Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Nonclassicality of a macroscopic qubit-ensemble via parity measurement induced disturbance

Lorenzo Braccini1,*, Debarshi Das2,†, Ben Zindorf1, Stephen D. Hogan1, John J. L. Morton3,4, and Sougato Bose1

  • *Contact author: lorenzo.braccini.18@ucl.ac.uk
  • †Contact author: dasdebarshi90@gmail.com

Phys. Rev. Research 8, 043092 – Published 26 October, 2026

DOI: https://doi.org/10.1103/kwpf-hm77

Abstract

We propose an experimental scheme to test the nonclassicality of a macroscopic ensemble of qubits through the violation of the classical notion of macrorealism (MR) via the fundamental measurement-induced disturbance of quantum systems. An electromagnetic resonator is used to probe the parity of the qubit ensemble. The action of sequential measurements allows the nonclassicality of the whole ensemble to manifest itself, in the ideal case, irrespective of its size. This enables to probe the macroscopic limits of quantum mechanics, as the qubit ensemble is, effectively, a single large spin of many ℏ units. Even as ℏ→0 in comparison to the total angular momentum of the ensemble, a constant amount of violation of MR is found in the noiseless case. However, environmental decoherence and inhomogeneity of qubit-electromagnetic field couplings precipitate the quantum-to-classical transition. This illustrates that Bohr's correspondence principle is not fundamental, but a consequence of practical limitations. We outline an implementation with a variety of qubits (superconducting qubits, spins in semiconductors, and Rydberg atoms) coupled to a coplanar waveguide resonator, and—via the corresponding noise analysis—find that violation of MR is detectable up to 100 qubits via current technology.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (120)

  1. V. Athalye, S. S. Roy, and T. S. Mahesh, Investigation of the Leggett-Garg inequality for precessing nuclear spins, Phys. Rev. Lett. 107, 130402 (2011).
  2. G. C. Knee, S. Simmons, E. M. Gauger, J. J. L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, K. M. Itoh, M. L. W. Thewalt, G. Andrew D. Briggs, and S. C. Benjamin, Violation of a Leggett–Garg inequality with ideal non-invasive measurements, Nat. Commun. 3, 606 (2012).
  3. A. Vaartjes, M. Nurizzo, L. H. Zaw, B. Wilhelm, X. Yu, D. Holmes, D. Schwienbacher, A. Kringhøj, M. R. van Blankenstein, A. M. Jakob, F. E. Hudson, K. M. Itoh, R. J. Murray, R. Blume-Kohout, N. Anand, and A. S. Dzurak, D. N. Jamieson, V. Scarani, and A. Morello, Certifying the quantumness of a nuclear spin qudit through its uniform precession, Newton 1, 100017 (2025).
  4. A. J. Leggett and A. Garg, Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? Phys. Rev. Lett. 54, 857 (1985).
  5. A. J. Leggett, Testing the limits of quantum mechanics: Motivation, state of play, prospects, J. Phys.: Condens. Matter 14, R415 (2002).
  6. A. J. Leggett, Realism and the physical world, Rep. Prog. Phys. 71, 022001 (2008).
  7. C. Emary, N. Lambert, and F. Nori, Leggett–Garg inequalities, Rep. Prog. Phys. 77, 016001 (2014).
  8. Also known as the no signaling in time condition [9].
  9. J. Kofler and C. Brukner, Condition for macroscopic realism beyond the Leggett-Garg inequalities, Phys. Rev. A 87, 052115 (2013).
  10. G. Schild and C. Emary, Maximum violations of the quantum-witness equality, Phys. Rev. A 92, 032101 (2015).
  11. G. C. Knee, K. Kakuyanagi, M.-C. Yeh, Y. Matsuzaki, H. Toida, H. Yamaguchi, S. Saito, A. J. Leggett, and W. J. Munro, A strict experimental test of macroscopic realism in a superconducting flux qubit, Nat. Commun. 7, 13253 (2016).
