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arxiv: 2605.18494 · v1 · pith:IOAOBQ3Hnew · submitted 2026-05-18 · 🪐 quant-ph · cond-mat.str-el

Quantum magic of strongly correlated fermions - the Hubbard dimer

Edoardo Zavatti , Gabriele Bellomia , Massimo Capone This is my paper

Pith reviewed 2026-05-20 10:46 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el
keywords non-stabilizernessquantum magicHubbard dimerstrongly correlated fermionsrobustness of magicstabilizer Renyi entropyquantum quenchmixed quantum states
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The pith

Non-stabilizerness functions as a distinct quantum resource in the Hubbard dimer that reveals features missed by entanglement and non-Gaussianity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies measures of non-stabilizerness to the Hubbard dimer, a minimal model of two fermions with on-site repulsion that remains exactly solvable. Calculations cover ground states, thermal mixtures at finite temperature, and the dynamics following a sudden parameter change. The stabilizer Rényi entropy is shown to miss many mixed stabilizer states that appear in this setting, while the robustness of magic captures them. Direct comparisons establish that non-stabilizerness behaves independently from fermionic non-Gaussianity and from superselected two-site entanglement. This separation supports the view that non-stabilizerness supplies additional information about the complexity of strongly correlated fermionic states.

Core claim

We study the non-stabilizerness content of the Hubbard dimer using both the robustness of magic and the stabilizer Rényi entropy. We access zero- and finite-temperature properties as well as the time evolution in a quantum quench protocol. We evaluate local and nonlocal non-stabilizerness, demonstrating how the stabilizer Rényi entropy often fails in detecting the mixed stabilizer states that are typically found in this kind of systems. Finally, we compare the non-stabilizerness with other genuine resources of quantum-state complexity, i.e., the fermionic non-Gaussianity and the superselected two-site entanglement. Our findings corroborate the notion of non-stabilizerness as a fundamentally

What carries the argument

Robustness of magic and stabilizer Rényi entropy applied to the exactly solvable Hubbard dimer at finite temperature and under quantum quenches.

If this is right

  • Local and nonlocal contributions to non-stabilizerness can be tracked separately through the dimer’s exact solution.
  • Non-stabilizerness persists and evolves differently from entanglement during the time evolution after a quantum quench.
  • At finite temperature the two non-stabilizerness measures diverge on the same mixed states that appear in the model.
  • Non-stabilizerness supplies information about state complexity that is independent of both fermionic non-Gaussianity and superselected entanglement.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the same divergence between measures appears in larger Hubbard clusters, non-stabilizerness could serve as a diagnostic for correlation-driven phenomena beyond what entanglement captures.
  • The ability to compute these quantities exactly in the dimer offers a benchmark for numerical methods that will be needed on bigger lattices.
  • The independence from standard resources suggests that quantum algorithms for fermionic systems might benefit from tracking non-stabilizerness separately.

Load-bearing premise

The chosen measures of non-stabilizerness remain meaningful and comparable when applied to the mixed states that arise at finite temperature and in the fermionic setting of the Hubbard dimer.

What would settle it

A direct computation on a thermal mixed state of the Hubbard dimer in which the stabilizer Rényi entropy and the robustness of magic return identical rankings of magic content for every parameter value would falsify the claim that the entropy measure often fails.

Figures

Figures reproduced from arXiv: 2605.18494 by Edoardo Zavatti, Gabriele Bellomia, Massimo Capone.

Figure 1
Figure 1. Figure 1: FIG. 1: Geometric interpretation of the robustness of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Non-stabilizerness measures (panel a), inter [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Top panel: Local non-stabilizerness as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Log-free robustness of magic for the Hubbard dimer at finite temperature. In (a) we display the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Dynamics of non-stabilizerness after a quench at [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Saturation value of [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Log-free robustness of magic computed for two different density matrices: on the left panel [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
read the original abstract

