Reconstructing quantum states from local data
We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are...
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Published in | Physical review letters Vol. 113; no. 26; p. 260501 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
United States
31.12.2014
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Abstract | We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed as the maximal entropy state. More generally, we show that if the state in question is a ground state of a local Hamiltonian with a degenerate space of locally indistinguishable ground states, then the maximal entropy state is close to the ground state projector. We also show that local reconstruction is possible for thermal states of local Hamiltonians. Finally, we discuss a procedure to certify that the reconstructed state is close to the true global state. We call the entropy of our reconstructed maximum entropy state the "reconstruction entropy," and we discuss its relation to emergent geometry in the context of holographic duality. |
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AbstractList | We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed as the maximal entropy state. More generally, we show that if the state in question is a ground state of a local Hamiltonian with a degenerate space of locally indistinguishable ground states, then the maximal entropy state is close to the ground state projector. We also show that local reconstruction is possible for thermal states of local Hamiltonians. Finally, we discuss a procedure to certify that the reconstructed state is close to the true global state. We call the entropy of our reconstructed maximum entropy state the "reconstruction entropy," and we discuss its relation to emergent geometry in the context of holographic duality. |
Author | Kim, Isaac H Swingle, Brian |
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BackLink | https://www.ncbi.nlm.nih.gov/pubmed/25615291$$D View this record in MEDLINE/PubMed |
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CitedBy_id | crossref_primary_10_1016_S0034_4877_16_30022_2 crossref_primary_10_1038_s41567_021_01232_0 crossref_primary_10_1103_PhysRevLett_122_150606 crossref_primary_10_1103_PhysRevB_93_205120 crossref_primary_10_1103_PhysRevB_93_045127 crossref_primary_10_1103_PhysRevX_8_021026 crossref_primary_10_1109_TIT_2016_2527683 crossref_primary_10_1007_JHEP06_2015_157 crossref_primary_10_1103_PhysRevD_98_046005 crossref_primary_10_1103_PhysRevX_8_031029 crossref_primary_10_1007_JHEP06_2015_067 crossref_primary_10_1088_1361_6633_ac51b5 crossref_primary_10_1088_1361_648X_abc4cf crossref_primary_10_22331_q_2019_07_08_159 crossref_primary_10_1364_OE_25_009010 crossref_primary_10_1007_JHEP11_2020_004 crossref_primary_10_22331_q_2020_09_02_315 crossref_primary_10_1016_j_optcom_2017_05_001 crossref_primary_10_1103_PhysRevB_106_104435 crossref_primary_10_22331_q_2024_04_30_1319 crossref_primary_10_1088_1402_4896_ad09a2 crossref_primary_10_1103_PhysRevResearch_3_013217 |
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