Quantum States of Fields for Quantum Split Sources

Lin-Qing Chen1,2, Flaminia Giacomini2,3, and Carlo Rovelli3,4,5

1Centre for Quantum Information and Communication, Université Libre de Bruxelles, 1050 Brussels, Belgium.
2Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
3Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada.
4Aix-Marseille University, Université de Toulon, CPT-CNRS, F-13288 Marseille, France.
5Department of Philosophy and the Rotman Institute of Philosophy, 1151 Richmond St. N London N6A5B7, Canada.

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

Abstract

Field mediated entanglement experiments probe the quantum superposition of macroscopically distinct field configurations. We show that this phenomenon can be described by using a transparent quantum field theoretical formulation of electromagnetism and gravity in the field basis. The strength of such a description is that it explicitly displays the superposition of macroscopically distinct states of the field. In the case of (linearised) quantum general relativity, this formulation exhibits the quantum superposition of geometries giving rise to the effect.

► BibTeX data

► References

[1] Sougato Bose, Anupam Mazumdar, Gavin W. Morley, Hendrik Ulbricht, Marko Toroš, Mauro Paternostro, Andrew Geraci, Peter Barker, M. S. Kim, and Gerard Milburn. Spin Entanglement Witness for Quantum Gravity. Phys. Rev. Lett., 119(24):240401, 2017. arXiv:1707.06050, doi:10.1103/​PhysRevLett.119.240401.
https:/​/​doi.org/​10.1103/​PhysRevLett.119.240401
arXiv:1707.06050

[2] Chiara Marletto and Vlatko Vedral. Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity. Phys. Rev. Lett., 119(24):240402, 2017. arXiv:1707.06036, doi:10.1103/​PhysRevLett.119.240402.
https:/​/​doi.org/​10.1103/​PhysRevLett.119.240402
arXiv:1707.06036

[3] Michael JW Hall and Marcel Reginatto. On two recent proposals for witnessing nonclassical gravity. J. Phys. A, 51(8):085303, 2018. arXiv:1707.07974, doi:10.1088/​1751-8121/​aaa734.
https:/​/​doi.org/​10.1088/​1751-8121/​aaa734
arXiv:1707.07974

[4] C Anastopoulos and Bei-Lok Hu. Comment on “A spin entanglement witness for quantum gravity” and on “Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity”. 2018. arXiv:1804.11315.
arXiv:1804.11315

[5] Alessio Belenchia, Robert M. Wald, Flaminia Giacomini, Esteban Castro-Ruiz, Časlav Brukner, and Markus Aspelmeyer. Quantum Superposition of Massive Objects and the Quantization of Gravity. Phys. Rev. D, 98(12):126009, 2018. arXiv:1807.07015, doi:10.1103/​PhysRevD.98.126009.
https:/​/​doi.org/​10.1103/​PhysRevD.98.126009
arXiv:1807.07015

[6] Alessio Belenchia, Robert M. Wald, Flaminia Giacomini, Esteban Castro-Ruiz, Časlav Brukner, and Markus Aspelmeyer. Information Content of the Gravitational Field of a Quantum Superposition. Int. J. Mod. Phys. D, 28(14):1943001, 2019. arXiv:1905.04496, doi:10.1142/​S0218271819430016.
https:/​/​doi.org/​10.1142/​S0218271819430016
arXiv:1905.04496

[7] Marios Christodoulou and Carlo Rovelli. On the possibility of laboratory evidence for quantum superposition of geometries. Phys. Lett. B, 792:64–68, 2019. arXiv:1808.05842, doi:10.1016/​j.physletb.2019.03.015.
https:/​/​doi.org/​10.1016/​j.physletb.2019.03.015
arXiv:1808.05842

[8] Richard Howl, Vlatko Vedral, Devang Naik, Marios Christodoulou, Carlo Rovelli, and Aditya Iyer. Non-Gaussianity as a signature of a quantum theory of gravity. PRX Quantum., 2:010325, 2021. arXiv:2004.01189, doi:10.1103/​PRXQuantum.2.010325.
https:/​/​doi.org/​10.1103/​PRXQuantum.2.010325
arXiv:2004.01189

[9] Ryan J Marshman, Anupam Mazumdar, and Sougato Bose. Locality and entanglement in table-top testing of the quantum nature of linearized gravity. Phys. Rev. A, 101(5):052110, 2020. arXiv:1907.01568, doi:10.1103/​PhysRevA.101.052110.
https:/​/​doi.org/​10.1103/​PhysRevA.101.052110
arXiv:1907.01568