  12. D. Das, D. Home, H. Ulbricht, and S. Bose, Mass-independent scheme to test the quantumness of a massive object, Phys. Rev. Lett. 132, 030202 (2024).
  13. F. Hanif, D. Das, J. Halliwell, D. Home, A. Mazumdar, H. Ulbricht, and S. Bose, Testing whether gravity acts as a quantum entity when measured, Phys. Rev. Lett. 133, 180201 (2024).
  14. J. H. Wesenberg, A. Ardavan, G. A. D. Briggs, J. J. L. Morton, R. J. Schoelkopf, D. I. Schuster, and K. Mølmer, Quantum computing with an electron spin ensemble, Phys. Rev. Lett. 103, 070502 (2009).
  15. Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng, A. Dréau, J.-F. Roch, A. Auffeves, F. Jelezko, J. Wrachtrup, M. F. Barthe, P. Bergonzo, and D. Esteve, Strong coupling of a spin ensemble to a superconducting resonator, Phys. Rev. Lett. 105, 140502 (2010).
  16. J. Chen, A. A. Zadorozhko, and D. Konstantinov, Strong coupling of a two-dimensional electron ensemble to a single-mode cavity resonator, Phys. Rev. B 98, 235418 (2018).
  17. Y. Ping, E. M. Gauger, and S. C. Benjamin, Measurement-based quantum computing with a spin ensemble coupled to a stripline cavity, New J. Phys. 14, 013030 (2012).
  18. N. Mohseni, M. Narozniak, A. N. Pyrkov, V. Ivannikov, J. P. Dowling, and T. Byrnes, Error suppression in adiabatic quantum computing with qubit ensembles, npj Quantum Inf. 7, 71 (2021).
  19. F. Troiani, A. Ghirri, M. G. A. Paris, C. Bonizzoni, and M. Affronte, Towards quantum sensing with molecular spins, J. Magn. Magn. Mater. 491, 165534 (2019).
  20. H. Wu, S. Yang, M. Oxborrow, M. Jiang, Q. Zhao, D. Budker, B. Zhang, and J. Du, Enhanced quantum sensing with room-temperature solid-state masers, Sci. Adv. 8, 48 (2022).
  21. M. Schaffry, E. M. Gauger, J. J. L. Morton, J. Fitzsimons, S. C. Benjamin, and B. W. Lovett, Quantum metrology with molecular ensembles, Phys. Rev. A 82, 042114 (2010).
  22. H. Wu, R. E. George, J. H. Wesenberg, K. Mølmer, D. I. Schuster, R. J. Schoelkopf, K. M. Itoh, A. Ardavan, J. J. L. Morton, and G. A. D. Briggs, Storage of multiple coherent microwave excitations in an electron spin ensemble, Phys. Rev. Lett. 105, 140503 (2010).
  23. D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio, J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D. Awschalom, and R. J. Schoelkopf, High-cooperativity coupling of electron-spin ensembles to superconducting cavities, Phys. Rev. Lett. 105, 140501 (2010).
  24. Y. Kubo, C. Grezes, A. Dewes, T. Umeda, J. Isoya, H. Sumiya, N. Morishita, H. Abe, S. Onoda, T. Ohshima, V. Jacques, A. Dréau, J.-F. Roch, I. Diniz, A. Auffeves, D. Vion, D. Esteve, and P. Bertet, Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble, Phys. Rev. Lett. 107, 220501 (2011).
  25. X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S.-I. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond, Nature (London) 478, 221 (2011).
  26. R. Amsüss, C. Koller, T. Nöbauer, S. Putz, S. Rotter, K. Sandner, S. Schneider, M. Schramböck, G. Steinhauser, H. Ritsch, J. Schmiedmayer, and J. Majer, Cavity QED with magnetically coupled collective spin states, Phys. Rev. Lett. 107, 060502 (2011).
  27. J. H. Wesenberg, Z. Kurucz, and K. Mølmer, Dynamics of the collective modes of an inhomogeneous spin ensemble in a cavity, Phys. Rev. A 83, 023826 (2011).
