{"payload":{"feedbackUrl":"https://github.com/orgs/community/discussions/53140","repo":{"id":447186617,"defaultBranch":"master","name":"MIproject","ownerLogin":"beddalumia","currentUserCanPush":false,"isFork":false,"isEmpty":false,"createdAt":"2022-01-12T11:12:34.000Z","ownerAvatar":"https://avatars.githubusercontent.com/u/56808633?v=4","public":true,"private":false,"isOrgOwned":false},"refInfo":{"name":"","listCacheKey":"v0:1684495715.82921","currentOid":""},"activityList":{"items":[{"before":"db08434c0f139193b6cee05cbcb354f05c3ec7d1","after":"b355094cc848c4a576b46ebdeb05e87b37e37487","ref":"refs/heads/master","pushedAt":"2024-03-10T01:00:59.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Add figure for entanglement as a function of doping","shortMessageHtmlLink":"Add figure for entanglement as a function of doping"}},{"before":"2f9ed1cf01862e6017eef84b5fb5da95001b7a94","after":"db08434c0f139193b6cee05cbcb354f05c3ec7d1","ref":"refs/heads/master","pushedAt":"2024-03-09T17:13:31.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Generalized SSR formulae for the 2-orbital entanglement","shortMessageHtmlLink":"Generalized SSR formulae for the 2-orbital entanglement"}},{"before":"de458856df08828e02374e422407cb1434daf459","after":"2f9ed1cf01862e6017eef84b5fb5da95001b7a94","ref":"refs/heads/master","pushedAt":"2024-03-09T13:54:34.000Z","pushType":"force_push","commitsCount":0,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Many updates related to the thesis","shortMessageHtmlLink":"Many updates related to the thesis"}},{"before":"0375842dc65edaeba21097bd98ef9ca766088cda","after":"de458856df08828e02374e422407cb1434daf459","ref":"refs/heads/master","pushedAt":"2024-03-09T13:50:36.000Z","pushType":"push","commitsCount":2,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Many updates related to the thesis","shortMessageHtmlLink":"Many updates related to the thesis"}},{"before":"1bad01c07c157fb20094746655b684942f341841","after":"0375842dc65edaeba21097bd98ef9ca766088cda","ref":"refs/heads/master","pushedAt":"2024-03-04T10:44:59.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Temporary and dirty implementation of negativity for ASCI data","shortMessageHtmlLink":"Temporary and dirty implementation of negativity for ASCI data"}},{"before":"82e1bc489b5f25f8b814c1375df5e5d03dc2729f","after":"1bad01c07c157fb20094746655b684942f341841","ref":"refs/heads/master","pushedAt":"2024-02-07T06:28:32.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Update CDMFT/ED driver\n\nTo conform with the latest library API.","shortMessageHtmlLink":"Update CDMFT/ED driver"}},{"before":"2afe84efd160a0e8b002f11a1e4816c5f25fc472","after":"82e1bc489b5f25f8b814c1375df5e5d03dc2729f","ref":"refs/heads/master","pushedAt":"2024-02-07T03:50:59.000Z","pushType":"push","commitsCount":2,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Update CDMFT/ED submodule","shortMessageHtmlLink":"Update CDMFT/ED submodule"}},{"before":"8f3e17b00d0437d1b5e9df0d0bb5074cf15c47af","after":"2afe84efd160a0e8b002f11a1e4816c5f25fc472","ref":"refs/heads/master","pushedAt":"2023-12-16T15:34:56.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Log/Log inset for `bond_entanglement` figure","shortMessageHtmlLink":"Log/Log inset for <code>bond_entanglement</code> figure"}},{"before":"14753652dc4ef3d34b7742a875dd369ff6463e4d","after":"8f3e17b00d0437d1b5e9df0d0bb5074cf15c47af","ref":"refs/heads/master","pushedAt":"2023-12-14T01:40:54.