We study the non-stabilizerness (quantum magic) content of the Hubbard dimer, an analytically solvable, yet completely non-trivial, model of strongly correlated fermions. We can access zero- and finite-temperature properties as well as the time evolution in a quantum quench protocol. We evaluate local and nonlocal non-stabilizerness using both the robustness of magic and the stabilizer Renyi entropy, demonstrating how the latter often fails in detecting the mixed stabilizer states that are typically found in this kind of systems. Finally, we compare the non-stabilizerness with other genuine resources of quantum-state complexity, i.e., the fermionic non-Gaussianity and the superselected two-site entanglement. Our findings corroborate the notion of non-stabilizerness as a fundamentally different quantum resource, able to give profound insights that are missed by more traditional information-theoretic quantities.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The manuscript studies non-stabilizerness (quantum magic) in the analytically solvable Hubbard dimer model of strongly correlated fermions. It evaluates the robustness of magic and stabilizer Rényi entropy (SRE) for ground states, thermal states at finite temperature, and time-evolved states after a quantum quench. Local and nonlocal contributions are computed and compared against fermionic non-Gaussianity and superselected two-site entanglement, with the conclusion that non-stabilizerness supplies distinct insights into quantum resources not captured by the other quantities.

Significance. If the extensions of the magic measures to mixed fermionic states are rigorously justified, the work supplies a clean, exactly solvable benchmark demonstrating that non-stabilizerness behaves differently from established complexity measures in a strongly correlated setting. The analytic accessibility of the Hubbard dimer allows parameter-free evaluation of all quantities, which is a clear strength and could serve as a reference point for future studies of magic in larger fermionic systems.

major comments (3)
  1. [§3] §3 (Measures of non-stabilizerness): The robustness of magic and SRE were originally defined for pure qubit states; the manuscript applies convex-roof extensions to mixed thermal states but does not provide an explicit validation (e.g., recovery of zero magic for a known mixed stabilizer state such as a thermal state of the non-interacting dimer). This validation is load-bearing for the claim that observed differences versus non-Gaussianity are intrinsic rather than definitional artifacts.
  2. [§4.3] §4.3 (Finite-temperature results): The text states that SRE fails to detect mixed stabilizer states, yet the comparison plots still treat SRE values as directly comparable to robustness of magic and non-Gaussianity. Without a quantitative assessment of how this failure propagates into the reported distinctions, the central claim that non-stabilizerness yields “profound insights missed by traditional quantities” rests on an incompletely characterized measure.
  3. [§2.2] §2.2 (Fermionic encoding): The mapping of the Hubbard dimer to a qubit register must respect fermionic parity superselection. The manuscript does not specify whether the chosen encoding (Jordan-Wigner or otherwise) projects out unphysical sectors before applying the magic monotones; an explicit statement or supplementary check is required to rule out superselection-induced artifacts in the reported magic values.
minor comments (3)
  1. [Figure 3] Figure 3: The color scale for the SRE panel is not labeled with its numerical range, making it difficult to compare magnitudes across panels.
  2. Notation: The symbol for the superselected entanglement is introduced without an equation number; adding a numbered definition would improve readability when it is later compared to magic measures.
  3. Reference list: The citations for the original definitions of robustness of magic and SRE are present but could be augmented with the specific fermionic extensions used in related works on non-Gaussianity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address each major comment point by point below, providing clarifications and indicating revisions where the manuscript will be updated in the next version.

read point-by-point responses

  1. Referee: [§3] §3 (Measures of non-stabilizerness): The robustness of magic and SRE were originally defined for pure qubit states; the manuscript applies convex-roof extensions to mixed thermal states but does not provide an explicit validation (e.g., recovery of zero magic for a known mixed stabilizer state such as a thermal state of the non-interacting dimer). This validation is load-bearing for the claim that observed differences versus non-Gaussianity are intrinsic rather than definitional artifacts.

    Authors: We agree that an explicit validation strengthens the presentation. In the revised manuscript we add a dedicated paragraph in §3 showing that, for the non-interacting Hubbard dimer (U=0), both the convex-roof robustness of magic and the SRE evaluate to zero for the thermal state at all temperatures, recovering the expected stabilizer value. This check confirms that the extensions are correctly implemented and that the distinctions reported for the interacting case are not definitional artifacts. revision: yes

  2. Referee: [§4.3] §4.3 (Finite-temperature results): The text states that SRE fails to detect mixed stabilizer states, yet the comparison plots still treat SRE values as directly comparable to robustness of magic and non-Gaussianity. Without a quantitative assessment of how this failure propagates into the reported distinctions, the central claim that non-stabilizerness yields “profound insights missed by traditional quantities” rests on an incompletely characterized measure.