[10] Tanjung Krisnanda, Guo Yao Tham, Mauro Paternostro, and Tomasz Paterek. Observable quantum entanglement due to gravity. npj Quantum Information, 6(1):1–6, 2020. arXiv:1906.08808, doi:10.1038/​s41534-020-0243-y.
https:/​/​doi.org/​10.1038/​s41534-020-0243-y
arXiv:1906.08808

[11] Chiara Marletto and Vlatko Vedral. Witnessing nonclassicality beyond quantum theory. Phys. Rev. D, 102(8):086012, 2020. arXiv:2003.07974, doi:10.1103/​PhysRevD.102.086012.
https:/​/​doi.org/​10.1103/​PhysRevD.102.086012
arXiv:2003.07974

[12] Thomas D. Galley, Flaminia Giacomini, and John H. Selby. A no-go theorem on the nature of the gravitational field beyond quantum theory. Quantum, 6:779, 2022. arXiv:2012.01441, doi:10.22331/​q-2022-08-17-779.
https:/​/​doi.org/​10.22331/​q-2022-08-17-779
arXiv:2012.01441

[13] Soham Pal, Priya Batra, Tanjung Krisnanda, Tomasz Paterek, and TS Mahesh. Experimental localisation of quantum entanglement through monitored classical mediator. Quantum, 5:478, 2021. arXiv:1909.11030, doi:10.22331/​q-2021-06-17-478.
https:/​/​doi.org/​10.22331/​q-2021-06-17-478
arXiv:1909.11030

[14] Daniel Carney, Holger Müller, and Jacob M. Taylor. Using an Atom Interferometer to Infer Gravitational Entanglement Generation. PRX Quantum, 2(3):030330, 2021. arXiv:2101.11629, doi:10.1103/​PRXQuantum.2.030330.
https:/​/​doi.org/​10.1103/​PRXQuantum.2.030330
arXiv:2101.11629

[15] Adrian Kent and Damián Pitalúa-García. Testing the nonclassicality of spacetime: What can we learn from bell–bose et al.-marletto-vedral experiments? Phys. Rev. D, 104(12):126030, 2021. arXiv:2109.02616, doi:10.1103/​PhysRevD.104.126030.
https:/​/​doi.org/​10.1103/​PhysRevD.104.126030
arXiv:2109.02616

[16] Daine L. Danielson, Gautam Satishchandran, and Robert M. Wald. Gravitationally mediated entanglement: Newtonian field versus gravitons. Phys. Rev. D, 105(8):086001, 2022. arXiv:2112.10798, doi:10.1103/​PhysRevD.105.086001.
https:/​/​doi.org/​10.1103/​PhysRevD.105.086001
arXiv:2112.10798

[17] Run Zhou, Ryan J. Marshman, Sougato Bose, and Anupam Mazumdar. Catapulting towards massive and large spatial quantum superposition. Phys. Rev. Res., 4(4):043157, 2022. arXiv:2206.04088, doi:10.1103/​PhysRevResearch.4.043157.
https:/​/​doi.org/​10.1103/​PhysRevResearch.4.043157
arXiv:2206.04088

[18] Daine L. Danielson, Gautam Satishchandran, and Robert M. Wald. Black holes decohere quantum superpositions. Int. J. Mod. Phys. D, 31(14):2241003, 2022. arXiv:2205.06279, doi:10.1142/​S0218271822410036.
https:/​/​doi.org/​10.1142/​S0218271822410036
arXiv:2205.06279

[19] Sougato Bose, Anupam Mazumdar, Martine Schut, and Marko Toroš. Mechanism for the quantum natured gravitons to entangle masses. Phys. Rev. D, 105(10):106028, 2022. arXiv:2201.03583, doi:10.1103/​PhysRevD.105.106028.
https:/​/​doi.org/​10.1103/​PhysRevD.105.106028
arXiv:2201.03583

[20] Emanuele Polino, Beatrice Polacchi, Davide Poderini, Iris Agresti, Gonzalo Carvacho, Fabio Sciarrino, Andrea Di Biagio, Carlo Rovelli, and Marios Christodoulou. Photonic Implementation of Quantum Gravity Simulator. 7 2022. arXiv:2207.01680.
arXiv:2207.01680

[21] Cécile M. DeWitt and Dean Rickles. The role of gravitation in physics: Report from the 1957 Chapel Hill Conference, volume 5. epubli, 2011.

