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arxiv: 2605.15008 · v1 · pith:SSGAKRQWnew · submitted 2026-05-14 · 🪐 quant-ph

Majorana Constellations: A Geometric Lens on Multipartite Entanglement and Geometric Phases

Chon-Fai Kam This is my paper

Pith reviewed 2026-06-30 20:24 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Majorana stellar representationmultipartite entanglementgeometric phasesBloch sphereconcurrencethree-tanglequantum spin statesSLOCC classification
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The pith

Majorana constellations on the Bloch sphere encode exact measures of multipartite entanglement and anomalous contributions to geometric phases.

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

The paper reviews how the Majorana stellar representation converts quantum spin states into sets of points on a sphere. This geometric encoding lets researchers read off entanglement quantities such as concurrence and the three-tangle straight from the positions and separations of those points. The same picture tracks the motion of the points during time evolution and isolates extra internal terms that appear in geometric phases. A reader would care because the method replaces some algebraically intensive calculations with direct geometric inspection and supplies a single visual language for symmetric multi-qubit systems. It also connects algebraic classification schemes to continuous pictures of state change.

Core claim

The Majorana stellar representation translates abstract quantum spin states into intuitive geometric constellations on the Bloch sphere, revealing symmetries, degeneracies, and correlations that traditional algebraic methods often obscure. By encoding entanglement directly into spatial coordinates, the constellation geometry yields exact measures of concurrence, three-tangle, and genuine multipartite entanglement, while its dynamical evolution uncovers internal anomalous contributions to geometric phases. This review synthesizes the entanglement-centric perspective, bridges discrete algebraic classifications such as SLOCC orbits with continuous geometric interpretations, and highlights polyn

What carries the argument

The Majorana stellar representation, which maps symmetric quantum states to constellations of points on the Bloch sphere so that entanglement and phase properties become visible spatial features.

If this is right

  • Exact numerical values for concurrence, three-tangle, and genuine multipartite entanglement follow directly from the relative positions of the constellation points.
  • Dynamical evolution of the points isolates anomalous internal contributions to Berry and Hannay geometric phases.
  • Multipartite entanglement invariants become evaluable in polynomial time rather than facing #P-hard algebraic bottlenecks.
  • Discrete SLOCC orbit classifications acquire continuous geometric counterparts through the topology and spacing of the points.
  • Applications in quantum metrology, state engineering, and condensed-matter physics arise from the visual tracking of entanglement and phase.

Where Pith is reading between the lines

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

  • Experimental setups could monitor entanglement by imaging or tracking the effective star positions in real time.
  • The geometric language may extend naturally to asymmetric or mixed states once the pure symmetric case is fully mapped.
  • Constellation topology could serve as a diagnostic for entanglement transitions in many-body systems studied in condensed matter.
  • Polynomial-time geometric evaluation opens the possibility of on-the-fly entanglement estimation inside quantum simulators or processors.

Load-bearing premise

Existing literature on Majorana representations is fragmented and lacks a unified treatment of entanglement-specific metrics and their higher-dimensional dynamics.

What would settle it

An explicit calculation for a known symmetric two- or three-qubit state in which the concurrence or three-tangle extracted from the constellation positions differs numerically from the standard algebraic value.

Figures

Figures reproduced from arXiv: 2605.15008 by Chon-Fai Kam.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

The Majorana stellar representation translates abstract quantum spin states into intuitive geometric constellations on the Bloch sphere, revealing symmetries, degeneracies, and correlations that traditional algebraic methods often obscure. Within quantum information science, this framework provides a powerful lens for characterizing symmetric multi-qubit and higher-spin systems. By encoding entanglement directly into spatial coordinates, the constellation geometry yields exact measures of concurrence, three-tangle, and genuine multipartite entanglement, while its dynamical evolution uncovers internal anomalous contributions to geometric phases. While interest in stellar representations has resurged, existing literature remains fragmented, lacking a unified treatment of these entanglement-specific metrics and their higher-dimensional dynamics. This review synthesizes the entanglement-centric perspective on Majorana representations, bridging discrete algebraic classifications (e.g., SLOCC orbits) with continuous geometric interpretations. Crucially, we highlight how this framework circumvents \#P-hard computational bottlenecks, leveraging polynomial-time tractability to evaluate multipartite invariants. We detail the interplay between constellation topology and higher-spin Berry/Hannay phases, explore extensions beyond pure symmetric states, and review applications in quantum metrology, state engineering, and condensed-matter physics. By foregrounding entanglement as the unifying theme, this comprehensive examination establishes Majorana stars as a fundamental geometric language, uniquely positioned to inspire new theoretical and experimental directions in quantum technologies.