  28. S. Saito, X. Zhu, R. Amsüss, Y. Matsuzaki, K. Kakuyanagi, T. Shimo-Oka, N. Mizuochi, K. Nemoto, W. J. Munro, and K. Semba, Towards realizing a quantum memory for a superconducting qubit: Storage and retrieval of quantum states, Phys. Rev. Lett. 111, 107008 (2013).
  29. V. Ranjan, G. de Lange, R. Schutjens, T. Debelhoir, J. P. Groen, D. Szombati, D. J. Thoen, T. M. Klapwijk, R. Hanson, and L. DiCarlo, Probing dynamics of an electron-spin ensemble via a superconducting resonator, Phys. Rev. Lett. 110, 067004 (2013).
  30. S. Probst, H. Rotzinger, S. Wünsch, P. Jung, M. Jerger, M. Siegel, A. V. Ustinov, and P. A. Bushev, Anisotropic rare-earth spin ensemble strongly coupled to a superconducting resonator, Phys. Rev. Lett. 110, 157001 (2013).
  31. B. Julsgaard and K. Mølmer, Fundamental limitations in spin-ensemble quantum memories for cavity fields, Phys. Rev. A 88, 062324 (2013).
  32. C. Grezes, B. Julsgaard, Y. Kubo, M. Stern, T. Umeda, J. Isoya, H. Sumiya, H. Abe, S. Onoda, T. Ohshima, V. Jacques, J. Esteve, D. Vion, D. Esteve, K. Mølmer, and P. Bertet, Multimode storage and retrieval of microwave fields in a spin ensemble, Phys. Rev. X 4, 021049 (2014).
  33. Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, Hybridizing ferromagnetic magnons and microwave photons in the quantum limit, Phys. Rev. Lett. 113, 083603 (2014).
  34. C. Grezes, B. Julsgaard, Y. Kubo, W. L. Ma, M. Stern, A. Bienfait, K. Nakamura, J. Isoya, S. Onoda, T. Ohshima, V. Jacques, D. Vion, D. Esteve, R. B. Liu, K. Mølmer, and P. Bertet, Storage and retrieval of microwave fields at the single-photon level in a spin ensemble, Phys. Rev. A 92, 020301(R) (2015).
  35. C. Grezes, Y. Kubo, B. Julsgaard, T. Umeda, J. Isoya, H. Sumiya, H. Abe, S. Onoda, T. Ohshima, K. Nakamura, I. Diniz, A. Auffeves, V. Jacques, J.-F. Roch, D. Vion, D. Esteve, K. Moelmer, and P. Bertet, Towards a spin-ensemble quantum memory for superconducting qubits, C. R. Phys. 17, 693 (2016).
  36. J. J. L. Morton and P. Bertet, Storing quantum information in spins and high-sensitivity ESR, J. Magn. Reson. 287, 128 (2018).
  37. J. O'Sullivan, O. W. Kennedy, K. Debnath, J. Alexander, C. W. Zollitsch, M. Šimėnas, A. Hashim, C. N. Thomas, S. Withington, I. Siddiqi, K. Mølmer, and J. J. Morton, Random-access quantum memory using chirped pulse phase encoding, Phys. Rev. X 12, 041014 (2022).
  38. M. H. Appel, A. Ghorbal, N. Shofer, L. Zaporski, S. Manna, S. F. C. da Silva, U. Haeusler, C. Le Gall, A. Rastelli, D. A. Gangloff, and M. Atatüre, Many-body quantum register for a spin qubit, Nat. Phys. 21, 368 (2025).
  39. S. Simmons, R. M. Brown, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, M. L. W. Thewalt, K. M. Itoh, and J. J. L. Morton, Entanglement in a solid-state spin ensemble, Nature (London) 470, 69 (2011).
  40. M. Zhong, M. P. Hedges, R. L. Ahlefeldt, J. G. Bartholomew, S. E. Beavan, S. M. Wittig, J. J. Longdell, and M. J. Sellars, Optically addressable nuclear spins in a solid with a six-hour coherence time, Nature (London) 517, 177 (2015).
