of quantum relative entropy","abstract":"Historically at the core of thermodynamics and information theory, entropy's use in quantum information extends to diverse topics including high-energy physics and operator algebras. Entropy can gauge the extent to which a quantum system departs from classicality, including by measuring entanglement and coherence, and in the form of entropic uncertainty relations between incompatible measurements. The theme of this dissertation is the quantum nature of entropy, and how exposure to a noisy environment limits and degrades non-classical features. An especially useful and general form of entropy is the quantum relative entropy, of which special cases include the von Neumann and Shannon entropies, coherent and mutual information, and a broad range of resource-theoretic measures. We use mathematical results on relative entropy to connect and unify features that distinguish quantum from classical information. We present generalizations of the strong subadditivity inequality and uncertainty-like entropy inequalities to subalgebras of operators on quantum systems for which usual independence assumptions fail. We construct new measures of non-classicality that simultaneously quantify entanglement and uncertainty, leading to a new resource theory of operations under which these forms of non-classicalty become interchangeable. Physically, our results deepen our understanding of how quantum entanglement relates to quantum uncertainty. We show how properties of entanglement limit the advantages of quantum superadditivity for information transmission through channels with high but detectable loss. Our method, based on the monogamy and faithfulness of the squashed entanglement, suggests a broader paradigm for bounding non-classical effects in lossy processes. We also propose an experiment to demonstrate superadditivity. Finally, we estimate decay rates in the form of modified logarithmic Sobolev inequalities for a variety of quantum channels, and in many cases we obtain the stronger, tensor-stable form known as a complete logarithmic Sobolev inequality. We compare these with our earlier results that bound relative entropy of the outputs of a particular class of quantum channels.","abstract_html":"Historically at the core of thermodynamics and information theory, entropy's use in quantum information extends to diverse topics including high-energy physics and operator algebras. Entropy can gauge the extent to which a quantum system departs from classicality, including by measuring entanglement and coherence, and in the form of entropic uncertainty relations between incompatible measurements. The theme of this dissertation is the quantum nature of entropy, and how exposure to a noisy environment limits and degrades non-classical features. An especially useful and general form of entropy is the quantum relative entropy, of which special cases include the von Neumann and Shannon entropies, coherent and mutual information, and a broad range of resource-theoretic measures. We use mathematical results on relative entropy to connect and unify features that distinguish quantum from classical information. We present generalizations of the strong subadditivity inequality and uncertainty-like entropy inequalities to subalgebras of operators on quantum systems for which usual independence assumptions fail. We construct new measures of non-classicality that simultaneously quantify entanglement and uncertainty, leading to a new resource theory of operations under which these forms of non-classicalty become interchangeable. Physically, our results deepen our understanding of how quantum entanglement relates to quantum uncertainty. We show how properties of entanglement limit the advantages of quantum superadditivity for information transmission through channels with high but detectable loss. Our method, based on the monogamy and faithfulness of the squashed entanglement, suggests a broader paradigm for bounding non-classical effects in lossy processes. We also propose an experiment to demonstrate superadditivity. Finally, we estimate decay rates in the form of modified logarithmic Sobolev inequalities for a variety of quantum channels, and in many cases we obtain the stronger, tensor-stable form known as a complete logarithmic Sobolev inequality. We compare these with our earlier results that bound relative entropy of the outputs of a particular class of quantum channels.","abstract_has_math":false,"creators":["Laracuente, Nicholas"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Junge, Marius","Kwiat, Paul G","Chitambar, Eric","Leggett, Anthony J"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-10-07T20:59:20Z","date_published":"2020-10-07T20:59:20Z","updated_at":"2026-07-22T22:24:48Z","subjects":["quantum information","operator algebras","mathematical physics","quantum entanglement","uncertainty relations","entropy"],"languages":["en"],"rights":["Copyright 2020 Nicholas LaRacuente"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/108418","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Junge, Marius","Kwiat, Paul G","Chitambar, Eric","Leggett, Anthony J"]},{"key":"dc:creator","label":"Author","values":["Laracuente, Nicholas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-10-07T20:59:20Z","2020-06-02","2020-08"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["quantum information","operator algebras","mathematical physics","quantum entanglement","uncertainty relations","entropy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Nicholas LaRacuente"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/108418"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Historically at the core of thermodynamics and information