Whenever a quantum environment emerges as a classical system, it behaves like a measuring apparatus

Caterina Foti1,2, Teiko Heinosaari3, Sabrina Maniscalco3, and Paola Verrucchi4,1,2

1Dipartimento di Fisica e Astronomia, Università di Firenze, I-50019, Sesto Fiorentino (FI), Italy
2INFN, Sezione di Firenze, I-50019, Sesto Fiorentino (FI), Italy
3QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FIN-20014, Turku, Finland
4ISC-CNR, at Dipartimento di Fisica e Astronomia, Università di Firenze, I-50019, Sesto Fiorentino (FI), Italy

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


We study the dynamics of a quantum system $\Gamma$ with an environment $\Xi$ made of $N$ elementary quantum components. We aim at answering the following questions: can the evolution of $\Gamma$ be characterized by some general features when $N$ becomes very large, regardless of the specific form of its interaction with each and every component of $\Xi$? In other terms: should we expect all quantum systems with a macroscopic environment to undergo a somehow similar evolution? And if yes, of what type? In order to answer these questions we use well established results from large-$N$ quantum field theories, particularly referring to the conditions ensuring a large-$N$ quantum model to be effectively described by a classical theory. We demonstrate that the fulfillment of these conditions, when properly imported into the framework of the open quantum systems dynamics, guarantees that the evolution of $\Gamma$ is always of the same type of that expected if $\Xi$ were a measuring apparatus, no matter the details of the actual interaction. On the other hand, such details are found to determine the specific basis w.r.t. which $\Gamma$ undergoes the decoherence dictated by the dynamical description of the quantum measurement process. This result wears two hats: on the one hand it clarifies the physical origin of the formal statement that, under certain conditions, any channel from $\rho_\Gamma$ to $\rho_\Xi$ takes the form of a measure-and-prepare map, as recently shown in Ref. [1]; on the other hand, it formalizes the qualitative argument that the reason why we do not observe state superpositions is the continual measurement performed by the environment.

► BibTeX data

► References

[1] F.G.S.L. Brandao, M. Piani, and P. Horodecki. Generic emergence of classical features in quantum darwinism. Nature Communications, 6: 7908, 2015. 10.1038/​ncomms8908.

[2] W. H. Zurek. Quantum darwinism. Nature Physics, 5: 181, 2009. 10.1038/​nphys1202.

[3] R. Horodecki, J.K. Korbicz, and P. Horodecki. Quantum origins of objectivity. Phys. Rev. A, 91: 032122, 2015. 10.1103/​PhysRevA.91.032122.

[4] P. Busch, P. Lahti, J. P. Pellonp, and K. Ylinen. Quantum Measurement. Springer Publishing Company, Incorporated, 1st edition, 2016. ISBN 3319433873, 9783319433875. 10.1007/​978-3-319-43389-9.

[5] M. Ozawa. Quantum measuring processes of continuous observables. Journal of Mathematical Physics, 25 (1): 79–87, 1984. 10.1063/​1.526000.

[6] P. Liuzzo Scorpo, A. Cuccoli, and P. Verrucchi. Parametric description of the quantum measurement process. EPL (Europhysics Letters), 111 (4): 40008, 2015a. 10.1209/​0295-5075/​111/​40008.

[7] T. Heinosaari and M. Ziman. The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement. Cambridge University Press, 2012. 10.1017/​CBO9781139031103.

[8] Laurence G. Yaffe. Large n limits as classical mechanics. Rev. Mod. Phys., 54: 407–435, 1982. 10.1103/​RevModPhys.54.407.

[9] D. Braun, F. Haake, and W.T. Strunz. Universality of decoherence. Phys. Rev. Lett., 86: 2913–2917, 2001. 10.1103/​PhysRevLett.86.2913.

[10] G. Chiribella and G.M. D'Ariano. Quantum information becomes classical when distributed to many users. Phys. Rev. Lett., 97: 250503, 2006. 10.1103/​PhysRevLett.97.250503.