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Massive update of `fig/` files\n\n> .m files have been checked to comply with the new API of QcmP-lab\n\n> .tex files have been made again pure tikz scripts (easier updates via\n  matlab2tikz and better usability within the thesis)\n\nTODO: I should converge better the U=0 Data and re-plot everything.","shortMessageHtmlLink":"Massive update of <code>fig/</code> files"}},{"before":"745c983a457049e577454291d498d307c8bf8710","after":"14753652dc4ef3d34b7742a875dd369ff6463e4d","ref":"refs/heads/master","pushedAt":"2023-12-14T00:57:02.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Custom name for the new submodule: `matlab2tikz` ---> `m2tex`\n\nFor a clearer meaning with respect to our files in fig/ directory.","shortMessageHtmlLink":"Custom name for the new submodule: <code>matlab2tikz</code> ---&gt; <code>m2tex</code>"}},{"before":"b0c179e6e2fb11bae1f49ee49304e13a3ff3c13b","after":"745c983a457049e577454291d498d307c8bf8710","ref":"refs/heads/master","pushedAt":"2023-12-14T00:53:25.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Add `matlab2tikz` as a git submodule\n\nTired to manage it independently.","shortMessageHtmlLink":"Add <code>matlab2tikz</code> as a git submodule"}},{"before":"d1e61e6e03f83718694f0f27f0dd9ebdda14d0b7","after":"b0c179e6e2fb11bae1f49ee49304e13a3ff3c13b","ref":"refs/heads/master","pushedAt":"2023-12-01T14:02:46.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Add negativity to the `bond_entanglement` figure\n\nTo compare it with the mutual information, essentially, since they are\ntwo competing upper bounds to the entanglement (modulo details to be\nunderstood regarding the relationship between the REE entanglement and\nthe distillable entanglement).","shortMessageHtmlLink":"Add negativity to the <code>bond_entanglement</code> figure"}},{"before":"f0430bc93ff09e4f48ccff8d810a0ff45a3662d9","after":"d1e61e6e03f83718694f0f27f0dd9ebdda14d0b7","ref":"refs/heads/master","pushedAt":"2023-12-01T11:24:59.000Z","pushType":"push","commitsCount":2,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Update `dmft-lab` submodule to new name `qcmp-lab`","shortMessageHtmlLink":"Update <code>dmft-lab</code> submodule to new name <code>qcmp-lab</code>"}},{"before":"b698e439da4d25cb1ceee48076b8a25edd42853d","after":"f0430bc93ff09e4f48ccff8d810a0ff45a3662d9","ref":"refs/heads/master","pushedAt":"2023-12-01T11:00:22.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"First try at computing entanglement negativity\n\nLooks good!","shortMessageHtmlLink":"First try at computing entanglement negativity"}},{"before":"1b8337de897f303ad139eacb9d1d0ef83044a47c","after":"b698e439da4d25cb1ceee48076b8a25edd42853d","ref":"refs/heads/master","pushedAt":"2023-11-29T16:23:59.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Fix pair-hopping rotation in P-SSR formula\n\nOnce again, a typo.","shortMessageHtmlLink":"Fix pair-hopping rotation in P-SSR formula"}},{"before":"ebf36a1263454d8481507d84acbee98ad049c032","after":"1b8337de897f303ad139eacb9d1d0ef83044a47c","ref":"refs/heads/master","pushedAt":"2023-10-22T00:50:43.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Revert \"Update BOND_ENTANGLEMENT figure\"\n\nThis reverts commit ebf36a1263454d8481507d84acbee98ad049c032.\n\nWe finally understood that no, the upper bound cannot be halved. In the\nlimit in which the composed system AB is pure, indeed we have\n\nI(A:B) = 2*E(A:B) = 2S(A) = 2S(B)\n\nAnd the factor of two is NOT a matter of convention / unit of measure.\n\nIn fact, it can be proven that for a pure AB system the so-called\n/quantum discord/ is exactly equal to the entanglement, so that\n\nI(A:B) = E(A:B) + D(A:B), where D is the discord.\n\nBut in the general case one still has\n\nI(A:B) ≥ E(A:B) + D(A:B) + C(A:B) (where C is the classical correlation)\n\nand there is no theorem regarding how E and D are related. So that the\nequality condition is not found in the trivial case in which C = 0 and\none has I = 2E = E + D, but in some nontrivial case in which C = D = 0.