  41. A. Bourassa, C. P. Anderson, K. C. Miao, M. Onizhuk, H. Ma, A. L. Crook, H. Abe, J. Ul-Hassan, T. Ohshima, N. T. Son, G. Galli, and D. D. Awschalom, Entanglement and control of single nuclear spins in isotopically engineered silicon carbide, Nat. Mater. 19, 1319 (2020).
  42. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).
  43. S. Sadana, L. Maccone, and U. Sinha, Testing quantum foundations with quantum computers, Phys. Rev. Res. 4, L022001 (2022).
  44. K. Joarder, D. Saha, D. Home, and U. Sinha, Loophole-free interferometric test of macrorealism using heralded single photons, PRX Quantum 3, 010307 (2022).
  45. S. Sadana, L. Maccone, and U. Sinha, Noise analysis for the Sorkin and Peres tests performed on a quantum computer, Quantum Inf. Process. 22, 317 (2023).
  46. P. P. Nath, D. Saha, D. Home, and U. Sinha, Single-system-based generation of certified randomness using Leggett-Garg inequality, Phys. Rev. Lett. 133, 020802 (2024).
  47. N. Gisin and A. Peres, Maximal violation of Bell's inequality for arbitrarily large spin, Phys. Lett. A 162, 15 (1992).
  48. A. Peres, Finite violation of a Bell inequality for arbitrarily large spin, Phys. Rev. A 46, 4413 (1992).
  49. D. Home and A. S. Majumdar, Incompatibility between quantum mechanics and classical realism in the “strong” macroscopic limit, Phys. Rev. A 52, 4959 (1995).
  50. A. Cabello, Bell's inequality for n spin-s particles, Phys. Rev. A 65, 062105 (2002).
  51. J. Kofler and C. Brukner, Classical world arising out of quantum physics under the restriction of coarse-grained measurements, Phys. Rev. Lett. 99, 180403 (2007).
  52. J. Kofler and C. Brukner, Conditions for quantum violation of macroscopic realism, Phys. Rev. Lett. 101, 090403 (2008).
  53. C. Budroni, T. Moroder, M. Kleinmann, and O. Gühne, Bounding temporal quantum correlations, Phys. Rev. Lett. 111, 020403 (2013).
  54. H. Jeong, Y. Lim, and M. S. Kim, Coarsening measurement references and the quantum-to-classical transition, Phys. Rev. Lett. 112, 010402 (2014).
  55. C. Budroni and C. Emary, Temporal quantum correlations and Leggett-Garg inequalities in multilevel systems, Phys. Rev. Lett. 113, 050401 (2014).
  56. S. Mal and A. S. Majumdar, Optimal violation of the Leggett-Garg inequality for arbitrary spin and emergence of classicality through unsharp measurements, Phys. Lett. A 380, 2265 (2016).
  57. S. Mal, D. Das, and D. Home, Quantum mechanical violation of macrorealism for large spin and its robustness against coarse-grained measurements, Phys. Rev. A 94, 062117 (2016).
  58. S. Mukherjee, A. Rudra, D. Das, S. Mal, and D. Home, Persistence of quantum violation of macrorealism for large spins even under coarsening of measurement times, Phys. Rev. A 100, 042114 (2019).
  59. S. Hill, R. S. Edwards, N. Aliaga-Alcalde, and G. Christou, Quantum coherence in an exchange-coupled dimer of single-molecule magnets, Science 302, 1015 (2003).
  60. E. del Barco, N. Vernier, J. M. Hernandez, J. Tejada, E. M. Chudnovsky, E. Molins, and G. Bellessa, Quantum coherence in Fe8 molecular nanomagnets, Europhys. Lett. 47, 722 (1999).
  61. E. del Barco, J. M. Hernandez, J. Tejada, N. Biskup, R. Achey, I. Rutel, N. Dalal, and J. Brooks, High-frequency resonant experiments in Fe8 molecular clusters, Phys. Rev. B 62, 3018 (2000).
