Decoherence Challenges in Nanoscience: A Quantum Phase Space Perspective
DOI:
https://doi.org/10.25159/3005-2602/21974Keywords:
quantum decoherence, pointer states, quantum phase space, nanoscience, quantum technologiesAbstract
Quantum decoherence is both the fundamental mechanism underlying the quantum-to-classical transition and a major challenge for the development of scalable nanoscale quantum technologies. This work introduces a quantum phase space (QPS) framework that provides a unified geometric description of decoherence. The framework is based on a dual structure consisting of an overcomplete continuous frame of minimum-uncertainty states |〈z〉⟩ that defines the QPS geometry, and an orthonormal basis {|n, 〈z(t)〉⟩} that satisfies the strict mathematical requirements for decoherence within the objectivity criterion of the spectrum broadcast structure for pointer states. Within this framework, the variance–covariance matrix of the QPS ground states serves as a universal indicator of decoherence regimes; it is time-independent ( ) for Markovian (memoryless) dynamics, and time-dependent ) for non-Markovian dynamics with memory and information backflow. To illustrate the formalism, the Hu–Paz–Zhang master equation is generalised to include simultaneous position and momentum couplings to the environment, leading to a generalised non-Markovian master equation characterised by a spectral-density matrix. The corresponding evolution equations for the first moments (〈p(t)〉, 〈x(t)〉) and for the ground covariance matrix establish a direct connection between microscopic environmental properties, classical-like trajectories and the QPS geometry. In the Markovian limit, the QPS geometry becomes time-independent, formalising the concept that a stationary environment selects and freezes a specific set of quasi-classical trajectories. The non-Markovian regime naturally describes memory effects, information backflow, recoherence, and evolving deformations of the uncertainty ellipse. The proposed framework provides a unified theoretical foundation for modelling decoherence in nanoscale systems involving simultaneous position and momentum interactions with the environment, including nanoelectromechanical resonators, optomechanical systems, and superconducting quantum circuits. The QPS framework may therefore bridge fundamental theory and practical quantum engineering, offering a promising coherent pathway to understand, control and exploit decoherence at the nanoscience frontier.
References
[1] M. Schlosshauer, “Decoherence, the measurement problem, and interpretations of quantum mechanics,” Rev. Mod. Phys., vol. 76, pp. 1267–1305, Feb. 2005, doi: 10.1103/RevModPhys.76.1267.
[2] W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys., vol. 75, p. 715, doi: 10.1103/RevModPhys.75.715.
[3] M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition. Springer Science, 2007, doi: 10.1007/978-3-540-35775-9.
[4] R. T. Ranaivoson et al., “Highlighting relations between Wave-particle duality, Uncertainty principle, Phase space and Microstates,” arXiv:2205.08538 [quant-ph], doi: 10.48550/arXiv.2205.08538.
[5] J. A. Wheeler and W. H. Zurek, Quantum Theory and Measurement. Princeton University Press, 1983, doi: 10.1515/9781400854554.
[6] N. T. Manampisoa, R. T. Ranaivoson, R. Raboanary, R. Andriambololona, R. H. M. Ravelonjato and N. Rabesiranana, “Joint momenta-coordinates states as pointer states in quantum decoherence,” 2023, arXiv:2509.18206 [quant-ph], doi: 10.48550/arXiv.2509.18206.
[7] A. A. Tomaz, R. S. Mattos and M. Barbatti, “The quantum measurement problem: a review of recent trends,” Philos. Mag., pp. 1–38, Dec. 2025, doi: 10.1080/14786435.2025.2601922.
[8] E. B. Karlsson, “The Quantum Measurement Problem,” Quantum Rep., vol. 7, no. 2, p. 28, Jun. 2025, doi: 10.3390/quantum7020028.
[9] H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems. Oxford University Press, 2007, doi: 10.1093/acprof:oso/9780199213900.001.0001.
[10] H. R. Naeij, “Open quantum system approaches to superconducting qubits,” Quantum Inf. Process., vol. 24, p. 220, Jul. 2025, doi: 10.1007/s11128-025-04838-y.