\nWe cannot assume D = E, outside the pure AB case, neither we can assume\nthat D = 0 for our system, so we are stuck with I(A:B) ≥ E(A:B).","shortMessageHtmlLink":"Revert \"Update BOND_ENTANGLEMENT figure\""}},{"before":"cd6ccaa7b75177d42a8b318ac7d1902ae8449ad5","after":"ebf36a1263454d8481507d84acbee98ad049c032","ref":"refs/heads/master","pushedAt":"2023-09-19T00:48:50.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Update BOND_ENTANGLEMENT figure\n\nI_ij --> I_ij / 2","shortMessageHtmlLink":"Update BOND_ENTANGLEMENT figure"}},{"before":"96b5b22ada21853d3940dd3bf30be40fe539a388","after":"cd6ccaa7b75177d42a8b318ac7d1902ae8449ad5","ref":"refs/heads/master","pushedAt":"2023-08-13T17:47:15.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"New color for 1x2 ED data + backport of all TikZ figures","shortMessageHtmlLink":"New color for 1x2 ED data + backport of all TikZ figures"}},{"before":"2a73b72fbbf129370560368fd96509722c214505","after":"96b5b22ada21853d3940dd3bf30be40fe539a388","ref":"refs/heads/master","pushedAt":"2023-08-13T17:34:12.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Slight update to some figs [intermediate]","shortMessageHtmlLink":"Slight update to some figs [intermediate]"}},{"before":"6168f1790de3f75ba2c266f34f116196b07d9c9d","after":"2a73b72fbbf129370560368fd96509722c214505","ref":"refs/heads/master","pushedAt":"2023-07-09T04:17:19.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Update .gitattributes\n\nAvoid lengthy TikZ scripts produced by mat2tikz to perturbe github linguist statistics.","shortMessageHtmlLink":"Update .gitattributes"}},{"before":"66f9f757c5d85e74876b0b812672acb9e3e01245","after":"6168f1790de3f75ba2c266f34f116196b07d9c9d","ref":"refs/heads/master","pushedAt":"2023-07-09T04:11:32.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Backport \"standalone update\" to TikZ figures\n\nRefer to https://github.com/bellomia/entanglement_mit_paper/commit/75e8c749134be87fa03e44e56912369db5334a4e","shortMessageHtmlLink":"Backport \"standalone update\" to TikZ figures"}},{"before":"96dd553904dabdff07649d43e090d56d2bec0594","after":"66f9f757c5d85e74876b0b812672acb9e3e01245","ref":"refs/heads/master","pushedAt":"2023-06-26T01:22:17.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Final polish to `bond_entanglement` script","shortMessageHtmlLink":"Final polish to <code>bond_entanglement</code> script"}},{"before":"c211f233ec593f1b5a53c178375d085b423fc8da","after":"96dd553904dabdff07649d43e090d56d2bec0594","ref":"refs/heads/master","pushedAt":"2023-06-25T22:35:19.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Improve layer management for `ssr_spy` figure","shortMessageHtmlLink":"Improve layer management for <code>ssr_spy</code> figure"}},{"before":"15deb9c55e136d25694651a3bc3dbe45d4552969","after":"c211f233ec593f1b5a53c178375d085b423fc8da","ref":"refs/heads/master","pushedAt":"2023-06-23T06:13:34.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Two new figure scripts","shortMessageHtmlLink":"Two new figure scripts"}},{"before":"cf052816a8809960821180d2119bdf6441536969","after":"15deb9c55e136d25694651a3bc3dbe45d4552969","ref":"refs/heads/master","pushedAt":"2023-06-23T03:49:33.000Z","pushType":"push","commitsCount":5,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Backport new aspect ratio for bond entanglement figure\n\nFrom the RevTex project.