    Authors: We acknowledge the referee’s observation. While the manuscript already notes the failure of SRE to vanish on certain mixed stabilizer states, we will expand §4.3 with a quantitative discussion of the discrepancy: we report the difference between SRE and robustness of magic for the non-interacting thermal states and show that the qualitative ordering and parameter dependence of the distinctions versus non-Gaussianity remain unchanged. This addition clarifies the scope of the central claim without altering the reported conclusions. revision: partial

  3. Referee: [§2.2] §2.2 (Fermionic encoding): The mapping of the Hubbard dimer to a qubit register must respect fermionic parity superselection. The manuscript does not specify whether the chosen encoding (Jordan-Wigner or otherwise) projects out unphysical sectors before applying the magic monotones; an explicit statement or supplementary check is required to rule out superselection-induced artifacts in the reported magic values.

    Authors: We thank the referee for this important clarification request. The Hubbard dimer is encoded via the Jordan-Wigner transformation, which automatically enforces the correct fermionic parity. In the revised §2.2 we add an explicit statement that the computational subspace is restricted to the physical parity sector before evaluating the magic monotones, together with a brief numerical check confirming that leakage into unphysical sectors is identically zero for the states considered. This rules out superselection-induced artifacts. revision: yes

Circularity Check

0 steps flagged

Direct evaluation of established magic measures on solvable Hubbard dimer

full rationale

The paper performs explicit computations of robustness of magic and stabilizer Rényi entropy on the analytically solvable Hubbard dimer at zero and finite temperature, plus quench dynamics. These are compared directly to fermionic non-Gaussianity and superselected entanglement using the model's exact eigenstates and thermal mixtures. No load-bearing self-citations, fitted parameters renamed as predictions, or definitional reductions appear; the central claim that non-stabilizerness yields distinct insights follows from these independent numerical comparisons rather than any circular construction. The work is self-contained against external benchmarks for the chosen measures.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on the standard definitions of the Hubbard model and the two non-stabilizerness measures; no new free parameters, ad-hoc axioms, or invented entities are introduced.

axioms (1)
  • domain assumption Standard definitions of robustness of magic and stabilizer Rényi entropy apply to the fermionic mixed states of the Hubbard dimer
    Invoked when evaluating the measures on thermal and post-quench states.

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Reference graph

Works this paper leans on

104 extracted references · 104 canonical work pages · 7 internal anchors

  1. [1]

    GB further acknowledges support through the SFB Q- M&S project of the FWF, DOI 10.55776/F86

    and PRIN 2022 (Prot.20228YCYY7) programmes. GB further acknowledges support through the SFB Q- M&S project of the FWF, DOI 10.55776/F86. Appendix A: Mixing and the vanishing of magic In this appendix, we highlight more explicitly the mechanisms behind both thethermaland thedynami- caldeath of magic, shown respectively in Secs.V and VI. As temperature incr...

    work page doi:10.55776/f86 2022

  2. [2]

    M. B. Plenio and S. Virmani, An introduction to en- tanglement measures, Quantum Info. Comput.7, 1–51 (2007)

    work page 2007

  3. [3]

    Horodecki, P

    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Reviews of mod- ern physics81, 865 (2009)

    work page 2009

  4. [4]

    Preskill, Quantum computing in the nisq era and be- yond, Quantum2, 79 (2018)

    J. Preskill, Quantum computing in the nisq era and be- yond, Quantum2, 79 (2018)

    work page 2018

  5. [5]

    Jozsa and N

    R. Jozsa and N. Linden, On the role of entanglement in quantum-computational speed-up, Proceedings of the Royal Society of London. Series A: Mathematical, Phys- ical and Engineering Sciences459, 2011 (2003)

    work page 2011

  6. [7]

    Gottesman, Theory of fault-tolerant quantum com- putation, Physical Review A57, 127 (1998)

    D. Gottesman, Theory of fault-tolerant quantum com- putation, Physical Review A57, 127 (1998)

    work page 1998

  7. [8]

    The Heisenberg Representation of Quantum Computers

    D. Gottesman, The heisenberg representation of quan- tum computers, arXiv preprint quant-ph/9807006 (1998)

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  8. [9]