[11] M. Onizhuk and G. Galli, “Colloquium: Decoherence of solid-state spin qubits: A computational perspective,” Rev. Mod. Phys., vol. 97, p. 021001, Apr. 2025, doi: 10.1103/RevModPhys.97.021001.
[12] T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe and J. L. O’Brien, “Quantum computers,” Nature, vol. 464, pp. 45–53, Mar. 2010, doi: 10.1038/nature08812.
[13] Y.-W. Lu, W. Li and X.-H. Wang, “Quantum and Classical Exceptional Points at the Nanoscale: Properties and Applications,” ACS Nano, vol. 19, no. 19, pp. 17953–17978, May 2025, doi: 10.1021/acsnano.4c15648.
[14] A. M. Tyryshkin et al., “Electron spin coherence exceeding seconds in high-purity silicon,” Nature Mater., vol. 11, pp. 143–147, Dec. 2011, doi: 10.1038/nmat3182.
[15] A. J. Heinrich et al., “Quantum-coherent nanoscience,” Nature Nanotechnol., vol. 16, pp. 1318–1329, Nov. 2021, doi: 10.1038/s41565-021-00994-1.
[16] R. Andriambololona, “Mécanique Quantique,” Collection Livres Interdisciplines Raoelina Andriambololona ( LIRA ) Laboratoire de Physique Nucléaire et de Physique Appliquée (LPNPA), Université de Madagascar, 1990.
[17] W. H. Zurek, “Decoherence and the Transition from Quantum to Classical,” Physics Today, vol. 44, no. 10, pp. 36–44, Oct. 1991, doi: 10.1063/1.881293.
[18] C. A. Brasil and L. A. de Castro, “Understanding the pointer states,” Eur. J. Phys., vol. 36, no. 6, p. 065024, Sept. 2015, doi: 10.1088/0143-0807/36/6/065024.
[19] P. Duruisseau, A. Touil and S. Deffner, “Pointer States and Quantum Darwinism with Two-Body Interactions,” Entropy, vol. 25, no. 12, p. 1573, Nov. 2023, doi: 10.3390/e25121573.
[20] D. A. Chisholm, G. M. Palma and L. Innocenti, “Emergence of quantum Darwinism and pointer states for noncommuting evolutions,” APS Open Sci., vol. 1, p. 000024, May 2026, doi: 10.1103/75jr-ltct.
[21] W. H. Zurek, “Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons,” Entropy, vol. 24, no. 11, p. 1520, Oct. 2022, doi: 10.3390/e24111520.
[22] A. Feller, G. Coeurét Cauquil and B. Roussel, “Einselection from incompatible decoherence channels,” Phys. Rev. A, vol. 101, p. 062107, Jun. 2020, doi: 10.1103/PhysRevA.101.062107.
[23] W. H. Zurek, S. Habib and J. P. Paz, “Coherent states via decoherence,” Phys. Rev. Lett., vol. 70, pp. 1187–1190, Mar. 1993, doi: 10.1103/PhysRevLett.70.1187.
[24] W. H. Zurek, “Preferred States, Predictability, Classicality and the Environment-Induced Decoherence,” Prog. Theor. Phys., vol. 89, no. 2, pp. 281–312, Feb. 1993, doi: 10.1143/ptp/89.2.281.
[25] D. Dalvit, J. Dziarmaga and W. Zurek, “Predictability sieve, pointer states, and the classicality of quantum trajectories,” Phys. Rev. A, vol. 72, p. 062101, Dec. 2005, doi: 10.1103/PhysRevA.72.062101.
[26] W. H. Zurek, “Quantum Darwinism,” Nature Phys., vol. 5, pp. 181–188, Mar. 2009, doi: 10.1038/nphys1202.
[27] R. Horodecki, J. K. Korbicz and P. Horodecki, “Quantum origins of objectivity,” Phys. Rev. A, vol. 91, p. 032122, Mar. 2015, doi: 10.1103/PhysRevA.91.032122.