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

0 major / 2 minor

Summary. This is a review synthesizing prior literature on the Majorana stellar representation of symmetric quantum states. It presents the constellation geometry on the Bloch sphere as encoding exact measures of concurrence, three-tangle, and genuine multipartite entanglement, while dynamical evolution of the constellations reveals anomalous contributions to geometric (Berry/Hannay) phases. The manuscript bridges SLOCC algebraic classifications with continuous geometric pictures, claims polynomial-time tractability for multipartite invariants that circumvents #P-hard bottlenecks, and surveys applications in metrology, state engineering, and condensed-matter physics.

Significance. If the compilation is accurate and balanced, the review could usefully organize a fragmented literature around an entanglement-centric geometric viewpoint, offering an intuitive language that may aid intuition and computation in symmetric-state quantum information. However, because the manuscript aggregates established results without new theorems, parameter-free derivations, or falsifiable predictions, its significance is primarily organizational rather than foundational.

minor comments (2)
  1. The abstract asserts that constellation geometry 'yields exact measures' of concurrence and three-tangle; a minor clarification in the introduction or §2 would explicitly note which prior references first derived these geometric expressions so readers can trace the original derivations.
  2. The claim that the framework 'circumvents #P-hard computational bottlenecks' via polynomial-time tractability should be accompanied, even in a review, by a brief pointer to the specific complexity result being invoked (e.g., the reference establishing the polynomial scaling for the relevant invariants).

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for the recommendation to accept. The summary accurately reflects the scope of the review as a synthesis of the Majorana stellar representation with an emphasis on entanglement measures and geometric phases.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

This is a review paper that synthesizes prior external results on Majorana stellar representations for symmetric states, entanglement measures (concurrence, three-tangle), and geometric phases. No original derivations, parameter fits, or predictions are advanced that reduce by construction to the paper's own equations or self-citations. All load-bearing claims explicitly reference the broader literature rather than internal definitions or ansatzes, satisfying the criteria for an independent synthesis with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

As a review the ledger is dominated by standard quantum mechanics and information axioms drawn from prior literature rather than new postulates introduced here.

axioms (1)
  • standard math Standard postulates of quantum mechanics for spin-j states and SLOCC equivalence
    Invoked throughout the synthesis of entanglement measures.

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discussion (0)

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Reference graph

Works this paper leans on

103 extracted references · 4 canonical work pages · 2 internal anchors

  1. [1]

    Nielsen and Isaac L

    Michael A. Nielsen and Isaac L. Chuang.Quantum Computation and Quantum Information. Cambridge University Press, 10th anniversary edition, 2010. 45

    2010

  2. [2]

    Wilde.Quantum Information Theory

    Mark M. Wilde.Quantum Information Theory. Cam- bridge University Press, 2nd edition, 2017

    2017

  3. [3]

    Quantum resource theories.Reviews of Modern Physics, 91(2):025001, 2019

    Eric Chitambar and Gilad Gour. Quantum resource theories.Reviews of Modern Physics, 91(2):025001, 2019

    2019

  4. [4]

    Cambridge University Press, 2nd edition, 2017

    Ingemar Bengtsson and Karol ˙Zyczkowski.Geometry of quantum states: an introduction to quantum en- tanglement. Cambridge University Press, 2nd edition, 2017

    2017

  5. [5]

    Quantum computing in the nisq era and beyond.Quantum, 2:79, 2018

    John Preskill. Quantum computing in the nisq era and beyond.Quantum, 2:79, 2018

    2018

  6. [6]

    Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heidelman, V. K. Radha, et al. Noisy intermediate-scale quantum al- gorithms.Reviews of Modern Physics, 94(1):015004, 2022

    2022

  7. [7]

    Security in quantum cryptography.Reviews of Modern Physics, 94(2):025008, 2022

    Christopher Portmann and Renato Renner. Security in quantum cryptography.Reviews of Modern Physics, 94(2):025008, 2022