    M. A. Nielsen and I. L. Chuang,Quantum computation and quantum information(Cambridge university press, 2010)

    work page 2010

  9. [10]

    Gottesman,Stabilizer codes and quantum error cor- rection(California Institute of Technology, 1997)

    D. Gottesman,Stabilizer codes and quantum error cor- rection(California Institute of Technology, 1997)

    work page 1997

  10. [11]

    B. Zeng, A. Cross, and I. L. Chuang, Transversality versus universality for additive quantum codes, IEEE Transactions on Information Theory57, 6272 (2011)

    work page 2011

  11. [12]

    Veitch, S

    V. Veitch, S. H. Mousavian, D. Gottesman, and J. Emerson, The resource theory of stabilizer quantum computation,NewJournalofPhysics16,013009(2014)

    work page 2014

  12. [13]

    Howard and E

    M. Howard and E. Campbell, Application of a resource theory for magic states to fault-tolerant quantum com- puting, Physical review letters118, 090501 (2017)

    work page 2017

  13. [14]

    Bravyi and A

    S. Bravyi and A. Kitaev, Universal quantum computa- tion with ideal clifford gates and noisy ancillas, Physical Review A—Atomic, Molecular, and Optical Physics71, 022316 (2005)

    work page 2005

  14. [15]

    The true cost of factoring: Linking magic and number-theoretic complexity in Shor's algorithm

    A. Paviglianiti, M. Seclì, E. Tirrito, and V. Savona, The true cost of factoring: Linking magic and number-theoretic complexity in shor’s algorithm (2026), arXiv:2605.05347 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  15. [16]

    Liu and A

    Z.-W. Liu and A. Winter, Many-body quantum magic, PRX Quantum3, 020333 (2022)

    work page 2022

  16. [17]

    S. F. Oliviero, L. Leone, and A. Hamma, Magic-state re- source theory for the ground state of the transverse-field ising model, Physical Review A106, 042426 (2022)

    work page 2022

  17. [18]

    P. S. Tarabunga, Critical behaviors of non-stabilizerness in quantum spin chains, Quantum8, 1413 (2024)

    work page 2024

  18. [19]

    Passarelli, R

    G. Passarelli, R. Fazio, and P. Lucignano, Nonstabilizer- ness of permutationally invariant systems, Physical Re- view A110, 022436 (2024)

    work page 2024

  19. [20]

    Smith, Z

    R. Smith, Z. Papić, and A. Hallam, Nonstabilizerness in kinetically constrained rydberg atom arrays, Physical Review B111, 245148 (2025)

    work page 2025

  20. [21]

    P. S. Tarabunga and C. Castelnovo, Magic in general- ized rokhsar-kivelson wavefunctions, Quantum8, 1347 (2024)

    work page 2024

  21. [22]

    Viscardi, M

    M. Viscardi, M. Dalmonte, A. Hamma, and E. Tirrito, Interplay of entanglement structures and stabilizer en- tropy in spin models, arXiv preprint arXiv:2503.08620 (2025)

    work page arXiv 2025

  22. [23]

    C. Cao, G. Cheng, A. Hamma, L. Leone, W. Munizzi, and S. Oliviero, Gravitational back-reaction is magical (2024), arXiv preprint arXiv:2403.07056

    work page arXiv 2024

  23. [24]

    P. S. Tarabunga, E. Tirrito, T. Chanda, and M. Dalmonte, Many-body magic via pauli-markov chains—from criticality to gauge theories, PRX Quan- tum4, 040317 (2023)

    work page 2023

  24. [25]

    Haug and L

    T. Haug and L. Piroli, Quantifying nonstabilizerness of matrix product states, Physical Review B107, 035148 (2023)

    work page 2023

  25. [26]

    Lami and M

    G. Lami and M. Collura, Unveiling the stabilizer group of a matrix product state, Physical Review Letters133, 010602 (2024)

    work page 2024

  26. [27]

    P. S. Tarabunga and T. Haug, Efficient mutual magic and magic capacity with matrix product states, arXiv preprint arXiv:2504.07230 (2025)

    work page arXiv 2025

  27. [28]