[28] J. K. Korbicz, “Roads to objectivity: Quantum Darwinism, Spectrum Broadcast Structures, and Strong quantum Darwinism – a review,” Quantum, vol. 5, p. 571, Nov. 2021, doi: 10.22331/q-2021-11-08-571.
[29] H.-P. Breuer, E.-M. Laine and J. Piilo, “Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems,” Phys. Rev. Lett., vol. 103, p. 210401, Nov. 2009, doi: 10.1103/PhysRevLett.103.210401.
[30] I. de Vega and D. Alonso, “Dynamics of non-Markovian open quantum systems,” Rev. Mod. Phys., vol. 89, p. 015001, Jan. 2017, doi: 10.1103/RevModPhys.89.015001.
[31] H.-P. Breuer, E.-M. Laine, J. Piilo and B. Vacchini, “Non-Markovian dynamics in open quantum systems,” Rev. Mod. Phys., vol. 88, p. 021002, Apr. 2016, doi: 10.1103/RevModPhys.88.021002.
[32] M. Malekakhlagh, A. Petrescu and H. E. Türeci, “Non-Markovian dynamics of a superconducting qubit in an open multimode resonator,” Phys. Rev. A, vol. 94, p. 063848, Dec. 2016, doi: 10.1103/PhysRevA.94.063848.
[33] T. Lacroix, B. W. Lovett and A. W. Chin, “From Non-Markovian Dissipation to Spatiotemporal Control of Quantum Nanodevices,” Quantum, vol. 8, p. 1305, Apr. 2024, doi: 10.22331/q-2024-04-03-1305.
[34] K. Brandner, “Dynamics of microscale and nanoscale systems in the weak-memory regime: A mathematical framework beyond the Markov approximation,” Phys. Rev. E, vol. 111, p. 014137, Jan. 2025, doi: 10.1103/PhysRevE.111.014137.
[35] M. Odeh et al., “Non-Markovian dynamics of a superconducting qubit in a phononic bandgap,” Nature Phys., vol. 21, pp. 406–411, Jan. 2025, doi: 10.1038/s41567-024-02740-5.
[36] R. T. Ranaivoson, R. Andriambololona, R. Hanitriarivo and R. H. M. Ravelonjato, “Invariant quadratic operators associated with linear canonical transformations and their eigenstates,” J. Phys. Commun., vol. 6, no. 9, p. 095010, doi: 10.1088/2399-6528/ac8520.
[37] R. H. M. Ravelonjato, R. T. Ranaivoson, R. Andriambololona, R. Raboanary, H. Rakotoson and N. Rabesiranana, “Quantum and Relativistic Corrections to Maxwell–Boltzmann Ideal Gas Model from a Quantum Phase Space Approach,” Found. Phys., vol. 53, p. 88, Oct. 2023, doi: 10.1007/s10701-023-00727-5.
[38] R. T. Ranaivoson, R. Andriambololona, H. Rakotoson, R. Raboanary, J. Rajaobelison and P. M. Randriantsoa, “Quantum phase space symmetry and sterile neutrinos,” J. Subat. Part. Cosmol., vol. 3, p. 100039, Jun. 2025, doi: 10.1016/j.jspc.2025.100039.
[39] T. G. Philbin, “Generalized coherent states,” Am. J. Phys., vol. 82, no. 8, pp. 742–748, Aug. 2014, doi: 10.1119/1.4876963.
[40] B. Bagchi, R. Ghosh and A. Khare, “A pedestrian introduction to coherent and squeezed states,” Int. J. Mod. Phys. A, vol. 35, no. 19, p. 2030011, 2020, doi: 10.1142/S0217751X20300112.
[41] V. V. Dodonov, “’Nonclassical’ states in quantum optics: a ‘squeezed’ review of the first 75 years,” J. Opt. B: Quantum Semiclass. Opt., vol. 4, no. 1, Jan. 2002, doi: 10.1088/1464-4266/4/1/201.
[42] Ó. Rosas-Ortiz, “Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations,” in Integrability, Supersymmetry and Coherent States. CRM Series in Mathematical Physics, S. Kuru, J. Negro and L. M. Nieto, Eds., Cham. Springer, 2019, pp. 187–230, doi: 10.1007/978-3-030-20087-9_7.