    2022

  8. [8]

    Challenging local realism with human choices.Nature, 557(7704):212– 216, 2018

    The BIG Bell Test Collaboration. Challenging local realism with human choices.Nature, 557(7704):212– 216, 2018

    2018

  9. [9]

    Leggett-garg macrorealism and temporal correlations

    Costantino Budroni, Giuseppe Vitagliano, et al. Leggett-garg macrorealism and temporal correlations. Reviews of Modern Physics, 94(4):045007, 2022

    2022

  10. [10]

    Entanglement of formation of an arbitrary state of two qubits.Physical Review Letters, 80(10):2245, 1998

    William K Wootters. Entanglement of formation of an arbitrary state of two qubits.Physical Review Letters, 80(10):2245, 1998

    1998

  11. [11]

    Distributed entanglement.Physical Review A, 61(5):052306, 2000

    Valerie Coffman, Joydip Kundu, and William K Woot- ters. Distributed entanglement.Physical Review A, 61(5):052306, 2000

    2000

  12. [12]

    Com- putable measure of entanglement.Physical Review A, 65(3):032314, 2002

    Guifr´ e Vidal and Reinhard F Werner. Com- putable measure of entanglement.Physical Review A, 65(3):032314, 2002

    2002

  13. [13]

    Entanglement detec- tion.Physics Reports, 474(1-6):1–75, 2009

    Otfried G¨ uhne and G´ eza T´ oth. Entanglement detec- tion.Physics Reports, 474(1-6):1–75, 2009

    2009

  14. [14]

    Atomi orientati in campo magnetico variabile.Il Nuovo Cimento, 9(2):43–50, 1932

    Ettore Majorana. Atomi orientati in campo magnetico variabile.Il Nuovo Cimento, 9(2):43–50, 1932

    1932

  15. [15]

    A. R. Usha Devi, Sudha, and A. K. Rajagopal. Majorana representation of symmetric multiqubit states.Quantum Information Processing, 11(3):685– 710, 2012

    2012

  16. [16]

    Theory of complex spectra

    Giulio Racah. Theory of complex spectra. I.Physical Review, 62(9-10):438, 1942

    1942

  17. [17]

    Eugene P. Wigner. On the matrices which reduce the nth indefinite Kronecker product of the representation of the continuous groups. Technical report, Princeton University, 1940. Reprinted in L. C. Biedenharn and H. van Dam (eds.),Quantum Theory of Angular Mo- mentum, Academic Press, New York, 1965

    1940

  18. [18]

    On angular momentum

    Julian Schwinger. On angular momentum. Technical Report NYO-3071, U.S. Atomic Energy Commission,

  19. [19]

    Reprinted in L. C. Biedenharn and H. van Dam (eds.),Quantum Theory of Angular Momentum, Aca- demic Press, New York, 1965

    1965

  20. [20]

    Cambridge University Press, 1984

    Roger Penrose and Wolfgang Rindler.Spinors and space-time: Volume 1, Two-spinor calculus and rela- tivistic fields. Cambridge University Press, 1984

    1984

  21. [21]

    On Bell non-locality without probabilities: More curious geometry.Foun- dations of Physics, 23(7):1065–1081, 1993

    Jason Zimba and Roger Penrose. On Bell non-locality without probabilities: More curious geometry.Foun- dations of Physics, 23(7):1065–1081, 1993

    1993

  22. [22]

    J. M. Radcliffe. Some properties of coherent spin states.Journal of Physics A: General Physics, 4(3):313, 1971

    1971

  23. [23]

    F. T. Arecchi, Eric Courtens, Robert Gilmore, and Harry Thomas. Atomic coherent states in quantum optics.Physical Review A, 6(6):2211, 1972

    1972

  24. [24]

    Leboeuf and A

    P. Leboeuf and A. Voros. Chaos-revealing multiplica- tive representation of quantum mechanics.Journal of Physics A: Mathematical and General, 23(10):1765, 1990

    1990

  25. [25]

    The berry phase for spin in the majorana representation.Journal of Physics A: Mathematical and General, 31(2):L53, 1998

    J H Hannay. The berry phase for spin in the majorana representation.Journal of Physics A: Mathematical and General, 31(2):L53, 1998

    1998

  26. [26]