  62. D. D. Awschalom, D. P. DiVincenzo, and J. F. Smyth, Macroscopic quantum effects in nanometer-scale magnets, Science 258, 414 (1992).
  63. D. D. Awschalom, J. F. Smyth, G. Grinstein, D. P. DiVincenzo, and D. Loss, Macroscopic quantum tunneling in magnetic proteins, Phys. Rev. Lett. 68, 3092 (1992).
  64. S. Gider, D. D. Awschalom, T. Douglas, S. Mann, and M. Chaparala, Classical and quantum magnetic phenomena in natural and artificial ferritin proteins, Science 268, 77 (1995).
  65. H. W. Lau, Z. Dutton, T. Wang, and C. Simon, Proposal for the creation and optical detection of spin cat states in Bose-Einstein condensates, Phys. Rev. Lett. 113, 090401 (2014).
  66. P. Gupta, A. Vaartjes, X. Yu, A. Morello, and B. C. Sanders, Robust macroscopic Schrödinger's cat on a nucleus, Phys. Rev. Res. 6, 013101 (2024).
  67. C. M. Ramsey, E. del Barco, S. Hill, S. J. Shah, C. C. Beedle, and D. N. Hendrickson, Quantum interference of tunnel trajectories between states of different spin length in a dimeric molecular nanomagnet, Nat. Phys. 4, 277 (2008).
  68. Z.-L. Xiang, S. Ashhab, J. Q. You, and F. Nori, Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems, Rev. Mod. Phys. 85, 623 (2013).
  69. A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, Quantum-information processing with circuit quantum electrodynamics, Phys. Rev. A 75, 032329 (2007).
  70. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature (London) 431, 162 (2004).
  71. I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, Coherent dynamics of a flux qubit coupled to a harmonic oscillator, Nature (London) 431, 159 (2004).
  72. N. Samkharadze, G. Zheng, N. Kalhor, D. Brousse, A. Sammak, U. C. Mendes, A. Blais, G. Scappucci, and L. M. K. Vandersypen, Strong spin-photon coupling in silicon, Science 359, 1123 (2018).
  73. X. Mi, M. Benito, S. Putz, D. M. Zajac, J. M. Taylor, G. Burkard, and J. R. Petta, A coherent spin–photon interface in silicon, Nature (London) 555, 599 (2018).
  74. A. J. Landig, J. V. Koski, P. Scarlino, U. C. Mendes, A. Blais, C. Reichl, W. Wegscheider, A. Wallraff, K. Ensslin, and T. Ihn, Coherent spin–photon coupling using a resonant exchange qubit, Nature (London) 560, 179 (2018).
  75. A. A. Morgan and S. D. Hogan, Coupling Rydberg atoms to microwave fields in a superconducting coplanar waveguide resonator, Phys. Rev. Lett. 124, 193604 (2020).
  76. J. De Santis, B. Dura-Kovács, M. Öncü, A. Bouscal, D. Vasileiadis, and J. Zeiher, Realization of a cavity-coupled Rydberg array, arXiv:2602.12152.
  77. J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Coupling superconducting qubits via a cavity bus, Nature (London) 449, 443 (2007).
  78. J. D. Pritchard, J. A. Isaacs, M. A. Beck, R. McDermott, and M. Saffman, Hybrid atom-photon quantum gate in a superconducting microwave resonator, Phys. Rev. A 89, 010301(R) (2014).
  79. R. Ruskov and A. N. Korotkov, Entanglement of solid-state qubits by measurement, Phys. Rev. B 67, 241305(R) (2003).
  80. K. Lalumière, J. M. Gambetta, and A. Blais, Tunable joint measurements in the dispersive regime of cavity QED, Phys. Rev. A 81, 040301(R) (2010).
  81. N. Roch, M.E. Schwartz, F. Motzoi, C. Macklin, R. Vijay, A.W. Eddins, A.N. Korotkov, K.B. Whaley, M. Sarovar, and I. Siddiqi, Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits, Phys. Rev. Lett. 112, 170501 (2014).