[43] S. Dey, A. Fring and V. Hussin, “A Squeezed Review on Coherent States and Nonclassicality for Non-Hermitian Systems with Minimal Length,” in Coherent States and Their Applications: A Contemporary Panorama, Springer Proceedings in Physics, vol. 205, 2018, pp. 209–242, doi: 10.1007/978-3-319-76732-1_11.
[44] B. L. Hu, J. P. Paz and Y. Zhang, “Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise,” Phys. Rev. D, vol. 45, pp. 2843–2861, Apr. 1992, doi: 10.1103/PhysRevD.45.2843.
[45] J. J. Halliwell and T. Yu, “Alternative derivation of the Hu-Paz-Zhang master equation of quantum Brownian motion,” Phys. Rev. D, vol. 53, pp. 2012–2019, Feb. 1996, doi: 10.1103/PhysRevD.53.2012.
[46] G. Homa, J. Z. Bernád and A. Csordás, “Analytical evaluation of the coefficients of the Hu-Paz-Zhang master equation: Ohmic spectral density, zero temperature, and consistency check,” Phys. Rev. A, vol. 108, p. 012210, Jul. 2023, doi: 10.1103/PhysRevA.108.012210.
[47] G. Homa, A. Csordás, M. A. Csirik and J. Z. Bernád, “Range of applicability of the Hu-Paz-Zhang master equation,” Phys. Rev. A, vol. 102, p. 022206, Aug. 2020, doi: 10.1103/PhysRevA.102.022206.
[48] K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum., vol. 76, no. 6, p. 061101, May 2005, doi: 10.1063/1.1927327.
[49] C. Seoánez, F. Guinea and A. H. Castro Neto, “Dissipation in graphene and nanotube resonators,” Phys. Rev. B, vol. 76, p. 125427, Sept. 2007, doi: 10.1103/PhysRevB.76.125427.
[50] J. Schäfer, B. A. Stickler and K. Hornberger, “Decoherence of dielectric particles by thermal emission,” Phys. Rev. Res., vol. 6, p. 043307, Dec. 2024, doi: 10.1103/PhysRevResearch.6.043307.
[51] S. A. Khan, A. A. Afroz and S. S. Ali, “Decoherence Impediments in Quantum Computing and Fundamental Challenges of Quantum Error Correction,” Asian J. Res. Comput. Sci., vol. 18, no. 12, pp. 228–239, Dec. 2025, doi: 10.9734/ajrcos/2025/v18i12800.
[52] T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong and Y. Hirayama, “Coherent manipulation of electronic states in a double quantum dot,” Phys. Rev. Lett., vol. 91, p. 226804, Nov. 2003, doi: 10.1103/PhysRevLett.91.226804.
[53] A. Ishizaki and G. R. Fleming, “Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: Reduced hierarchy equation approach,” J. Chem. Phys., vol. 130, p. 234111, Jun. 2009, doi: 10.1063/1.3155372.
[54] D. Suter and G. A. Álvarez, “Colloquium: Protecting quantum information against environmental noise,” Rev. Mod. Phys., vol. 88, p. 041001, Oct. 2016, doi: 10.1103/RevModPhys.88.041001.
[55] K.-T. Chiang and W.-M. Zhang, “Non-Markovian decoherence dynamics of strong-coupling hybrid quantum systems: A master equation approach,” Phys. Rev. A, vol. 103, p. 013714, Jan. 2021, doi: 10.1103/PhysRevA.103.013714.
[56] F. Lastra, S. A. Reyes and S. Wallentowitz, “Analytical model of non-Markovian decoherence in donor-based charge quantum bits,” J. Phys. B: At. Mol. Opt. Phys., vol. 44, p. 015504, Dec. 2011, doi: 10.1088/0953-4075/44/1/015504.
[57] A. Ablimit, D. Hitjan and A. Abliz, “Non-Markovian Dynamics of Geometric Quantum Discord in a Double Quantum Dot System,” J. Low Temp. Phys., vol. 205, pp. 126–134, Oct. 2021, doi: 10.1007/s10909-021-02621-8.