    The majorana representation of polariza- tion, and the berry phase of light.Journal of Modern Optics, 45(5):1001–1008, 1998

    J H Hannay. The majorana representation of polariza- tion, and the berry phase of light.Journal of Modern Optics, 45(5):1001–1008, 1998

    1998

  27. [27]

    Majorana representation of the states of spinor Bose-Einstein condensates.Physical Review A, 75(3):033610, 2007

    Harri M¨ akel¨ a and Kalle-Antti Suominen. Majorana representation of the states of spinor Bose-Einstein condensates.Physical Review A, 75(3):033610, 2007

    2007

  28. [28]

    Ther- modynamic limit of the Lipkin-Meshkov-Glick model

    Pedro Ribeiro, Julien Vidal, and R´ emy Mosseri. Ther- modynamic limit of the Lipkin-Meshkov-Glick model. Physical Review Letters, 99(5):050402, 2007

    2007

  29. [29]

    Oper- ational families of entanglement classes for symmetric n-qubit states.Physical Review Letters, 103(7):070503, 2009

    Thierry Bastin, Sara Krins, Pierre Mathonet, Michel Godefroid, Lucas Lamata, and Enrique Solano. Oper- ational families of entanglement classes for symmetric n-qubit states.Physical Review Letters, 103(7):070503, 2009

    2009

  30. [30]

    The maximally entangled symmetric state in terms of the geometric measure.New Journal of Physics, 12(7):073025, 2010

    Martin Aulbach, Damian Markham, and Mio Murao. The maximally entangled symmetric state in terms of the geometric measure.New Journal of Physics, 12(7):073025, 2010

    2010

  31. [31]

    Damian J. H. Markham. Entanglement and symmetry in permutation-symmetric states.Physical Review A, 83(4):042332, 2011

    2011

  32. [32]

    Barycentric measure of quantum entanglement.Physical Review A, 85(4):042314, 2012

    Wojciech Ganczarek, Marek Ku´ s, and Karol ˙Zyczkowski. Barycentric measure of quantum entanglement.Physical Review A, 85(4):042314, 2012

    2012

  33. [33]

    Quantum metrol- ogy from a quantum information science perspective

    G´ eza T´ oth and I˜ nigo Apellaniz. Quantum metrol- ogy from a quantum information science perspective. Journal of Physics A: Mathematical and Theoretical, 47(42):424006, 2014

    2014

  34. [34]

    Serrano-Ens´ astiga and D

    E. Serrano-Ens´ astiga and D. Braun. Majorana rep- resentation for mixed states.Physical Review A, 46 101(2):022332, 2020

    2020

  35. [35]

    Klimov, Gerd Leuchs, and Luis L

    Fr´ ed´ eric Bouchard, Andrei B. Klimov, Gerd Leuchs, and Luis L. S´ anchez-Soto. Multipoles from Majo- rana constellations.Physical Review A, 109(1):012214, 2024

    2024

  36. [36]

    Goldberg, Andrei B

    Aaron Z. Goldberg, Andrei B. Klimov, Markus Grassl, Gerd Leuchs, and Luis L. S´ anchez-Soto. Extremal quantum states.Physical Review A, 98(4):043614, 2018

    2018

  37. [37]

    Klimov, Luis L

    Markus Grassl, Andrei B. Klimov, Luis L. S´ anchez- Soto, and Gerd Leuchs. Codes for the quantum sky. New Journal of Physics, 20(1):013009, 2018

    2018

  38. [38]

    Tensor classifiers for anticoherent states.Physical Review Letters, 114(8):080401, 2015

    Olivier Giraud, Daniel Braun, David Bagrette, and Thierry Bastin. Tensor classifiers for anticoherent states.Physical Review Letters, 114(8):080401, 2015

    2015

  39. [39]

    S´ anchez-Soto, Andrei B

    Fr´ ed´ eric Bouchard, Luis L. S´ anchez-Soto, Andrei B. Klimov, Aaron Z. Goldberg, and Gerd Leuchs. The quantum sky of Majorana stars.arXiv preprint arXiv:2601.20922, 2026

    work page arXiv 2026

  40. [40]

    Zibrov, Manuel Endres, Markus Greiner, et al

    Hannes Bernien, Sylvain Schwartz, Alexander Keesling, Harry Levine, Ahmed Omran, Hannes Pichler, Soonwon Choi, Alexander S. Zibrov, Manuel Endres, Markus Greiner, et al. Probing many-body dynamics on a 51-atom quantum simulator.Nature, 551(7682):579–584, 2017

    2017

  41. [41]

    Wang, Harry Levine, Alexan- der Keesling, Giulia Semenek, Ahmed Omran, Dolev Bluvstein, Soonwon Choi, Hannes Pichler, Wen Wei Choi, et al

    Sepehr Ebadi, Tout T. Wang, Harry Levine, Alexan- der Keesling, Giulia Semenek, Ahmed Omran, Dolev Bluvstein, Soonwon Choi, Hannes Pichler, Wen Wei Choi, et al. Quantum phases of matter on a 256- atom programmable quantum simulator.Nature, 595(7866):227–232, 2021

    2021

  42. [42]

    Classification of spaces defining gravitational fields.Uchenye Zapiski Kazan- skogo Gosudarstvennogo Universiteta, 114(8):55–69, 1954

    Aleksei Zinovevich Petrov. Classification of spaces defining gravitational fields.Uchenye Zapiski Kazan- skogo Gosudarstvennogo Universiteta, 114(8):55–69, 1954

    1954

  43. [43]

    Classification of spaces defining gravitational fields (translated by j

    Aleksei Zinovevich Petrov. Classification of spaces defining gravitational fields (translated by j. jezierski & m. a. h. maccallum).General Relativity and Gravi- tation, 32(8):1665–1685, 2000

    2000

  44. [44]

    Chaotic analytic zero points: exact statis- tics for those of a random spin state.Journal of Physics A: Mathematical and General, 29(5):101, 1996

    J H Hannay. Chaotic analytic zero points: exact statis- tics for those of a random spin state.Journal of Physics A: Mathematical and General, 29(5):101, 1996

    1996

  45. [45]

    Stamper-Kurn and Masahito Ueda

    Dan M. Stamper-Kurn and Masahito Ueda. Spinor bose gases: Symmetries, magnetism, and quantum dy- namics.Reviews of Modern Physics, 85(3):1191, 2013

    2013

  46. [46]

    Bastin, S

    T. Bastin, S. Krins, P. Mathonet, M. Bamps, and L. Martin. Operational family classification of sym- metric mixedn-qubit states.Physical Review Letters, 103(7):070503, 2009

    2009

  47. [47]

    Entanglement and symmetry in permutation-symmetric states.Physical Review A, 83(4):042332, 2011

    Damian J Markham. Entanglement and symmetry in permutation-symmetric states.Physical Review A, 83(4):042332, 2011

    2011

  48. [48]

    Anticoherent spin states via the majo- rana representation.Electronic Journal of Theoretical Physics, 3(10):143–156, 2006

    Jason Zimba. Anticoherent spin states via the majo- rana representation.Electronic Journal of Theoretical Physics, 3(10):143–156, 2006

    2006

  49. [49]

    Stellar representation of non-Gaussian quantum states.Physical Review Letters, 124(6):063605, 2020

    Ulysse Chabaud, Damian Markham, and Fr´ ed´ eric Grosshans. Stellar representation of non-Gaussian quantum states.Physical Review Letters, 124(6):063605, 2020

    2020

  50. [50]

    Classical deterministic complexity of Edmonds’ problem and quantum entanglement

    Leonid Gurvits. Classical deterministic complexity of Edmonds’ problem and quantum entanglement. In Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, pages 10–19, 2003

    2003

  51. [51]

    Strong NP-hardness of the geomet- ric measure of entanglement.Quantum Information & Computation, 10(3&4):343–360, 2010

    Sevag Gharibian. Strong NP-hardness of the geomet- ric measure of entanglement.Quantum Information & Computation, 10(3&4):343–360, 2010

    2010

  52. [52]

    Computational complexity of pro- jected entangled pair states.Physical Review Letters, 98(14):140506, 2007

    Norbert Schuch, Michael M Wolf, Frank Verstraete, and J Ignacio Cirac. Computational complexity of pro- jected entangled pair states.Physical Review Letters, 98(14):140506, 2007

    2007

  53. [53]

    Classification of multipartite entan- gled states by multidimensional determinants.Physical Review A, 67(1):012108, 2003

