We consider fundamental limits on the detectable size of macroscopic quantum superpositions. We argue that a full quantum mechanical treatment of system plus measurement device is required, and that a (classical) reference frame for phase or direction needs to be established to certify the quantum state. When taking the size of such a classical reference frame into account, we show that to reliably distinguish a quantum superposition state from an incoherent mixture requires a measurement device that is quadratically bigger than the superposition state. Whereas for moderate system sizes such as generated in previous experiments this is not a stringent restriction, for macroscopic superpositions of the size of a cat the required effort quickly becomes intractable, requiring measurement devices of the size of the Earth. We illustrate our results using macroscopic superposition states of photons, spins, and position. Finally, we also show how this limitation can be circumvented by dealing with superpositions in relative degrees of freedom.
Measurement devices are often treated within quantum mechanics as classical systems, with no intrinsic uncertainty, capable of resolving each degree of freedom with unlimited precision. Whereas this is a very good approximation when the measurement device is way larger than the quantum system of interest, it quickly becomes problematic when considering quantum superpositions of larger and larger size. Using the fundamental symmetries of physical laws only, we show that, in many relevant cases, the size of the measurement device has to be quadratically larger than the size of the macroscopic superposition in question in order for this to hold. Moreover, if this is not the case the superposition in question cannot be distinguished form a mere classical mixture. Within a simplified model, our result shows that in order to observe a cat in a superposition of facing the right way up or upside-down one requires a measurement device whose size is equal to the whole Earth.
 J. S. Bell, Physics 1, 195 (1964).
 P. Sekatski, N. Gisin, and N. Sangouard, Phys. Rev. Lett. 113, 090403 (2014a).
 F. De Martini, F. Sciarrino, and C. Vitelli, Phys. Rev. Lett. 100, 253601 (2008).
 B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Science 342, 607 (2013).
 A. Tiranov, J. Lavoie, P. C. Strassmann, N. Sangouard, M. Afzelius, F. Bussières, and N. Gisin, Phys. Rev. Lett. 116, 190502 (2016).
 A. Peres and P. Scudo, in Quantum Theory: Reconsiderations of Foundations, Math. Modelling in Physics, Engineering and Cognitive Sciences, edited by A. Khrennikov (Växjö University Press, Växjö, Sweden, 2002) p. 283.
 A. J. Leggett, J. Phys. Condens. Matter 14, R415 (2002).
 C. W. Helstrom, Quantum detection and estimation theory (Elsevier, 1976).
 J. Bae and L.-C. Kwek, J. Phys. A 48, 083001 (2015).
 A. Messiah, Quantum Mechanics, two volumes (Dover Publications, New York, 1999).
 M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge university press, 2010).
 A. López Incera, P. Sekatski, and W. Dür, (in preparation).
 S. Sternberg, Group Theory and Physics (Cambridge University Press, 1994).
 Anne-Catherine de la Hamette and Thomas D. Galley, "Quantum reference frames for general symmetry groups", Quantum 4, 367 (2020).
 Florian Fröwis, Pavel Sekatski, Wolfgang Dür, Nicolas Gisin, and Nicolas Sangouard, "Macroscopic quantum states: Measures, fragility, and implementations", Reviews of Modern Physics 90 2, 025004 (2018).
 P. R. Dieguez and R. M. Angelo, "Information-reality complementarity: The role of measurements and quantum reference frames", Physical Review A 97 2, 022107 (2018).
 R. Y. Teh, S. Kiesewetter, P. D. Drummond, and M. D. Reid, "Creation, storage, and retrieval of an optomechanical cat state", Physical Review A 98 6, 063814 (2018).
 Nuriya Nurgalieva and Renato Renner, "Testing quantum theory with thought experiments", Contemporary Physics 61 3, 193 (2020).
 G. S. Thekkadath, D. S. Phillips, J. F. F. Bulmer, W. R. Clements, A. Eckstein, B. A. Bell, J. Lugani, T. A. W. Wolterink, A. Lita, S. W. Nam, T. Gerrits, C. G. Wade, and I. A. Walmsley, "Tuning between photon-number and quadrature measurements with weak-field homodyne detection", Physical Review A 101 3, 031801 (2020).
 Andrea López-Incera, Pavel Sekatski, and Wolfgang Dür, "All macroscopic quantum states are fragile and hard to prepare", Quantum 3, 118 (2019).
The above citations are from Crossref's cited-by service (last updated successfully 2022-01-23 04:23:07). The list may be incomplete as not all publishers provide suitable and complete citation data.
On SAO/NASA ADS no data on citing works was found (last attempt 2022-01-23 04:23:08).
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.