[58] H.-J. Joo et al., “Actively tunable laser action in GeSn nanomechanical oscillators,” Nat. Nanotechnol., vol. 19, pp. 1116–1121, Apr. 2024, doi: 10.1038/s41565-024-01662-w.
[59] N. J. Engelsen, A. Beccari and T. J. Kippenberg, “Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution,” Nat. Nanotechnol., vol. 19, pp. 725–737, Mar. 2024, doi: 10.1038/s41565-023-01597-8.
[60] S. Savel’ev, A. L. Rakhmanov, X. Hu, A. Kasumov and F. Nori, “Quantum electromechanics: Quantum tunneling near resonance and qubits from buckling nanoscale bars,” Phys. Rev. B, vol. 75, p. 165417, Apr. 2007, doi: 10.1103/PhysRevB.75.165417.
[61] A. Y. Cleland, E. A. Wollack and A. H. Safavi-Naeini, “Studying phonon coherence with a quantum sensor,” Nat. Commun., vol. 15, p. 4979, Jun. 2024, doi: 10.1038/s41467-024-48306-0.
[62] A. B. Bozkurt, O. Golami, Y. Yu, H. Tian and M. Mirhosseini, “A mechanical quantum memory for microwave photons,” Nat. Phys., vol. 21, pp. 1469–1474, Aug. 2025, doi: 10.1038/s41567-025-02975-w.
[63] Á. Rivas, S. F. Huelga and M. B. Plenio, “Entanglement and Non-Markovianity of Quantum Evolutions,” Phys. Rev. Lett., vol. 105, p. 050403, Jul. 2010, doi: 10.1103/PhysRevLett.105.050403.
[64] H.-P. Breuer, “Foundations and measures of quantum non-Markovianity,” J. Phys. B: At. Mol. Opt. Phys., vol. 45, no. 15, p. 154001, Jul. 2012, doi: 10.1088/0953-4075/45/15/154001.
[65] C.-M. Li, N. Lambert, Y.-N. Chen, G.-Y. Chen and F. Nori, “Witnessing Quantum Coherence: from solid-state to biological systems,” Sci. Rep., vol. 2, p. 885, Nov. 2012, doi: 10.1038/srep00885.
[66] J. Piilo, S. Maniscalco, K. Härkönen and K.-A. Suominen, “Non-Markovian Quantum Jumps,” Phys. Rev. Lett., vol. 100, no. 18, p. 180402, May 2008, doi: 10.1103/PhysRevLett.100.180402.
[67] F. F. Fanchini et al., “Non-Markovianity through Accessible Information,” Phys. Rev. Lett., vol. 112, no. 21, p. 210402, May 2014, doi: 10.1103/PhysRevLett.112.210402.
[68] S. L. Wu, W. Ma, Z.-M. Wang, P. Brumer and L.-A. Wu, “Steady-state coherences under partial collective non-Markovian decoherence,” Phys. Rev. Res., vol. 7, no. 4, p. 043221, Nov. 2025, doi: 10.1103/nktx-4ltm.
[69] R. T. Ranaivoson, R. Andriambololona, H. Rakotoson and R. Raboanary, “Linear Canonical Transformations in relativistic quantum physics,” Physica Scripta, vol. 96, no. 6, p. 065204, Mar. 2021, doi: 10.1088/1402-4896/abeba5.
[70] R. P. Feynman and F. L. Vernon, “The theory of a general quantum system interacting with a linear dissipative system,” Ann. Phys., vol. 24, pp. 118–173, Oct. 1963, doi: 10.1016/0003-4916(63)90068-X.
[71] Á. Rivas and S. F. Huelga, Open Quantum Systems: An Introduction. Berlin, Springer, 2012, doi: 10.1007/978-3-642-23354-8.
[72] C. H. Fleming, A. Roura and B. L. Hu, “Exact analytical solutions to the master equation of quantum Brownian motion for a general environment,” Ann. Phys., vol. 326, no. 5, pp. 1207–1258, May 2011, doi: 10.1016/j.aop.2010.12.003.
