Role of matter coherence in entanglement due to gravity

Akira Matsumura

Department of Physics, Kyushu University, Fukuoka, 819-0395, Japan

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We investigate the quantum nature of gravity in terms of the coherence of quantum objects. As a basic setting, we consider two gravitating objects each in a superposition state of two paths. The evolution of objects is described by the completely positive and trace-preserving (CPTP) map with a population-preserving property. This property reflects that the probability of objects being on each path is preserved. We use the $\ell_1$-norm of coherence to quantify the coherence of objects. In the present paper, the quantum nature of gravity is characterized by an entangling map, which is a CPTP map with the capacity to create entanglement. We introduce the entangling-map witness as an observable to test whether a given map is entangling. We show that, whenever the gravitating objects initially have a finite amount of the $\ell_1$-norm of coherence, the witness tests the entangling map due to gravity. Interestingly, we find that the witness can test such a quantum nature of gravity, even when the objects do not get entangled. This means that the coherence of gravitating objects always becomes the source of the entangling map due to gravity. We further discuss a decoherence effect and an experimental perspective in the present approach.

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[1] S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M Toro$\check{\text{s}}$, 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).

[2] C. Marletto and V. Vedral, ``Gravitationally Induced Entanglement between Two Massive Particles is Sufficient Evidence of Quantum Effects in Gravity'', Phys. Rev. Lett. 119, 240402 (2017).

[3] H. Chau Nguyen and F. Bernards, ``Entanglement dynamics of two mesoscopic objects with gravitational interaction'', Eur. Phys. J. D 74, 69 (2020).

[4] H. Chevalier, A. J. Paige, and M. S. Kim, ``Witnessing the nonclassical nature of gravity in the presence of unknown interactions'', Phys. Rev. A 102, 022428 (2020).

[5] T. W. van de Kamp, R. J. Marshman, S. Bose, and A. Mazumdar, ``Quantum gravity witness via entanglement of masses: Casimir screening'', Phys. Rev. A 102, 062807 (2020).

[6] D. Miki, A. Matsumura, and K. Yamamoto, ``Entanglement and decoherence of massive particles due to gravity'', Phys. Rev. D 103, 026017 (2021).

[7] J. Tilly, R. J. Marshman, A. Mazumdar and S. Bose, ``Qudits for Witnessing Quantum Gravity Induced Entanglement of Masses Under Decoherence'', Phys. Rev. A 104, 052416 (2021).

[8] T. Krisnanda, G. Y. Tham, M. Paternostro, and T. Paterek, ``Observable quantum entanglement due to gravity'', Quantum Inf. 6, 12 (2020).

[9] S. Qvarfort, S. Bose, and A. Serafini, ``Mesoscopic entanglement through central–potential interactions'', J. Phys. B: At. Mol. Opt. Phys. 53, 235501 (2020).

[10] A. A. Balushi, W. Cong, and R. B. Mann, ``Optomechanical quantum Cavendish experiment'', Phys. Rev. A 98 043811 (2018).

[11] H. Miao, D. Martynov, H. Yang, and A. Datta, ``Quantum correlations of light mediated by gravity'', Phys. Rev. A 101 063804 (2020).

[12] A. Matsumura, K. Yamamoto, ``Gravity-induced entanglement in optomechanical systems'', Phys. Rev. D 102 106021 (2020).

[13] D. Miki, A. Matsumura, K. Yamamoto, ``Non-Gaussian entanglement in gravitating masses: The role of cumulants'', Phys. Rev. D 105, 026011 (2022).

[14] D. Carney, H. Muller, and J. M. Taylor, ``Using an Atom Interferometer to Infer Gravitational Entanglement Generation'', Phys. Rev. X Quantum 2 030330 (2021).

[15] J. S. Pedernales, K. Streltsov and M. Plenio, ``Enhancing Gravitational Interaction between Quantum Systems by a Massive Mediator'', Phys. Rev. Lett. 128, 110401 (2022).