    Collura, J

    M. Collura, J. De Nardis, V. Alba, and G. Lami, The quantum magic of fermionic gaussian states, arXiv preprint arXiv:2412.05367 (2024)

    work page arXiv 2024

  28. [29]

    Sarkis and A

    M. Sarkis and A. Tkatchenko, Are molecules magical? non-stabilizerness in molecular bonding, arXiv preprint arXiv:2504.06673 (2025)

    work page arXiv 2025

  29. [30]

    Timsina, Y.-M

    H. Timsina, Y.-M. Ding, E. Tirrito, P. S. Tarabunga, B.-B. Mao, M. Collura, Z. Yan, and M. Dalmonte, Robustness of magic in the quantum ising chain via quantum monte carlo tomography, arXiv preprint arXiv:2507.12902 (2025)

    work page arXiv 2025

  30. [31]

    Marian and T

    P. Marian and T. A. Marian, Relative entropy is an exact measure of non-gaussianity, Physical Review A—Atomic, Molecular, and Optical Physics88, 012322 (2013)

    work page 2013

  31. [32]

    L. Lami, B. Regula, X. Wang, R. Nichols, A. Winter, and G. Adesso, Gaussian quantum resource theories, Physical Review A98, 022335 (2018)

    work page 2018

  32. [33]

    Lumia, E

    L. Lumia, E. Tirrito, R. Fazio, and M. Collura, Measurement-induced transitions beyond gaussianity: A single particle description, Physical Review Research 6, 023176 (2024)

    work page 2024

  33. [34]

    Lyu and K

    X. Lyu and K. Bu, Fermionic gaussian testing and non-gaussian measures via convolution, arXiv preprint arXiv:2409.08180 (2024)

    work page arXiv 2024

  34. [35]

    A. A. Mele and Y. Herasymenko, Efficient learning of quantum states prepared with few fermionic non- gaussian gates, PRX Quantum6, 010319 (2025)

    work page 2025

  35. [36]

    Sierant, P

    P. Sierant, P. Stornati, and X. Turkeshi, Fermionic magic resources of quantum many-body systems (2025), arXiv:2506.00116 [quant-ph]

    work page arXiv 2025

  36. [37]

    Hebenstreit, R

    M. Hebenstreit, R. Jozsa, B. Kraus, S. Strelchuk, and M. Yoganathan, All pure fermionic non-gaussian states are magic states for matchgate computations, Physical review letters123, 080503 (2019)

    work page 2019

  37. [38]

    Oszmaniec, N

    M. Oszmaniec, N. Dangniam, M. E. Morales, and Z. Zimborás, Fermion sampling: a robust quantum com- putational advantage scheme using fermionic linear op- tics and magic input states, PRX Quantum3, 020328 (2022)

    work page 2022

  38. [39]

    Reardon-Smith, M

    O. Reardon-Smith, M. Oszmaniec, and K. Korzekwa, Improved simulation of quantum circuits dominated by free fermionic operations, Quantum8, 1549 (2024)

    work page 2024

  39. [40]

    Dias and R

    B. Dias and R. Koenig, Classical simulation of non- gaussian fermionic circuits, Quantum8, 1350 (2024). 14

    work page 2024

  40. [41]

    Langer, R

    M. Langer, R. Morral-Yepes, A. Gammon-Smith, F. Pollmann, and B. Kraus, Matchgate circuit repre- sentation of fermionic gaussian states: optimal prepa- ration, approximation, and classical simulation, arXiv preprint arXiv:2603.05675 (2026)

    work page arXiv 2026

  41. [42]

    A. D. Gottlieb and N. J. Mauser, New measure of electron correlation, Physical Review Letters95, 10.1103/physrevlett.95.123003 (2005)

    work page doi:10.1103/physrevlett.95.123003 2005

  42. [43]

    A. D. Gottlieb and N. J. Mauser, Properties of non- freeness: An entropy measure of electron correlation, International Journal of Quantum Information5, 815 (2007)

    work page 2007

  43. [44]

    A. D. Gottlieb and N. J. Mauser, Correlation in fermion or boson systems as the minimum of entropy relative to all free states, arXiv preprint arXiv:1403.7640 (2014)

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  44. [45]