\n\n4x6 -> 3x7\n\nTo enhance the difference between P-SSR and N-SSR entanglement at low U.","shortMessageHtmlLink":"Backport new aspect ratio for bond entanglement figure"}},{"before":"c48eaeb8d790791f5ef6058fb1205d4708f188cb","after":"cf052816a8809960821180d2119bdf6441536969","ref":"refs/heads/master","pushedAt":"2023-06-22T15:17:39.153Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Try improving direct pdf export via Secli's black magic on `shells.m`\n\nVery interesting, maybe not yet comparable with the TikZ output.\nBut promising for the pure state representations...","shortMessageHtmlLink":"Try improving direct pdf export via Secli's black magic on <code>shells.m</code>"}},{"before":"527d388c1103af60e32d18a97e386128cb64a627","after":"c48eaeb8d790791f5ef6058fb1205d4708f188cb","ref":"refs/heads/master","pushedAt":"2023-06-16T03:18:06.675Z","pushType":"push","commitsCount":2,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Backport from TikZ\n\nWe changed many things directly on the latex project for the paper.\nHere we backport the changes to the MATLAB and TikZ scripts.","shortMessageHtmlLink":"Backport from TikZ"}},{"before":"545d2fe5f0d4a2f4fb7dbd9f617f87073acf46b7","after":"527d388c1103af60e32d18a97e386128cb64a627","ref":"refs/heads/master","pushedAt":"2023-05-29T21:29:06.896Z","pushType":"push","commitsCount":1,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Let's leave the *bond* naming convention in figures\n\n1. It can be misleading (bond formation entanglement?)\n2. Editors do not like unnecessary newly introduced slang\n3. Also we should avoid claiming novelty to this extent","shortMessageHtmlLink":"Let's leave the *bond* naming convention in figures"}},{"before":"f6aeaa69ce39c9082023ac91f718de60451fccf0","after":"545d2fe5f0d4a2f4fb7dbd9f617f87073acf46b7","ref":"refs/heads/master","pushedAt":"2023-05-23T08:13:54.971Z","pushType":"push","commitsCount":2,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"Improved color scheme for ED curves.","shortMessageHtmlLink":"Improved color scheme for ED curves."}},{"before":null,"after":"5356160dd03f04f3fb82fb4aeb25c316dd4ae37f","ref":"refs/heads/memento","pushedAt":"2023-05-19T11:28:35.829Z","pushType":"branch_creation","commitsCount":0,"pusher":{"login":"beddalumia","name":"Gabriele Bellomia","path":"/beddalumia","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/56808633?s=80&v=4"},"commit":{"message":"SSRs do spoil (in some sense) additivity!\n\nWhat am I committing here?\n\n> just a try at modifying the superslection_factor figure, to include\n  a panel for S2, with the naive idea to make evident the cancellation\n  between a huge factor for S1 and huge factor for S2, giving the nice\n  almost identity factor for 2S2-S1. This just not works and there are\n  profound reasons behind...hence this update would never be merged to\n  master and will stay here as a memento.\n\nWhat I mean?\n\n> if I apply a SSR to the total bond correlation, which is a mutual info\n  I could naively expect that, given MI = 2S1 - S2, the SSR would give:\n\n    MI|SSR = 2 * S1|SSR - S2|SSR\n\n  This notation is truly misleading and could lead to severe paradoxes,\n  like thinking that SSR and algebraic operations do not commute.\n\nHow is this solved?\n\n> changing how we phrase and write the terms, i.e. we can write\n\n  MI|SSR = 2 * S1|SSR - S2|SSR\n\n  but we need to make sure to understand that S1|SSR is NOT the local\n  entanglement and S2|SSR the quasilocal entanglement under the SSR.\n\n————————————————————————————————————————————————————————————————————————\n\nLET'S CLARIFY THE CONCEPT...\n\nElaborating a bit I believe we may want to keep a clear cut between the\nmathematical and the physical names.\n\n- Von Neumann entropies and mutual information are mathematical objects,\n  and the latter is defined in terms for the former.