[73] U. Weiss, Quantum Dissipative Systems, 5th ed. World Scientific, 2021, doi: 10.1142/12402.
[74] A. O. Caldeira and A. J. Leggett, “Path integral approach to quantum Brownian motion,” Physica A, vol. 121, no. 3, pp. 587–616, Sept. 1983, https://doi.org/10.1016/0378-4371(83)90013-4.
[75] Y.-W. Huang and W.-M. Zhang, “Exact master equation for generalized quantum Brownian motion with momentum-dependent system-environment couplings,” Phys. Rev. Res., vol. 4, no. 3, p. 033151, Aug. 2022, doi: 10.1103/PhysRevResearch.4.033151.
[76] L. Ferialdi and A. Smirne, “Momentum coupling in non-Markovian quantum Brownian motion,” Phys. Rev. A, vol. 96, no. 1, p. 012109, Jul. 2017, doi: 10.1103/PhysRevA.96.012109.
[77] S. Bhattacharjee, K. Mandal and S. Sinha, “Decoherence of a charged Brownian particle in a magnetic field: an analysis of the roles of coupling via position and momentum variables,” J. Phys. A: Math. Theor., vol. 57, no. 37, p. 375304, Aug. 2024, doi: 10.1088/1751-8121/ad707e.
[78] A. A. Shevyrin, A. K. Bakarov, A. A. Shklyaev and A. G. Pogosov, “Electronic state back action on mechanical motion in a quantum point contact coupled to a nanomechanical resonator,” Appl. Phys. Lett., vol. 125, no. 19, p. 192105, Nov. 2024, doi: 10.1063/5.0235485.
[79] N. A. Vaidya and D. H. Santamore, “Effect of noise fluctuation of a quantum tunneling device coupled to a substrate,” Phys. Rev. B, vol. 95, no. 15, p. 155439, Apr. 2017, doi: 10.1103/PhysRevB.95.155439.
[80] A. Noguchi, R. Yamazaki, Y. Tabuchi and Y. Nakamura, “Single-photon quantum regime of artificial radiation pressure on a surface acoustic wave resonator,” Nat. Commun., vol. 11, no. 1, p. 1183, Mar. 2020, doi: 10.1038/s41467-020-14910-z.
[81] Y. Zhou, X. Xu, Y. Zhang and B. Yao, “Observation of high-order imaginary Poynting momentum optomechanics in structured light,” Proc. Natl. Acad. Sci., vol. 119, no. 44, p. e2209721119, Oct. 2022, doi: 10.1073/pnas.2209721119.
[82] G. Burkard, R. H. Koch and D. P. DiVincenzo, “Multilevel quantum description of decoherence in superconducting qubits,” Phys. Rev. B, vol. 69, no. 6, p. 064503, Feb. 2004, doi: 10.1103/PhysRevB.69.064503.
[83] G. Marchegiani and G. Catelani, “Nonequilibrium regimes for quasiparticles in superconducting qubits with gap-asymmetric junctions,” Commun. Phys., vol. 8, p. 120, Mar. 2025, doi: 10.1038/s42005-025-02052-x.
[84] A. Ranni et al., “Decoherence in a crystal-phase defined double quantum dot charge qubit strongly coupled to a high-impedance resonator,” Phys. Rev. Res, vol. 6, no. 4, p. 043134, Nov. 2024, doi: 10.1103/PhysRevResearch.6.043134.
[85] F. Ye, A. Ellaboudy, D. Albrecht, R. Vudatha, N. T. Jacobson and J. M. Nichol, “Characterization of individual charge fluctuators in Si/SiGe quantum dots,” Phys. Rev. B, vol. 110, no. 23, p. 235305, Dec. 2024, doi: 10.1103/PhysRevB.110.235305.
[86] A. Youssefi, S. Kono, M. Chegnizadeh and T. J. Kippenberg, “A squeezed mechanical oscillator with millisecond quantum decoherence,” Nat. Phys., vol. 19, pp. 1697–1702, Aug. 2023, doi: 10.1038/s41567-023-02135-y.