  82. R. L. Delva, J. Mielke, G. Burkard, and J. R. Petta, Measurement-based entanglement of semiconductor spin qubits, Phys. Rev. B 110, 035304 (2024).
  83. C. Budroni, G. Vitagliano, G. Colangelo, R. J. Sewell, O. Gühne, G. Tóth, and M. W. Mitchell, Quantum nondemolition measurement enables macroscopic Leggett-Garg tests, Phys. Rev. Lett. 115, 200403 (2015).
  84. L. Rosales-Zárate, B. Opanchuk, Q. Y. He, and M. D. Reid, Leggett-Garg tests of macrorealism for bosonic systems including double-well Bose-Einstein condensates and atom interferometers, Phys. Rev. A 97, 042114 (2018).
  85. G. Vitagliano and C. Budroni, Leggett-Garg macrorealism and temporal correlations, Phys. Rev. A 107, 040101 (2023).
  86. B. Zindorf, L. Braccini, D. Das, and S. Bose, How “quantum” is your quantum computer? Macrorealism-based benchmarking via mid-circuit parity measurements, arXiv:2511.15881.
  87. Increasing by 1 order of magnitude the best known results of detection of violation of MR on QCs [89, 91, 92, 93, 94].
  88. In a many-world interpretation, when reading out the outcome of a measurement, the target-probe entangles with the rest of the world, under a unitary that cannot be reversed.
  89. E. Huffman and A. Mizel, Violation of noninvasive macrorealism by a superconducting qubit: Implementation of a Leggett-Garg test that addresses the clumsiness loophole, Phys. Rev. A 95, 032131 (2017).
  90. The single measurement part refers to the case when the final measurement is performed without the first measurement described in Sec.  2c. On the other hand, the double measurement part is the case when the first and final measurements are performed.
  91. H.-Y. Ku, N. Lambert, F.-J. Chan, C. Emary, Y.-N. Chen, and F. Nori, Experimental test of non-macrorealistic cat states in the cloud, npj Quantum Inf. 6, 98 (2020).
  92. A. Santini and V. Vitale, Experimental violations of Leggett-Garg inequalities on a quantum computer, Phys. Rev. A 105, 032610 (2022).
  93. P. P. Nath, A. Sinha, and U. Sinha, Certified random number generation using quantum computers, Front. Quantum Sci. Technol. 4, 1661544 (2025).
  94. D. Melegari, M. Cardi, and P. Solinas, Quantum simulations of macrorealism violation via the QNDM protocol, arXiv:2502.17040.
  95. A. D. Greentree, J. Koch, and J. Larson, Fifty years of Jaynes–Cummings physics, J. Phys. B: At. Mol. Opt. Phys. 46, 220201 (2013).
  96. R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954).
  97. J. Schliemann, Coherent quantum dynamics: What fluctuations can tell, Phys. Rev. A 92, 022108 (2015).
  98. Z.-Q. Wang, Y.-P. Wang, J. Yao, R.-C. Shen, W.-J. Wu, J. Qian, J. Li, S.-Y. Zhu, and J. Q. You, Giant spin ensembles in waveguide magnonics, Nat. Commun. 13, 7580 (2022).
  99. J. Ma, X. Wang, C. P. Sun, and F. Nori, Quantum spin squeezing, Phys. Rep. 509, 89 (2011).
  100. M. Tavis and T. Cummings, Exact solution for an N -molecule—Radiation-field Hamiltonian, Phys. Rev. 170, 379 (1968).
  101. A CS is defined as the quantum state describing the displacement vacuum |α〉=eαa†−α*a|0〉, with α=∈C. A CS is the eigenstate of the annihilation operator, a|α〉=α|α〉, and, in the n-basis representation, takes the form |α〉=e−12|α|2∑n(α)n/n!|n〉. They form an overcomplete basis.
  102. A. Ferraro, S. Olivares, and M. G. A. Paris, Gaussian states in continuous variable quantum information, arXiv:quant-ph/0503237.