[22] H Dieter Zeh. Feynman's interpretation of quantum theory. The European Physical Journal H, 36(1):63–74, 2011. arXiv:0804.3348, doi:10.1140/​epjh/​e2011-10035-2.
https:/​/​doi.org/​10.1140/​epjh/​e2011-10035-2
arXiv:0804.3348

[23] M. P. Blencowe. Effective Field Theory Approach to Gravitationally Induced Decoherence. Phys. Rev. Lett., 111(2):021302, 2013. arXiv:1211.4751, doi:10.1103/​PhysRevLett.111.021302.
https:/​/​doi.org/​10.1103/​PhysRevLett.111.021302
arXiv:1211.4751

[24] C. Anastopoulos and B. L. Hu. A Master Equation for Gravitational Decoherence: Probing the Textures of Spacetime. Class. Quant. Grav., 30:165007, 2013. arXiv:1305.5231, doi:10.1088/​0264-9381/​30/​16/​165007.
https:/​/​doi.org/​10.1088/​0264-9381/​30/​16/​165007
arXiv:1305.5231

[25] C. Anastopoulos and Bei-Lok Hu. Probing a Gravitational Cat State. Class. Quant. Grav., 32(16):165022, 2015. arXiv:1504.03103, doi:10.1088/​0264-9381/​32/​16/​165022.
https:/​/​doi.org/​10.1088/​0264-9381/​32/​16/​165022
arXiv:1504.03103

[26] Matteo Carlesso, Mauro Paternostro, Hendrik Ulbricht, and Angelo Bassi. When Cavendish meets Feynman: A quantum torsion balance for testing the quantumness of gravity. 2017. arXiv:1710.08695.
arXiv:1710.08695

[27] M Bahrami, A Bassi, S McMillen, M Paternostro, and H Ulbricht. Is gravity quantum? 2015. arXiv:1507.05733.
arXiv:1507.05733

[28] LH Ford. Gravitational radiation by quantum systems. Ann. Phys., 144(2):238–248, 1982. doi:10.1016/​0003-4916(82)90115-4.
https:/​/​doi.org/​10.1016/​0003-4916(82)90115-4

[29] Dvir Kafri and JM Taylor. A noise inequality for classical forces. 2013. arXiv:1311.4558.
arXiv:1311.4558

[30] D Kafri, JM Taylor, and GJ Milburn. A classical channel model for gravitational decoherence. New J. Phys., 16(6):065020, 2014. arXiv:1401.0946, doi:10.1088/​1367-2630/​16/​6/​065020.
https:/​/​doi.org/​10.1088/​1367-2630/​16/​6/​065020
arXiv:1401.0946

[31] Natacha Altamirano, Paulina Corona-Ugalde, Robert B Mann, and Magdalena Zych. Gravity is not a pairwise local classical channel. Class. Quant. Grav., 35(14):145005, 2018. arXiv:1612.07735, doi:10.1088/​1361-6382/​aac72f.
https:/​/​doi.org/​10.1088/​1361-6382/​aac72f
arXiv:1612.07735

[32] Charis Anastopoulos and Bei-Lok Hu. Quantum superposition of two gravitational cat states. Class. Quant. Grav., 37(23):235012, 2020. arXiv:2007.06446, doi:10.1088/​1361-6382/​abbe6f.
https:/​/​doi.org/​10.1088/​1361-6382/​abbe6f
arXiv:2007.06446

[33] Charis Anastopoulos, Mihalis Lagouvardos, and Konstantina Savvidou. Gravitational effects in macroscopic quantum systems: a first-principles analysis. Class. Quant. Grav., 38(15):155012, 2021. arXiv:2103.08044, doi:10.1088/​1361-6382/​ac0bf9.
https:/​/​doi.org/​10.1088/​1361-6382/​ac0bf9
arXiv:2103.08044

[34] Tobias Westphal, Hans Hepach, Jeremias Pfaff, and Markus Aspelmeyer. Measurement of gravitational coupling between millimetre-sized masses. Nature, 591(7849):225–228, 2021. arXiv:2009.09546, doi:10.1038/​s41586-021-03250-7.
https:/​/​doi.org/​10.1038/​s41586-021-03250-7
arXiv:2009.09546