[11] F. Galve, R. Zambrini, and S. Maniscalco. Non-markovianity hinders quantum darwinism. Scientific Reports, 6: 19607, 2016. 10.1038/​srep19607.

[12] G.L. Giorgi, F. Galve, and R. Zambrini. Quantum darwinism and non-markovian dissipative dynamics from quantum phases of the spin-1/​2 $xx$ model. Phys. Rev. A, 92: 022105, 2015. 10.1103/​PhysRevA.92.022105.

[13] L. Rigovacca, A. Farace, A. De Pasquale, and V. Giovannetti. Gaussian discriminating strength. Phys. Rev. A, 92: 042331, 2015. 10.1103/​PhysRevA.92.042331.

[14] P.A. Knott, T. Tufarelli, M. Piani, and G. Adesso. Generic emergence of objectivity of observables in infinite dimensions. Phys. Rev. Lett., 121: 160401, 2018. 10.1103/​PhysRevLett.121.160401.

[15] J. K. Korbicz, E. A. Aguilar, P. Ć wikliński, and P. Horodecki. Generic appearance of objective results in quantum measurements. Phys. Rev. A, 96: 032124, 2017. 10.1103/​PhysRevA.96.032124.

[16] G. Pleasance and B.M. Garraway. Application of quantum darwinism to a structured environment. Phys. Rev. A, 96: 062105, 2017. 10.1103/​PhysRevA.96.062105.

[17] P. Busch, P.J. Lahti, and P Mittelstaedt. The quantum theory of measurement. Springer-Verlag, Berlin, 1996. 10.1007/​978-3-540-37205-9.

[18] D. Calvani, A. Cuccoli, N. I. Gidopoulos, and P. Verrucchi. Parametric representation of open quantum systems and cross-over from quantum to classical environment. Proceedings of the National Academy of Sciences, 110 (17): 6748–6753, 2013a. 10.1073/​pnas.1217776110.

[19] D. Calvani. The Parametric Representation of an Open Quantum System. PhD thesis, Università degli Studi di Firenze, 2012.

[20] D. Calvani, A. Cuccoli, N. I. Gidopoulos, and P. Verrucchi. Dynamics of open quantum systems using parametric representation with coherent states. Open Systems & Information Dynamics, 20 (3): 1340002, 2013b. 10.1142/​S1230161213400027.

[21] P. Liuzzo Scorpo, A. Cuccoli, and P. Verrucchi. Getting information via a quantum measurement: The role of decoherence. Int. J. Theor. Phys., 54 (12): 4356–4366, 2015b. ISSN 1572-9575. 10.1007/​s10773-015-2548-8.

[22] C. Foti, A. Cuccoli, and P. Verrucchi. Quantum dynamics of a macroscopic magnet operating as an environment of a mechanical oscillator. Phys. Rev. A, 94: 062127, 2016. 10.1103/​PhysRevA.94.062127.

[23] M.A.C. Rossi, C. Foti, A. Cuccoli, J. Trapani, P. Verrucchi, and M.G.A. Paris. Effective description of the short-time dynamics in open quantum systems. Phys. Rev. A, 96: 032116, 2017. 10.1103/​PhysRevA.96.032116.

[24] W.M. Zhang, D.H. Feng, and R. Gilmore. Coherent states: Theory and some applications. Rev. Mod. Phys., 62: 867–927, 1990. 10.1103/​RevModPhys.62.867.

[25] A.M. Perelomov. Coherent states for arbitrary Lie group. Communications in Mathematical Physics, 26 (3): 222–236, 1972. ISSN 0010-3616. 10.1007/​BF01645091.

[26] E. H. Lieb. The classical limit of quantum spin systems. Communications in Mathematical Physics, 31 (4): 327–340, 1973. 10.1007/​BF01646493.

[27] S. Gnutzmann and M. Kus. Coherent states and the classical limit on irreducible su(3) representations. Journal of Physics A: Mathematical and General, 31 (49): 9871, 1998. 10.1088/​0305-4470/​31/​49/​011.

[28] L. Querini. How quantum dynamics shape macroscopic evidences. Master thesis, University of Florence, 2016.