  103. M. Schlosshauer, Decoherence and the Quantum-To-Classical Transition (Springer International Publishing, Heidelberg, Germany, 2007).
  104. F. Bibak, C. Cepollaro, N. M. Sánchez, B. Dakić, and Č. Brukner, The classical limit of quantum mechanics through coarse-grained measurements, arXiv:2503.15642.
  105. M. Wilde and A. Mizel, Addressing the clumsiness loophole in a Leggett-Garg test of macrorealism, Found. Phys. 42, 256 (2012).
  106. C. Robens, W. Alt, D. Meschede, C. Emary, and A. Alberti, Ideal negative measurements in quantum walks disprove theories based on classical trajectories, Phys. Rev. X 5, 011003 (2015).
  107. S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroš, M. Paternostro, A. A. Geraci, P. F. Barker, M. S. Kim, and G. Milburn, Spin entanglement witness for quantum gravity, Phys. Rev. Lett. 119, 240401 (2017).
  108. Y. Margalit, O. Dobkowski, Z. Zhou, O. Amit, Y. Japha, S. Moukouri, D. Rohrlich, A. Mazumdar, S. Bose, C. Henkel, and R. Folman, Realization of a complete Stern-Gerlach interferometer: Toward a test of quantum gravity, Sci. Adv. 7, eabg2879 (2021).
  109. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, Generating optical Schrödinger kittens for quantum information processing, Science 312, 83 (2006).
  110. A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, Generation of optical ‘Schrödinger cats' from photon number states, Nature (London) 448, 784 (2007).
  111. B. D'Anjou and G. Burkard, Optimal dispersive readout of a spin qubit with a microwave resonator, Phys. Rev. B 100, 245427 (2019).
  112. J. Kang, C. Kim, Y. Kim, and Y. Kwon, New design of three-qubit system with three transmons and a single fixed-frequency resonator coupler, Sci. Rep. 15, 12134 (2025).
  113. R. E. Collin, Foundation of Microwave Engineering, IEEE Press Series on Electromagnetic Wave Theory (Wiley-IEEE Press, Hoboken, New Jersey, 2023).
  114. M. Göppl, A. Fragner, M. Baur, R. Bianchetti, S. Filipp, J. M. Fink, P. J. Leek, G. Puebla, L. Steffen, and A. Wallraff, Coplanar waveguide resonators for circuit quantum electrodynamics, J. Appl. Phys. 104, 113904 (2008).
  115. A. Megrant, C. Neill, R. Barends, B. Chiaro, Y. Chen, L. Feigl, J. Kelly, E. Lucero, M. Mariantoni, P. J. J. O'Malley, D. Sank, A. Vainsencher, J. Wenner, T. C. White, Y. Yin, J. Zhao, C. J. Palmstrøm, J. M. Martinis, and A. N. Cleland, Planar superconducting resonators with internal quality factors above one million, Appl. Phys. Lett. 100, 113510 (2012).
  116. B. Zeng, D. L. Zhou, and L. You, Measuring the parity of an N-qubit state, Phys. Rev. Lett. 95, 110502 (2005).
  117. A. Kolli, B. W. Lovett, S. C. Benjamin, and T. M. Stace, All-optical measurement-based quantum-information processing in quantum dots, Phys. Rev. Lett. 97, 250504 (2006).
  118. D. Ristè, M. Dukalski, C. A. Watson, G. de Lange, M. J. Tiggelman, Y. M. Blanter, K. W. Lehnert, R. N. Schouten, and L. DiCarlo, Deterministic entanglement of superconducting qubits by parity measurement and feedback, Nature (London) 502, 350 (2013).
  119. R. J. Birrittella, P. M. Alsing, and C. C. Gerry, The parity operator: Applications in quantum metrology, AVS Quantum Sci. 3, 014701 (2021).
  120. D. F. Walls and G. J. Milburn, Effect of dissipation on quantum coherence, Phys. Rev. A 31, 2403 (1985).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation