Papers
Topics
Authors
Recent
2000 character limit reached

Inherent quantum resources in stationary spin chains (2405.16974v4)

Published 27 May 2024 in quant-ph and cond-mat.quant-gas

Abstract: The standard way to generate many-body quantum correlations is via a dynamical protocol: an initial product state is transformed by interactions that generate non-classical correlations at later times. Here, we show that many-body Bell correlations are inherently present in the eigenstates of a variety of spin-1/2 chains. In particular, we show that the eigenstates and thermal states of the collective Lipkin-Meshkov-Glick model possess many-body Bell correlations. We demonstrate that the Bell correlations can take on quantized values that change discontinuously with variations in the total magnetization. Finally, we show that these many-body Bell correlations persist even in the presence of both diagonal and off-diagonal disorder.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (47)
  1. A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777 (1935).
  2. E. Schrödinger, Die gegenwärtige Situation in der Quantenmechanik, Naturwissenschaften 23, 807 (1935).
  3. J. S. Bell, On the einstein podolsky rosen paradox, Physics 1, 195 (1964).
  4. I. Frérot, M. Fadel, and M. Lewenstein, Probing quantum correlations in many-body systems: a review of scalable methods, Reports on Progress in Physics 86, 114001 (2023).
  5. A. Tavakoli, Semi-device-independent certification of independent quantum state and measurement devices, Phys. Rev. Lett. 125, 150503 (2020).
  6. J. Fraxanet, T. Salamon, and M. Lewenstein, The coming decades of quantum simulation (2022).
  7. H.-Y. Huang, J. Preskill, and M. Soleimanifar, Certifying almost all quantum states with few single-qubit measurements (2024), arXiv:2404.07281 [quant-ph] .
  8. M. Kliesch and I. Roth, Theory of quantum system certification, PRX Quantum 2, 010201 (2021).
  9. M. Kitagawa and M. Ueda, Squeezed spin states, Phys. Rev. A 47, 5138 (1993).
  10. J. K. Korbicz, J. I. Cirac, and M. Lewenstein, Spin squeezing inequalities and entanglement of n𝑛nitalic_n qubit states, Phys. Rev. Lett. 95, 120502 (2005).
  11. H. Lipkin, N. Meshkov, and A. Glick, Validity of many-body approximation methods for a solvable model: (i). exact solutions and perturbation theory, Nuclear Physics 62, 188 (1965).
  12. N. Meshkov, A. Glick, and H. Lipkin, Validity of many-body approximation methods for a solvable model: (ii). linearization procedures, Nuclear Physics 62, 199 (1965).
  13. A. Glick, H. Lipkin, and N. Meshkov, Validity of many-body approximation methods for a solvable model: (iii). diagram summations, Nuclear Physics 62, 211 (1965).
  14. R. Botet, R. Jullien, and P. Pfeuty, Size scaling for infinitely coordinated systems, Phys. Rev. Lett. 49, 478 (1982).
  15. S. Lerma-H and J. Dukelsky, The lipkin-meshkov-glick model from the perspective of the su(1,1) richardson-gaudin models, Journal of Physics: Conference Series 492, 012013 (2014).
  16. R. Botet and R. Jullien, Large-size critical behavior of infinitely coordinated systems, Phys. Rev. B 28, 3955 (1983).
  17. Y. Huang, T. Li, and Z.-q. Yin, Symmetry-breaking dynamics of the finite-size lipkin-meshkov-glick model near ground state, Phys. Rev. A 97, 012115 (2018a).
  18. K. Hammam, G. Manzano, and G. De Chiara, Quantum coherence enables hybrid multitask and multisource regimes in autonomous thermal machines, Phys. Rev. Res. 6, 013310 (2024).
  19. X. He, J. He, and J. Zheng, Thermal entangled quantum heat engine, Physica A: Statistical Mechanics and its Applications 391, 6594 (2012).
  20. Y.-H. Ma, S.-H. Su, and C.-P. Sun, Quantum thermodynamic cycle with quantum phase transition, Phys. Rev. E 96, 022143 (2017).
  21. M. Łobejko, P. Mazurek, and M. Horodecki, Thermodynamics of Minimal Coupling Quantum Heat Engines, Quantum 4, 375 (2020).
  22. S. Çakmak, M. Çandır, and F. Altintas, Construction of a quantum carnot heat engine cycle, Quantum Information Processing 19, 314 (2020).