\n\n- Local (and quasilocal) entanglement and total correlation are physical\n  quantities, that happen to correspond to one mathematical object under\n  some assumptions, but to some other thing under other assumptions.\n\nWithout SSRs everything is simple cause the (quasi)local entanglement is\ngiven by the relevant von Neumann entropies of the relevant RDMs and the\ntotal correlation is the mutual information between two orbitals, hence\nwe have additivity in the sense that the total correlation comes from an\nalgebraic sum of local and quasilocal entanglement.\n\nWith SSRs there's care to be taken since local & quasilocal entanglement\nare not von Neumann entropies, yet the total correlation is still defined\nas a mutual information, acting on a filtered RDM.\nHence it comes from an algebraic sum of von Neumann entropies, but not of\nentanglement measures, since they are not von Neumann entropies.\n\n—————————————————————————————————————————————————————————————————————————\n\nLET'S TRY TO FIND AN IMPROVED NOTATION THEN...\n\nSo, let's call E1 the measure of entanglement between a single site and\nthe whole. S1 is instead just the mathematical definition of von Neumann\nentropy of the RDM1 (same for E2, S2 and RDM2 for the dimer quantities,\ninstead of single site).\n\nWhithout SSRs we have that E1 = S1, E2 = S2 and MI = 2S1 - S2, hence the\nalgebra works fine cause you literally have MI == 2E1 - E2.\n\nBut with SSRs it's not true that E1 = S1 and E2 = S2.\nFor E2 I'm not sure, we would need to derive something following the\nideas in that JCTC for the dimer case.\nBut for E1 the formula is definitely not S1|{SSR on the RDM1}.\nIt is a completely different formula than the von Neumann entropy acting\non the untouched RDM for the single site.\nIt can be derived of course as coming from imposing the SSR on the whole\nDM, but this is irrelavant here.\n\nThat's why when you compute MI with the SSR you do something to the RDM2\nand then get some S1|SSR and S2|SSR to plug in the MI|SSR formula, but\nyou don't have additivity with E1|SSR and E2|SSR, cause these two aren't\nvon Neumann entropies anymore.\nWhy the dimer and single site entanglement are not von Neumann entropies\nanymore? Because applying SSRs to the whole DM you make it in general an\nimpure state and von Neumann entropies of its reduced systems are not\nmeasures of entanglement anymore.\n\n————————————————————————————————————————————————————————————————————————\n\nFINALLY A COMMENT ON WHY S1|SSR IS EXACTLY THE SAME AS S1\n\nThis is another source of confusion... S2|SSR is different from S2, but\nnot a correct expression for E2|SSR, ok. Further, while we know there is\nan inequality associated to the SSRs (E2|SSR ≤ E2) this is not valid for\nS2 and S2|SSR.\n\nBut having S1|SSR == S1 can become even more confusing... we are doing a\nrestriction on the RDM2 and this leads to a different S2, but how can it\nleave unchanged S1, a functional of RDM1, which is a trace of RDM2?\n\nHere my best (technical) answer:\n\n      We know SSRs are local. Hence each local N or parity has to be\n      conserved. When we trace from either an untouched or SSR RDM2,\n      we need to keep the \"to be traced site\" state fixed. Hence we\n      cannot mix up its local N or parity. Thus the elements we set\n      to zero by applying the SSRs never enter the trace defining the\n      single site RDM.","shortMessageHtmlLink":"SSRs do spoil (in some sense) additivity!"}}],"hasNextPage":true,"hasPreviousPage":false,"activityType":"all","actor":null,"timePeriod":"all","sort":"DESC","perPage":30,"cursor":"djE6ks8AAAAEETYl7AA","startCursor":null,"endCursor":null}},"title":"Activity · beddalumia/MIproject"}