    Akimasa Miyake. Classification of multipartite entan- gled states by multidimensional determinants.Physical Review A, 67(1):012108, 2003

    2003

  54. [54]

    Leslie G. Valiant. The complexity of computing the permanent.Theoretical Computer Science, 8(2):189– 201, 1979

    1979

  55. [55]

    Two algorithmic results for the traveling salesman problem.Mathematics of Opera- tions Research, 21(1):65–84, 1996

    Alexander I Barvinok. Two algorithmic results for the traveling salesman problem.Mathematics of Opera- tions Research, 21(1):65–84, 1996

    1996

  56. [56]

    Coherent States: New Insights into Quantum Mechan- ics with Applications

    Chon-Fai Kam, Wei-Min Zhang, and Da-Hsuan Feng. Coherent States: New Insights into Quantum Mechan- ics with Applications. Springer, 2023

    2023

  57. [57]

    Some formal properties of the density matrix.Proceedings of the Physico-Mathematical So- ciety of Japan

    Kˆ odi Husimi. Some formal properties of the density matrix.Proceedings of the Physico-Mathematical So- ciety of Japan. 3rd Series, 22(4):264–314, 1940

    1940

  58. [58]

    Stars of the quantum universe: Ex- tremal quantum states defined by the Majorana rep- resentation.Physical Review A, 92(3):031801, 2015

    Gunnar Bj¨ ork, Andrei B Klimov, Luis L S´ anchez-Soto, and Gerd Leuchs. Stars of the quantum universe: Ex- tremal quantum states defined by the Majorana rep- resentation.Physical Review A, 92(3):031801, 2015

    2015

  59. [59]

    Bogomolny, O

    E. Bogomolny, O. Bohigas, and P. Leboeuf. Quantum chaotic dynamics and random polynomials.Journal of Statistical Physics, 85(5):639–679, 1996

    1996

  60. [60]

    Ex- act spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections.Phys- ical Review E, 78(2):021106, 2008

    Pedro Ribeiro, Julien Vidal, and R´ emy Mosseri. Ex- act spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections.Phys- ical Review E, 78(2):021106, 2008

    2008

  61. [61]

    On distributions in representation space.Sov

    RL Stratonovich. On distributions in representation space.Sov. Phys. JETP, 4(6):891–898, 1956

    1956

  62. [62]

    Wigner distribution of a general angular-momentum state: Applications to a collection of two-level atoms.Physical Review A, 49(5):4101, 1994

    Jonathan P Dowling, Girish S Agarwal, and Wolf- gang P Schleich. Wigner distribution of a general angular-momentum state: Applications to a collection of two-level atoms.Physical Review A, 49(5):4101, 1994

    1994

  63. [63]

    Negativity of the Wigner function as an indicator of non-classicality

    Anatole Kenfack and Karol ˙Zyczkowski. Negativity of the Wigner function as an indicator of non-classicality. Journal of Optics B: Quantum and Semiclassical Op- 47 tics, 6(10):396, 2004

    2004

  64. [64]

    On a Hilbert space of analytic functions and an associated integral transform part I

    Valentine Bargmann. On a Hilbert space of analytic functions and an associated integral transform part I. Communications on Pure and Applied Mathematics, 14(3):187–214, 1961

    1961

  65. [65]

    Permutationally invariant quantum tomogra- phy.Phys

    G´ eza T´ oth, Witlef Wieczorek, David Gross, Roland Krischek, Christian Schwemmer, and Harald Wein- furter. Permutationally invariant quantum tomogra- phy.Phys. Rev. Lett., 105:250403, Dec 2010

    2010

  66. [66]

    Three-tangle of a general three-qubit state in the representation of ma- jorana stars.Phys

    Chon-Fai Kam and Ren-Bao Liu. Three-tangle of a general three-qubit state in the representation of ma- jorana stars.Phys. Rev. A, 101:032318, Mar 2020

    2020

  67. [67]

    Three-axis spin squeezed states asso- ciated with excited-state quantum phase transitions

    Chon-Fai Kam. Three-axis spin squeezed states asso- ciated with excited-state quantum phase transitions. arXiv preprint arXiv:2512.24472, 2025

    work page arXiv 2025

  68. [68]

    Classical optical analogues of excited- state quantum phase transitions in a squeezing- enhanced generalized lipkin–meshkov–glick model