[35] Uroš Delić, Manuel Reisenbauer, Kahan Dare, David Grass, Vladan Vuletić, Nikolai Kiesel, and Markus Aspelmeyer. Cooling of a levitated nanoparticle to the motional quantum ground state. Science, 367(6480):892–895, 2020. doi:10.1126/​science.aba3993.
https:/​/​doi.org/​10.1126/​science.aba3993

[36] Lorenzo Magrini, Philipp Rosenzweig, Constanze Bach, Andreas Deutschmann-Olek, Sebastian G. Hofer, Sungkun Hong, Nikolai Kiesel, Andreas Kugi, and Markus Aspelmeyer. Real-time optimal quantum control of mechanical motion at room temperature. Nature, 595(7867):373–377, 2021. arXiv:2012.15188, doi:10.1038/​s41586-021-03602-3.
https:/​/​doi.org/​10.1038/​s41586-021-03602-3
arXiv:2012.15188

[37] Felix Tebbenjohanns, M Luisa Mattana, Massimiliano Rossi, Martin Frimmer, and Lukas Novotny. Quantum control of a nanoparticle optically levitated in cryogenic free space. Nature, 595(7867):378–382, 2021. doi:10.1038/​s41586-021-03617-w.
https:/​/​doi.org/​10.1038/​s41586-021-03617-w

[38] Yaakov Y Fein, Philipp Geyer, Patrick Zwick, Filip Kiałka, Sebastian Pedalino, Marcel Mayor, Stefan Gerlich, and Markus Arndt. Quantum superposition of molecules beyond 25 kda. Nat. Phys., 15(12):1242–1245, 2019. doi:10.1038/​s41567-019-0663-9.
https:/​/​doi.org/​10.1038/​s41567-019-0663-9

[39] T Kovachy, P Asenbaum, C Overstreet, CA Donnelly, SM Dickerson, A Sugarbaker, JM Hogan, and MA Kasevich. Quantum superposition at the half-metre scale. Nature, 528(7583):530–533, 2015. doi:10.1038/​nature16155.
https:/​/​doi.org/​10.1038/​nature16155

[40] Chris Overstreet, Peter Asenbaum, Joseph Curti, Minjeong Kim, and Mark A. Kasevich. Observation of a gravitational Aharonov-Bohm effect. Science, 375(6577):abl7152, 2021. doi:10.1126/​science.abl7152.
https:/​/​doi.org/​10.1126/​science.abl7152

[41] Markus Aspelmeyer. When Zeh Meets Feynman: How to Avoid the Appearance of a Classical World in Gravity Experiments. Fundam. Theor. Phys., 204:85–95, 2022. arXiv:2203.05587, doi:10.1007/​978-3-030-88781-0_5.
https:/​/​doi.org/​10.1007/​978-3-030-88781-0_5
arXiv:2203.05587

[42] Marios Christodoulou, Andrea Di Biagio, Richard Howl, and Carlo Rovelli. Gravity entanglement, quantum reference systems, degrees of freedom. Class. Quant. Grav., 40(4):047001, 2023. arXiv:2207.03138, doi:10.1088/​1361-6382/​acb0aa.
https:/​/​doi.org/​10.1088/​1361-6382/​acb0aa
arXiv:2207.03138

[43] Vasileios Fragkos, Michael Kopp, and Igor Pikovski. On inference of quantization from gravitationally induced entanglement. AVS Quantum Sci., 4:045601, 2022. arXiv:2206.00558, doi:10.1116/​5.0101334.
https:/​/​doi.org/​10.1116/​5.0101334
arXiv:2206.00558

[44] Marios Christodoulou, Andrea Di Biagio, Markus Aspelmeyer, Časlav Brukner, Carlo Rovelli, and Richard Howl. Locally mediated entanglement through gravity from first principles. 2 2022. arXiv:2202.03368.
arXiv:2202.03368

[45] Brian Hatfield. Quantum field theory of point particles and strings. CRC Press, 2018.