theory, entropy's use in quantum information extends to diverse topics including high-energy physics and operator algebras. Entropy can gauge the extent to which a quantum system departs from classicality, including by measuring entanglement and coherence, and in the form of entropic uncertainty relations between incompatible measurements. The theme of this dissertation is the quantum nature of entropy, and how exposure to a noisy environment limits and degrades non-classical features. An especially useful and general form of entropy is the quantum relative entropy, of which special cases include the von Neumann and Shannon entropies, coherent and mutual information, and a broad range of resource-theoretic measures. We use mathematical results on relative entropy to connect and unify features that distinguish quantum from classical information. We present generalizations of the strong subadditivity inequality and uncertainty-like entropy inequalities to subalgebras of operators on quantum systems for which usual independence assumptions fail. We construct new measures of non-classicality that simultaneously quantify entanglement and uncertainty, leading to a new resource theory of operations under which these forms of non-classicalty become interchangeable. Physically, our results deepen our understanding of how quantum entanglement relates to quantum uncertainty. We show how properties of entanglement limit the advantages of quantum superadditivity for information transmission through channels with high but detectable loss. Our method, based on the monogamy and faithfulness of the squashed entanglement, suggests a broader paradigm for bounding non-classical effects in lossy processes. We also propose an experiment to demonstrate superadditivity. Finally, we estimate decay rates in the form of modified logarithmic Sobolev inequalities for a variety of quantum channels, and in many cases we obtain the stronger, tensor-stable form known as a complete logarithmic Sobolev inequality. We compare these with our earlier results that bound relative entropy of the outputs of a particular class of quantum channels.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms","The student, Nicholas Laracuente, accepted the attached license on 2020-05-26 at 23:44.","The student, Nicholas Laracuente, submitted this Dissertation for approval on 2020-05-27 at 10:29.","This Dissertation was approved for publication on 2020-06-02 at 15:24.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15420 on 2020-10-02 at 15:09:58","Made available in DSpace on 2020-10-07T20:59:20Z (GMT). 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Entropy can gauge the extent to which a quantum system departs from classicality, including by measuring entanglement and coherence, and in the form of entropic uncertainty relations between incompatible measurements. The theme of this dissertation is the quantum nature of entropy, and how exposure to a noisy environment limits and degrades non-classical features. An especially useful and general form of entropy is the quantum relative entropy, of which special cases include the von Neumann and Shannon entropies, coherent and mutual information, and a broad range of resource-theoretic measures. We use mathematical results on relative entropy to connect and unify features that distinguish quantum from classical information. We present generalizations of the strong subadditivity inequality and uncertainty-like entropy inequalities to subalgebras of operators on quantum systems for which usual independence assumptions fail. We construct new measures of non-classicality that simultaneously quantify entanglement and uncertainty, leading to a new resource theory of operations under which these forms of non-classicalty become interchangeable. Physically, our results deepen our understanding of how quantum entanglement relates to quantum uncertainty. We show how properties of entanglement limit the advantages of quantum superadditivity for information transmission through channels with high but detectable loss. Our method, based on the monogamy and faithfulness of the squashed entanglement, suggests a broader paradigm for bounding non-classical effects in lossy processes. We also propose an experiment to demonstrate superadditivity. Finally, we estimate decay rates in the form of modified logarithmic Sobolev inequalities for a variety of quantum channels, and in many cases we obtain the stronger, tensor-stable form known as a complete logarithmic Sobolev inequality. We compare these with our earlier results that bound relative entropy of the outputs of a particular class of quantum channels.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms","The student, Nicholas Laracuente, accepted the attached license on 2020-05-26 at 23:44.","The student, Nicholas Laracuente, submitted this Dissertation for approval on 2020-05-27 at 10:29.","This Dissertation was approved for publication on 2020-06-02 at 15:24.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15420 on 2020-10-02 at 15:09:58","Made available in DSpace on 2020-10-07T20:59:20Z (GMT). No. of bitstreams: 2 LARACUENTE-DISSERTATION-2020.pdf: 1890347 bytes, checksum: 8b0ad95755fafee63263a73fb9058c2c (MD5) LICENSE.txt: 4216 bytes, checksum: c54c0f396b69f237a12357026ea630ce (MD5) Previous issue date: 2020-06-02"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/108418"],"dc:language":["en"],"dc:rights":["Copyright 2020 Nicholas LaRacuente"],"dc:subject":["quantum information","operator algebras","mathematical physics","quantum entanglement","uncertainty relations","entropy"],"dc:title":["On the nature and decay of quantum relative entropy"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:48Z"}