  23. E. M. Centamori, M. Campisi, and V. Giovannetti, Spin-chain based quantum thermal machines (2023), arXiv:2303.15574 [quant-ph] .
  24. M. H. B. Chakour, A. E. Allati, and Y. Hassouni, Entangled quantum refrigerator based on two anisotropic spin-1/2 heisenberg xyz chain with dzyaloshinskii–moriya interaction, The European Physical Journal D 75, 42 (2021).
  25. L. A. Williamson and M. J. Davis, Many-body enhancement in a spin-chain quantum heat engine, Phys. Rev. B 109, 024310 (2024).
  26. J. Vidal, G. Palacios, and C. Aslangul, Entanglement dynamics in the lipkin-meshkov-glick model, Phys. Rev. A 70, 062304 (2004).
  27. R. Orús, S. Dusuel, and J. Vidal, Equivalence of critical scaling laws for many-body entanglement in the lipkin-meshkov-glick model, Phys. Rev. Lett. 101, 025701 (2008).
  28. A. Sen(De) and U. Sen, Entanglement mean field theory: Lipkin–meshkov–glick model, Quantum Information Processing 11, 675 (2012).
  29. C. Wang, Y.-Y. Zhang, and Q.-H. Chen, Quantum correlations in collective spin systems, Phys. Rev. A 85, 052112 (2012).
  30. S. M. Hengstenberg, C. E. P. Robin, and M. J. Savage, Multi-body entanglement and information rearrangement in nuclear many-body systems: a study of the lipkin–meshkov–glick model, The European Physical Journal A 59, 231 (2023).
  31. and, , and and, Thermal entanglement in lipkin—meshkov—glick model, Communications in Theoretical Physics 56, 61 (2011).
  32. L. Shao and L. Fu, Spin squeezing generated by the anisotropic central spin model, Phys. Rev. A 109, 052618 (2024).
  33. G. Chen, J. Q. Liang, and S. Jia, Interaction-induced lipkin-meshkov-glick model in a bose-einstein condensate inside an optical cavity, Opt. Express 17, 19682 (2009).
  34. J. Larson, Circuit qed scheme for the realization of the lipkin-meshkov-glick model, Europhysics Letters 90, 54001 (2010).
  35. L.-P. Yang and Z. Jacob, Engineering first-order quantum phase transitions for weak signal detection, Journal of Applied Physics 126, 174502 (2019), https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/1.5121558/15237507/174502_1_online.pdf .
  36. S. Morrison and A. S. Parkins, Dynamical quantum phase transitions in the dissipative lipkin-meshkov-glick model with proposed realization in optical cavity qed, Phys. Rev. Lett. 100, 040403 (2008).
  37. A. L. Grimsmo and A. S. Parkins, Dissipative dicke model with nonlinear atom–photon interaction, Journal of Physics B: Atomic, Molecular and Optical Physics 46, 224012 (2013).
  38. I. Hobday, P. Stevenson, and J. Benstead, Variance minimisation of the lipkin-meshkov-glick model on a quantum computer (2024), arXiv:2403.08625 [quant-ph] .
  39. M. Żukowski and Č. Brukner, Bell’s theorem for general n-qubit states, Phys. Rev. Lett. 88, 210401 (2002).
  40. A. Niezgoda, M. Panfil, and J. Chwedeńczuk, Quantum correlations in spin chains, Phys. Rev. A 102, 042206 (2020).
  41. A. Niezgoda and J. Chwedeńczuk, Many-body nonlocality as a resource for quantum-enhanced metrology, Phys. Rev. Lett. 126, 210506 (2021).
  42. J. Chwedenczuk, Many-body Bell inequalities for bosonic qubits, SciPost Phys. Core 5, 025 (2022).
  43. See [varshalovich1988quantum] for the details on the rotation matrices in the SU(2) group.
  44. D. A. Hamza and J. Chwedeńczuk, Bell correlations of a thermal fully-connected spin chain in a vicinity of a quantum critical point (2024), arXiv:2403.02383 [quant-ph] .
  45. O. Katz and C. Monroe, Programmable quantum simulations of bosonic systems with trapped ions, Phys. Rev. Lett. 131, 033604 (2023).
  46. O. Katz, M. Cetina, and C. Monroe, n𝑛nitalic_n-body interactions between trapped ion qubits via spin-dependent squeezing, Phys. Rev. Lett. 129, 063603 (2022).
  47. M. Gärttner, P. Hauke, and A. M. Rey, Relating out-of-time-order correlations to entanglement via multiple-quantum coherences, Phys. Rev. Lett. 120, 040402 (2018).
Citations (2)

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Collections

Sign up for free to add this paper to one or more collections.

Tweets

Sign up for free to view the 3 tweets with 0 likes about this paper.