[46] K. Kuchar. Ground state functional of the linearized gravitational field. J. Math. Phys., 11:3322–3334, 1970. doi:10.1063/​1.1665133.
https:/​/​doi.org/​10.1063/​1.1665133

[47] C. P. Burgess. Quantum gravity in everyday life: General relativity as an effective field theory. Living Rev. Rel., 7:5–56, 2004. arXiv:0311082, doi:10.12942/​lrr-2004-5.
https:/​/​doi.org/​10.12942/​lrr-2004-5
arXiv:0311082

[48] John F. Donoghue. General relativity as an effective field theory: The leading quantum corrections. Phys. Rev. D, 50:3874–3888, 1994. arXiv:9405057, doi:10.1103/​PhysRevD.50.3874.
https:/​/​doi.org/​10.1103/​PhysRevD.50.3874
arXiv:9405057

[49] John Donoghue. Quantum gravity as a low energy effective field theory. Scholarpedia, 12(4):32997, 2017. doi:10.4249/​scholarpedia.32997.
https:/​/​doi.org/​10.4249/​scholarpedia.32997

[50] Zvi Bern. Perturbative quantum gravity and its relation to gauge theory. Living Reviews in Relativity, 5(1):1–57, 2002. arXiv:0206071, doi:10.12942/​lrr-2002-5.
https:/​/​doi.org/​10.12942/​lrr-2002-5
arXiv:0206071

[51] Paul A. M. Dirac. Gauge invariant formulation of quantum electrodynamics. Can. J. Phys., 33:650, 1955. doi:10.1139/​p55-081.
https:/​/​doi.org/​10.1139/​p55-081

[52] Glenn Barnich. The Coulomb solution as a coherent state of unphysical photons. Gen. Rel. Grav., 43:2527–2530, 2011. arXiv:1001.1387, doi:10.1007/​s10714-010-0984-6.
https:/​/​doi.org/​10.1007/​s10714-010-0984-6
arXiv:1001.1387

[53] Hadrien Chevalier, AJ Paige, and MS Kim. Witnessing the nonclassical nature of gravity in the presence of unknown interactions. Phys. Rev. A, 102(2):022428, 2020. doi:10.1103/​PhysRevA.102.022428.
https:/​/​doi.org/​10.1103/​PhysRevA.102.022428

[54] J. A. Wheeler. Geometrodynamics. Academic, New York, 1962.

[55] Richard L. Arnowitt, Stanley Deser, and Charles W. Misner. The Dynamics of general relativity. Gen. Rel. Grav., 40:1997–2027, 2008. arXiv:gr-qc/​0405109, doi:10.1007/​s10714-008-0661-1.
https:/​/​doi.org/​10.1007/​s10714-008-0661-1
arXiv:gr-qc/0405109

[56] Sean M. Carroll. Spacetime and Geometry. Cambridge University Press, 7 2019.

[57] Magdalena Zych, Fabio Costa, Igor Pikovski, and Časlav Brukner. Bell’s theorem for temporal order. Nature Commun., 10(1):3772, 2019. arXiv:1708.00248, doi:10.1038/​s41467-019-11579-x.
https:/​/​doi.org/​10.1038/​s41467-019-11579-x
arXiv:1708.00248

Cited by

[1] Thomas D. Galley, Flaminia Giacomini, and John H. Selby, "Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible", Quantum 7, 1142 (2023).

[2] Nick Huggett, Niels Linnemann, and Mike D. Schneider, Quantum Gravity in a Laboratory? (2023) ISBN:9781009327541.

[3] Chris Overstreet, Joseph Curti, Minjeong Kim, Peter Asenbaum, Mark A. Kasevich, and Flaminia Giacomini, "Inference of gravitational field superposition from quantum measurements", Physical Review D 108 8, 084038 (2023).

[4] Marios Christodoulou, Andrea Di Biagio, Richard Howl, and Carlo Rovelli, "Gravity entanglement, quantum reference systems, degrees of freedom", Classical and Quantum Gravity 40 4, 047001 (2023).

[5] Isaac Layton, Jonathan Oppenheim, and Zachary Weller-Davies, "A healthier semi-classical dynamics", arXiv:2208.11722, (2022).

[6] Ofek Bengyat, Andrea Di Biagio, Markus Aspelmeyer, and Marios Christodoulou, "Gravity Mediated Entanglement between Oscillators as Quantum Superposition of Geometries", arXiv:2309.16312, (2023).

[7] Yoshimasa Hidaka, Satoshi Iso, and Kengo Shimada, "Entanglement generation and decoherence in a two-qubit system mediated by relativistic quantum field", Physical Review D 107 8, 085003 (2023).

[8] Lin-Qing Chen and Flaminia Giacomini, "Quantum effects in gravity beyond the Newton potential from a delocalised quantum source", arXiv:2402.10288, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-04-15 12:46:29) and SAO/NASA ADS (last updated successfully 2024-04-15 12:46:30). The list may be incomplete as not all publishers provide suitable and complete citation data.