Trade-off relations between quantum coherence and measure of many-body localization
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929662701076480 |
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| author | Garg, Arti Pati, Arun Kumar |
| author_facet | Garg, Arti Pati, Arun Kumar |
| contents | 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 for a pure quantum state, $l_1$-norm of quantum coherence and the relative entropy of coherence satisfy complementarity relations with IPR. For a mixed state, IPR and the $l_2$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Trade-off relations between quantum coherence and measure of many-body localization Garg, Arti Pati, Arun Kumar Disordered Systems and Neural Networks 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 for a pure quantum state, $l_1$-norm of quantum coherence and the relative entropy of coherence satisfy complementarity relations with IPR. For a mixed state, IPR and the $l_2$-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. |
| title | Trade-off relations between quantum coherence and measure of many-body localization |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2409.10449 |