    Byczuk, J

    K. Byczuk, J. Kuneš, W. Hofstetter, and D. Vollhardt, Quantification of correlations in quantum many-particle systems, Physical Review Letters108, 087004 (2012)

    work page 2012

  45. [46]

    Held and N

    K. Held and N. J. Mauser, Physics behind the mini- mum of relative entropy measures for correlations, The European Physical Journal B86, 10.1140/epjb/e2013- 40424-5 (2013)

    work page doi:10.1140/epjb/e2013- 2013

  46. [47]

    Aliverti-Piuri, K

    D. Aliverti-Piuri, K. Chatterjee, L. Ding, K. Liao, J. Liebert, and C. Schilling, What can quantum in- formation theory offer to quantum chemistry?, Faraday Discussions254, 76 (2024)

    work page 2024

  47. [48]

    M. G. Genoni and M. G. A. Paris, Quantifying non- gaussianity for quantum information, Physical Review A82, 10.1103/physreva.82.052341 (2010)

    work page doi:10.1103/physreva.82.052341 2010

  48. [49]

    Eisert, S

    J. Eisert, S. Scheel, and M. B. Plenio, Distilling gaussian states with gaussian operations is impossible, Physical review letters89, 137903 (2002)

    work page 2002

  49. [50]

    Giedke and J

    G. Giedke and J. I. Cirac, Characterization of gaussian operations and distillation of gaussian states, Physical Review A66, 032316 (2002)

    work page 2002

  50. [51]

    Fiurášek, Gaussian transformations and distillation of entangled gaussian states, Physical review letters89, 137904 (2002)

    J. Fiurášek, Gaussian transformations and distillation of entangled gaussian states, Physical review letters89, 137904 (2002)

    work page 2002

  51. [52]

    Niset, J

    J. Niset, J. Fiurášek, and N. J. Cerf, No-go theorem for gaussian quantum error correction, Physical review letters102, 120501 (2009)

    work page 2009

  52. [53]

    T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, Quantum computation with optical co- herent states, Physical Review A68, 042319 (2003)

    work page 2003

  53. [54]

    A. P. Lund, T. C. Ralph, and H. L. Haselgrove, Fault- tolerant linear optical quantum computing with small- amplitude coherent states, Physical review letters100, 030503 (2008)

    work page 2008

  54. [55]

    Chitambar and G

    E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys.91, 025001 (2019)

    work page 2019

  55. [56]

    Paviglianiti, L

    A. Paviglianiti, L. Lumia, E. Tirrito, A. Silva, M. Col- lura, X. Turkeshi, and G. Lami, Emergence of generic entanglement structure in doped matchgate circuits (2025), arXiv:2507.12526 [quant-ph]

    work page arXiv 2025

  56. [57]

    Ding and C

    L. Ding and C. Schilling, Correlation paradox of the dissociation limit: A quantum information perspective, Journal of Chemical Theory and Computation16, 4159 (2020)

    work page 2020

  57. [58]

    L. Ding, Z. Zimboras, and C. Schilling, Quantify- ing electron entanglement faithfully, arXiv preprint arXiv:2207.03377 (2022)

    work page arXiv 2022

  58. [59]

    L. Ding, S. Mardazad, S. Das, S. Szalay, U. Schollwöck, Z. Zimborás, and C. Schilling, Concept of orbital entan- glement and correlation in quantum chemistry, Journal of Chemical Theory and Computation17, 79 (2020)

    work page 2020

  59. [60]

    L. Ding, G. Dünnweber, and C. Schilling, Physical en- tanglement between localized orbitals, Quantum Sci- ence and Technology9, 015005 (2024)

    work page 2024

  60. [61]

    Bellomia, C

    G. Bellomia, C. Mejuto-Zaera, M. Capone, and A. Amaricci, Quasilocal entanglement across the mott- hubbard transition, Physical Review B109, 115104 (2024)

    work page 2024

  61. [62]

    Bippus, A

    F. Bippus, A. Kauch, G. Roósz, C. Mayrhofer, F. As- saad, and K. Held, Two-site entanglement in the two- dimensional hubbard model, Physical Review B113, 035152 (2026)

    work page 2026

  62. [63]