[29] C. Foti. On the macroscopic limit of quantum systems. PhD thesis, Università degli Studi di Firenze, 2019.

[30] M. Schlosshauer. Decoherence and the Quantum-To-Classical Transition. The Frontiers Collection. Springer, 2007. 10.1007/​978-3-540-35775-9.

[31] F. A. Berezin. Models of gross-neveu type are quantization of a classical mechanics with nonlinear phase space. Comm. Math. Phys., 63 (2): 131–153, 1978. 10.1007/​BF01220849.

Cited by

[1] Giovanni Spaventa and Paola Verrucchi, "Nature and Origin of Operators Entering the Master Equation of an Open Quantum System", Open Systems & Information Dynamics 29 02, 2250010 (2022).

[2] P. Renault, J. Nokkala, G. Roeland, N.Y. Joly, R. Zambrini, S. Maniscalco, J. Piilo, N. Treps, and V. Parigi, "Experimental Optical Simulator of Reconfigurable and Complex Quantum Environment", PRX Quantum 4 4, 040310 (2023).

[3] A. Coppo, A. Cuccoli, C. Foti, and P. Verrucchi, "From a quantum theory to a classical one", Soft Computing 24 14, 10315 (2020).

[4] Xiao-Liang Qi and Daniel Ranard, "Emergent classicality in general multipartite states and channels", Quantum 5, 555 (2021).

[5] Zhelun Zhang and Yi-Zhuang You, "Observing Schrödinger’s cat with artificial intelligence: emergent classicality from information bottleneck", Machine Learning: Science and Technology 5 1, 015051 (2024).

[6] Karl Svozil, "Quantum Randomness is Chimeric", Entropy 23 5, 519 (2021).

[7] Guillermo Perna and Esteban Calzetta, "Limits on quantum measurement engines", Physical Review E 109 4, 044102 (2024).

[8] Caterina Foti, Alessandro Coppo, Giulio Barni, Alessandro Cuccoli, and Paola Verrucchi, "Time and classical equations of motion from quantum entanglement via the Page and Wootters mechanism with generalized coherent states", Nature Communications 12 1, 1787 (2021).

[9] Guillermo García-Pérez, Diana A. Chisholm, Matteo A. C. Rossi, G. Massimo Palma, and Sabrina Maniscalco, "Decoherence without entanglement and quantum Darwinism", Physical Review Research 2 1, 012061 (2020).

[10] A. A. Andrianov, M. V. Ioffe, E. A. Izotova, and O. O. Novikov, "A perturbation algorithm for the pointers of Franke–Gorini–Kossakowski–Lindblad–Sudarshan equation", The European Physical Journal Plus 135 6, 531 (2020).

[11] Adriano M. Palmieri, Federico Bianchi, Matteo G. A. Paris, and Claudia Benedetti, "Multiclass classification of dephasing channels", Physical Review A 104 5, 052412 (2021).

[12] Nina Megier, Walter T. Strunz, and Kimmo Luoma, "Continuous quantum measurement for general Gaussian unravelings can exist", Physical Review Research 2 4, 043376 (2020).

[13] Alessandro Coppo, Nicola Pranzini, and Paola Verrucchi, "Threshold size for the emergence of classical-like behavior", Physical Review A 106 4, 042208 (2022).

[14] Nicola Pranzini and Paola Verrucchi, "Premeasurement reliability and accessibility of quantum measurement apparatuses", Physical Review A 109 3, 032203 (2024).

[15] A. De Pasquale, C. Foti, A. Cuccoli, V. Giovannetti, and P. Verrucchi, "Dynamical model for positive-operator-valued measures", Physical Review A 100 1, 012130 (2019).

[16] K. G. Hernández, S. E. Aguilar, and J. Bernal, "On the correspondence principle for the Klein-Gordon and Dirac Equations", arXiv:1907.05842, (2019).

The above citations are from Crossref's cited-by service (last updated successfully 2024-04-15 05:34:16) and SAO/NASA ADS (last updated successfully 2024-04-15 05:34:19). The list may be incomplete as not all publishers provide suitable and complete citation data.