    Chon-Fai Kam. Classical optical analogues of excited- state quantum phase transitions in a squeezing- enhanced generalized lipkin–meshkov–glick model. Optics Communications, page 132910, 2026

    2026

  69. [69]

    Quantal phase factors accom- panying adiabatic changes.Proceedings of the Royal Society of London

    Michael Victor Berry. Quantal phase factors accom- panying adiabatic changes.Proceedings of the Royal Society of London. A. Mathematical and Physical Sci- ences, 392(1802):45–57, 1984

    1984

  70. [70]

    Berry phases of higher spins due to internal geometry of majorana con- stellation and relation to quantum entanglement.New Journal of Physics, 23(7):073020, 2021

    Chon-Fai Kam and Ren-Bao Liu. Berry phases of higher spins due to internal geometry of majorana con- stellation and relation to quantum entanglement.New Journal of Physics, 23(7):073020, 2021

    2021

  71. [71]

    Matrix per- manent and quantum entanglement of permutation invariant states.Journal of Mathematical Physics, 51(9):092203, 2010

    Tzu-Chieh Wei and Simone Severini. Matrix per- manent and quantum entanglement of permutation invariant states.Journal of Mathematical Physics, 51(9):092203, 2010

    2010

  72. [72]

    Angle variable holonomy in adia- batic excursion of an integrable hamiltonian.Journal of Physics A: Mathematical and General, 18(2):221, 1985

    John H Hannay. Angle variable holonomy in adia- batic excursion of an integrable hamiltonian.Journal of Physics A: Mathematical and General, 18(2):221, 1985

    1985

  73. [73]

    2+ 1 dimensional de sitter universe emerging from the gauge structure of a nonlinear quantum system.Scientific reports, 7(1):9756, 2017

    Chon-Fai Kam and Ren-Bao Liu. 2+ 1 dimensional de sitter universe emerging from the gauge structure of a nonlinear quantum system.Scientific reports, 7(1):9756, 2017

    2017

  74. [74]

    Quantum-enhanced measurements: beating the standard quantum limit.Science, 306(5700):1330– 1336, 2004

    Vittorio Giovannetti, Seth Lloyd, and Lorenzo Mac- cone. Quantum-enhanced measurements: beating the standard quantum limit.Science, 306(5700):1330– 1336, 2004

    2004

  75. [75]

    Quantum metrology with nonclassical states of atomic ensem- bles.Reviews of Modern Physics, 90(3):035005, 2018

    Luca Pezz` e, Augusto Smerzi, Markus K Oberthaler, Roman Schmied, and Philipp Treutlein. Quantum metrology with nonclassical states of atomic ensem- bles.Reviews of Modern Physics, 90(3):035005, 2018

    2018

  76. [76]

    Statistical distance and the geometry of quantum states.Physical Review Letters, 72(22):3439, 1994

    Samuel L Braunstein and Carlton M Caves. Statistical distance and the geometry of quantum states.Physical Review Letters, 72(22):3439, 1994

    1994

  77. [77]

    Spin squeezing and re- duced quantum noise in spectroscopy.Physical Review A, 46(11):R6797, 1992

    David J Wineland, John J Bollinger, Wayne M Itano, FL Moore, and DJ Heinzen. Spin squeezing and re- duced quantum noise in spectroscopy.Physical Review A, 46(11):R6797, 1992

    1992

  78. [78]

    Quantum spin squeezing.Physics Reports, 509(2- 3):89–165, 2011

    Jian Ma, Xiaoguang Wang, CP Sun, and Franco Nori. Quantum spin squeezing.Physics Reports, 509(2- 3):89–165, 2011

    2011

  79. [79]

    Distributing many points on a sphere.The mathematical intelli- gencer, 19(1):5–11, 1997

    Edward B Saff and Arno BJ Kuijlaars. Distributing many points on a sphere.The mathematical intelli- gencer, 19(1):5–11, 1997

    1997

  80. [80]

    Multiqubit symmetric states with high geo- metric entanglement.Physical Review A, 81(6):062347, 2010

    J Martin, O Giraud, PA Braun, D Braun, and T Bastin. Multiqubit symmetric states with high geo- metric entanglement.Physical Review A, 81(6):062347, 2010

    2010

Showing first 80 references.