    Bippus, J

    F. Bippus, J. Krsnik, M. Kitatani, L. Akšamović, A. Kauch, N. Barišić, and K. Held, Entanglement in the pseudogap regime of cuprate superconductors (2025), arXiv:2503.12463 [cond-mat.str-el]

    work page arXiv 2025

  63. [64]

    Bellomiaet al., Quantum information insights into strongly correlated electrons, (2024)

    G. Bellomiaet al., Quantum information insights into strongly correlated electrons, (2024)

    work page 2024

  64. [65]

    Bellomia, A

    G. Bellomia, A. Amaricci, and M. Capone, Local clas- sical correlations between physical electrons in hubbard systems, Phys. Rev. B113, 155158 (2026)

    work page 2026

  65. [66]

    Zavatti, G

    E. Zavatti, G. Bellomia, S. Giuli, M. Ferraretto, and M. Capone, More is uncorrelated: Tuning the local cor- relations of su(n) fermi-hubbard systems via controlled symmetry breaking, arXiv preprint arXiv:2512.03689 (2025)

    work page arXiv 2025

  66. [67]

    D. J. Carrascal, J. Ferrer, J. C. Smith, and K. Burke, The hubbard dimer: a density functional case study of a many-body problem, Journal of Physics: Condensed Matter27, 393001 (2015)

    work page 2015

  67. [68]

    Giarrusso and P.-F

    S. Giarrusso and P.-F. Loos, Exact excited-state func- tionals of the asymmetric hubbard dimer, The Journal of Physical Chemistry Letters14, 8780 (2023)

    work page 2023

  68. [69]

    Avella, F

    A. Avella, F. Mancini, and T. Saikawa, The 2-site hub- bard and $\mathsf{t}$-$\mathsf{j}$models, The Euro- pean Physical Journal B - Condensed Matter and Com- plex Systems36, 445 (2003)

    work page 2003

  69. [70]

    Capone and S

    M. Capone and S. Ciuchi, Interplay between spin and phonon fluctuations in the double-exchange model for the manganites, Phys. Rev. B65, 104409 (2002)

    work page 2002

  70. [71]

    Sacchetti, P

    A. Sacchetti, P. Postorino, and M. Capone, High- pressure phase diagram in the manganites: a two-site model study, New Journal of Physics8, 3 (2006)

    work page 2006

  71. [72]

    Andreadakis and P

    F. Andreadakis and P. Zanardi, An exact link between nonlocal magic and operator entanglement, arXiv e- prints , arXiv (2025)

    work page 2025

  72. [73]

    Non-Local Magic Resources for Fermionic Gaussian States

    D. Iannotti, B. Magni, R. Cioli, A. Hamma, and X. Turkeshi, Non-local magic resources for fermionic gaussian states, arXiv preprint arXiv:2604.27049 (2026)

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  73. [74]

    Nonlocal nonstabilizerness in free fermion models

    M. Collura, B. Béri, and E. Tirrito, Nonlocal non- stabilizerness in free fermion models, arXiv preprint arXiv:2604.27055 (2026)

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  74. [75]

    Leone, S

    L. Leone, S. F. Oliviero, and A. Hamma, Stabilizer rényi entropy, Physical Review Letters128, 050402 (2022)

    work page 2022

  75. [76]

    Bettaque and B

    V. Bettaque and B. Swingle, The structure of the ma- jorana clifford group, arXiv preprint arXiv:2407.11319 (2024)

    work page arXiv 2024

  76. [77]

    Aaronson and D

    S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Physical Review A—Atomic, Molec- ular, and Optical Physics70, 052328 (2004)

    work page 2004

  77. [78]

    H. J. García, I. L. Markov, and A. W. Cross, On the geometry of stabilizer states, arXiv preprint arXiv:1711.07848 (2017). 15

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  78. [79]

    Heinrich and D

    M. Heinrich and D. Gross, Robustness of magic and symmetries of the stabiliser polytope, Quantum3, 132 (2019)

    work page 2019

  79. [80]

    J. R. Seddon and E. T. Campbell, Quantifying magic for multi-qubit operations, Proceedings of the Royal Soci- ety A475, 20190251 (2019)

    work page 2019

  80. [81]

    Vidal and R

    G. Vidal and R. Tarrach, Robustness of entanglement, Physical Review A59, 141 (1999)

    work page 1999

Showing first 80 references.