[16] A. Matsumura, Y. Nambu and K. Yamamoto, ``Leggett-Garg inequalities for testing quantumness of gravity'', Phys. Rev. A 106,012214 (2022).

[17] M. Bahrami, A. Großardt, S. Donadi and A. Bassi, ``The Schrödinger–Newton equation and its foundations'', New J. Phys. 16, 115007 (2014).

[18] D. Kafri, J. M. Taylor, and G. J. Milburn, ``A classical channel model for gravitational decoherence'', New J. Phys. 16, 065020 (2014).

[19] T. Baumgratz, M. Cramer, and M. B. Plenio, ``Quantifying Coherence'', Phys. Rev. Lett. 113, 140401 (2014).

[20] A. W. Harrow and M. A. Nielsen, ``Robustness of quantum gates in the presence of noise'', Phys. Rev. A 68, 012308 (2003).

[21] F. G. S. L. Brand$\tilde{\text{a}}$o and M. B. Plenio, ``A Reversible Theory of Entanglement and its Relation to the Second Law'', Commun. Math. Phys. 295, 829 (2010).

[22] M. A. Nielsen and I. Chuang, ``Quantum Computation and Quantum Information'' (Cambridge University Press, Cambridge, England, 2002).

[23] A. Matsumura, ``Path-entangling operation and quantum gravitational interaction'', Phys. Rev. A 105, 042425 (2022).

[24] S. Bose, A. Mazumdar, M. Schut, and M. Toro$\check{\text{s}}$, ``Mechanism for the quantum natured gravitons to entangle masses'', Phys. Rev. D 105, 106028 (2022).

[25] R. J. Marshman, A. Mazumdar, and S. Bose, ``Locality and entanglement in table-top testing of the quantum nature of linearized gravity'', Phys. Rev. A 101, 052110 (2020).

[26] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, ``Quantum entanglement'', Rev. Mod. Phys. 81, (2009) 865.

[27] R. Werner, ``Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model'', Phys. Rev. A 40, 4277 (1989).

[28] A. Peres, ``Separability Criterion for Density Matrices'', Phys. Rev. Lett. 77, (1996) 1413.

[29] M. Horodecki, R. Horodecki, and P. Horodecki, ``Separability of mixed states: necessary and sufficient conditions'', Phys. Lett. A 223, (1996) 1-8.

[30] G. Vidal and R. F. Werner, ``Computable measure of entanglement'', Phys. Rev. A 65, 032314 (2002).

[31] E. M. Rains, ``Entanglement purification via separable superoperators'', arXiv: quant-ph/​9707002(1997).

[32] V. Vedral and M. B. Plenio, ``Entanglement measures and purification procedures'', Phys. Rev. A 57, 1619 (1998).

[33] E. Chitambar, D. Leung, L. Mančinska, M. Ozols, and A. Winter, ``Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)'', Commun. Math. Phys. 328, 303 (2014).

[34] J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein, ``Entangling Operations and Their Implementation Using a Small Amount of Entanglement'', Phys. Rev. Lett. 86, 544 (2001).

[35] A. Jamiolkowski, ``Linear transformations which preserve trace and positive semidefiniteness of operators", Rep. Math. Phys. 3, 275 (1972).

[36] M.-D. Choi, ``Completely positive linear maps on complex matrices'', Linear Algebra Appl. 10, 285 (1975).

[37] S. Pal, P. Batra, T. Krisnanda, T. Paterek, and T. S. Mahesh, ``Experimental localisation of quantum entanglement through monitored classical mediator", Quantum 5, 478 (2021).

[38] T. Krisnanda, M. Zuppardo, M. Paternostro, and T. Paterek, and T. S. Mahesh, ``Revealing Nonclassicality of Inaccessible Objects'', Phys. Rev. Lett. 119, 120402 (2017).

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