[87] C. Chia, D. Huang, V. Leong, J. F. Kong and K. E. J. Goh, “Hybrid Quantum Systems with Artificial Atoms in Solid State,” Adv. Quantum Technol., vol. 7, no. 5, p. 2300461, Apr. 2024, doi: 10.1002/qute.202300461.
[88] A. Isar, “Uncertainty, Entropy and Decoherence of the Damped Harmonic Oscillator in the Lindblad Theory of Open Quantum Systems,” Prog. Phys., vol. 47, no. 7, pp. 855–879, Aug. 1999, doi: 10.1002/(SICI)1521-3978(199909)47:7/8<855::AID-PROP855>3.0.CO;2-Z.
[89] P. M. Randriantsoa, R. T. Ranaivoson, R. Andriambololona, R. Raboanary, W. C. Solofoarisina and A. F. H. Rasamimanana, “Geometric structure of the relativistic quantum phase space,” 2026, https://doi.org/10.2139/ssrn.7169885.
[90] A. F. H. Rasamimanana, R. T. Ranaivoson, R. Raboanary, R. Andriambololona, W. C. Solofoarisina and P. M. Randriantsoa, “Contractions of the relativistic quantum LCT group and the emergence of spacetime symmetries,” 2026, arXiv:2603.21333v2 [quant-ph], doi: 10.48550/arXiv.2603.21333.
[91] P. M. Randriantsoa, R. T. Ranaivoson, R. Andriambololona, R. Raboanary, W. C. Solofoarisina and A. F. H. Rasamimanana, “Casimir operators for the relativistic quantum phase space symmetry group,” 2025, arXiv:2512.18262v2 [quant-ph], doi: 10.2139/ssrn.7169885.
[92] S. Donadi and M. Fadel, “Quantum gravitational decoherence of a mechanical oscillator from spacetime fluctuations,” Phys. Rev. D, vol. 111, no. 2, p. 026009, Jan. 2025, doi: 10.1103/PhysRevD.111.026009.
[93] I. Pikovski, M. Zych, F. Costa and Č. Brukner, “Universal decoherence due to gravitational time dilation,” Nat. Phys., vol. 11, pp. 668–672, Jun. 2015, doi: 10.1038/nphys3366.
[94] D. K. Ferry, L. Huang, R. Yang, Y.-C. Lai and R. Akis, “Open quantum dots in graphene: Scaling relativistic pointer states,” J. Phys.: Conf. Ser., vol. 220, p. 012015, Aug. 2010, doi: 10.1088/1742-6596/220/1/012015.
[95] S.-H. Shang and S.-M. Wu, “Quantum steering of GHZ and W states in relativistic motion,” Eur. Phys. J. C, vol. 85, no. 7, p. 790, Jul. 2025, doi: 10.1140/epjc/s10052-025-14516-z.
[96] D. L. Danielson, G. Satishchandran and R. M. Wald, “Local description of decoherence of quantum superpositions by black holes and other bodies,” Phys. Rev. D, vol. 111, no. 2, p. 025014, Jan. 2025, doi: 10.1103/PhysRevD.111.025014.
[97] F. Sano and J. Tokuda, “False and genuine decoherence in the early universe: a local observer and time-averaged observables,” J. High Energy Phys., vol. 2025, no. 7, p. 266, Jul. 2025, doi: 10.1007/JHEP07(2025)266.
[98] S. Bose et al., “Massive quantum systems as interfaces of quantum mechanics and gravity,” Rev. Mod. Phys., vol. 97, no. 1, p. 015003, Feb. 2025, doi: 10.1103/RevModPhys.97.015003.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Ravo Tokiniaina Ranaivoson, Angelo Mamitiana Ralaikoto, Diary Lova Ratsimbazafy, Rivo Herivola Manjakamanana Ravelonjato, Roland Raboanary, Raoelina Andriambololona, Nomenjanahary Tanjonirina Manampisoa, Fanamby Sahondraniandriana
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2026-08-11
Published 2026-10-21
