{"title":"量子相干性与多体定位测量之间的权衡关系","authors":"Arti Garg, Arun Kumar Pati","doi":"arxiv-2409.10449","DOIUrl":null,"url":null,"abstract":"Quantum coherence, a fundamental resource in quantum computing and quantum\ninformation, often competes with localization effects that affects quantum\nstates in disordered systems. In this work, we prove exact trade-off relations\nbetween quantum coherence and a measure of localization and many-body\nlocalization, namely, the inverse participation ratio (IPR). We prove that the\nl1-norm of quantum coherence and the relative entropy of coherence for a pure\nquantum state satisfy complementarity relations with IPR. For a mixed state,\nIPR and the l2-norm of quantum coherence as well as relative entropy of\ncoherence satisfy trade-off inequalities. These relations suggest that quantum\ncoherence, in disordered quantum systems is also an ideal characterization of\nthe delocalisation to many-body localisation transition, much like IPR, which\nis a well-known diagnostic of MBL. These relations also provide insight into\nthe unusual properties of bipartite entanglement entropy across the MBL\ntransition. We believe that these trade-off relations can help in better\nunderstanding of how coherence can be preserved or lost in realistic many-body\nquantum systems, which is vital for developing robust quantum technologies and\nuncovering new phases of quantum matter.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"201 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Trade-off relations between quantum coherence and measure of many-body localization\",\"authors\":\"Arti Garg, Arun Kumar Pati\",\"doi\":\"arxiv-2409.10449\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Quantum coherence, a fundamental resource in quantum computing and quantum\\ninformation, often competes with localization effects that affects quantum\\nstates in disordered systems. In this work, we prove exact trade-off relations\\nbetween quantum coherence and a measure of localization and many-body\\nlocalization, namely, the inverse participation ratio (IPR). We prove that the\\nl1-norm of quantum coherence and the relative entropy of coherence for a pure\\nquantum state satisfy complementarity relations with IPR. For a mixed state,\\nIPR and the l2-norm of quantum coherence as well as relative entropy of\\ncoherence satisfy trade-off inequalities. These relations suggest that quantum\\ncoherence, in disordered quantum systems is also an ideal characterization of\\nthe delocalisation to many-body localisation transition, much like IPR, which\\nis a well-known diagnostic of MBL. These relations also provide insight into\\nthe unusual properties of bipartite entanglement entropy across the MBL\\ntransition. We believe that these trade-off relations can help in better\\nunderstanding of how coherence can be preserved or lost in realistic many-body\\nquantum systems, which is vital for developing robust quantum technologies and\\nuncovering new phases of quantum matter.\",\"PeriodicalId\":501066,\"journal\":{\"name\":\"arXiv - PHYS - Disordered Systems and Neural Networks\",\"volume\":\"201 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Disordered Systems and Neural Networks\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10449\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Disordered Systems and Neural Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10449","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Trade-off relations between quantum coherence and measure of many-body localization
Quantum coherence, a fundamental resource in quantum computing and quantum
information, often competes with localization effects that affects quantum
states in disordered systems. In this work, we prove exact trade-off relations
between quantum coherence and a measure of localization and many-body
localization, namely, the inverse participation ratio (IPR). We prove that the
l1-norm of quantum coherence and the relative entropy of coherence for a pure
quantum state satisfy complementarity relations with IPR. For a mixed state,
IPR and the l2-norm of quantum coherence as well as relative entropy of
coherence satisfy trade-off inequalities. These relations suggest that quantum
coherence, in disordered quantum systems is also an ideal characterization of
the delocalisation to many-body localisation transition, much like IPR, which
is a well-known diagnostic of MBL. These relations also provide insight into
the unusual properties of bipartite entanglement entropy across the MBL
transition. We believe that these trade-off relations can help in better
understanding of how coherence can be preserved or lost in realistic many-body
quantum systems, which is vital for developing robust quantum technologies and
uncovering new phases of quantum matter.