Experimental localisation of quantum entanglement through monitored classical mediator

Soham Pal1, Priya Batra1, Tanjung Krisnanda2, Tomasz Paterek2,3,4, and T. S. Mahesh1

1Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
2School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
3MajuLab, International Joint Research Unit UMI 3654, CNRS, Université Côte d'Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore
4Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland

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


Quantum entanglement is a form of correlation between quantum particles that cannot be increased via local operations and classical communication. It has therefore been proposed that an increment of quantum entanglement between probes that are interacting solely via a mediator implies non-classicality of the mediator. Indeed, under certain assumptions regarding the initial state, entanglement gain between the probes indicates quantum coherence in the mediator. Going beyond such assumptions, there exist other initial states which produce entanglement between the probes via only local interactions with a classical mediator. In this process the initial entanglement between any probe and the rest of the system "flows through" the classical mediator and gets localised between the probes. Here we theoretically characterise maximal entanglement gain via classical mediator and experimentally demonstrate, using liquid-state NMR spectroscopy, the optimal growth of quantum correlations between two nuclear spin qubits interacting through a mediator qubit in a classical state. We additionally monitor, i.e., dephase, the mediator in order to emphasise its classical character. Our results indicate the necessity of verifying features of the initial state if entanglement gain between the probes is used as a figure of merit for witnessing non-classical mediator. Such methods were proposed to have exemplary applications in quantum optomechanics, quantum biology and quantum gravity.

► BibTeX data

► References

[1] A. Al Balushi, W. Cong, and R. B. Mann. Optomechanical quantum Cavendish experiment. Phys. Rev. A, 98: 043811, 2018. URL https:/​/​doi.org/​10.1103/​PhysRevA.98.043811.

[2] P. Batra, V. R. Krithika, and T. S. Mahesh. Push-pull optimization of quantum controls. Phys. Rev. Res., 2 (1): 013314, 2020. URL https:/​/​doi.org/​10.1103/​PhysRevResearch.2.013314.

[3] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters. Mixed-state entanglement and quantum error correction. Phys. Rev. A, 54: 3824, 1996. URL https:/​/​doi.org/​10.1103/​PhysRevA.54.3824.

[4] S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toros, 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. URL https:/​/​doi.org/​10.1103/​PhysRevLett.119.240401.

[5] S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack. Separability of very noisy mixed states and implications for NMR quantum computing. Phys. Rev. Lett., 83: 1054, 1999. URL https:/​/​doi.org/​10.1103/​PhysRevLett.83.1054.

[6] J. Cavanagh, W. J. Fairbrother, A. G. Palmer, and N. J. Skelton. Protein NMR spectroscopy: Principles and practice. Elsevier, 1995.

[7] E. Chitambar and G. Gour. Quantum resource theories. Rev. Mod. Phys., 91: 025001, 2019. URL https:/​/​doi.org/​10.1103/​RevModPhys.91.025001.

[8] T. K. Chuan, L. Maillard, K. Modi, T. Paterek, M. Paternostro, and M. Piani. Quantum discord bounds the amount of distributed entanglement. Phys. Rev. Lett., 109 (7): 070501, 2012. URL https:/​/​doi.org/​10.1103/​PhysRevLett.109.070501.

[9] T. S. Cubitt, F. Verstraete, W. Dür, and J. I. Cirac. Separable states can be used to distribute entanglement. Phys. Rev. Lett., 91 (3): 037902, 2003. URL https:/​/​doi.org/​10.1103/​PhysRevLett.91.037902.

[10] A. Fedrizzi, M. Zuppardo, G. G. Gillett, M. A. Broome, M. Almeida, M. Paternostro, A. White, and T. Paterek. Experimental distribution of entanglement with separable carriers. Phys. Rev. Lett., 111 (23): 230504, 2013. URL https:/​/​doi.org/​10.1103/​PhysRevLett.111.230504.

[11] L. Henderson and V. Vedral. Classical, quantum and total correlations. J. Phys. A, 34 (35): 6899, 2001. URL https:/​/​doi.org/​10.1088/​0305-4470/​34/​35/​315.

[12] M. Horodecki. Simplifying monotonicity conditions for entanglement measures. Open Sys. Inf. Dyn., 12: 231, 2005. URL https:/​/​doi.org/​10.1007/​s11080-005-0920-5.

[13] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki. Quantum entanglement. Rev. Mod. Phys., 81 (2): 865, 2009. URL https:/​/​doi.org/​10.1103/​RevModPhys.81.865.

[14] H. Katiyar, A. Shukla, R. K. Rao, and T. S. Mahesh. Violation of entropic Leggett-Garg inequality in nuclear spins. Phys. Rev. A, 87: 052102, 2013. URL https:/​/​doi.org/​10.1103/​PhysRevA.87.052102.

[15] W. Y. Kon, T. Krisnanda, P. Sengupta, and T. Paterek. Nonclassicality of spin structures in condensed matter: An analysis of Sr$_{14}$Cu$_{24}$O$_{41}$. Phys. Rev. B, 100 (23): 235103, 2019. URL https:/​/​doi.org/​10.1103/​PhysRevB.100.235103.

[16] T. Krisnanda. Distribution of quantum entanglement: Principles and applications. arXiv:2003.08657., 2020.

[17] T. Krisnanda, M. Zuppardo, M. Paternostro, and T. Paterek. Revealing nonclassicality of inaccessible objects. Phys. Rev. Lett., 119: 120402, 2017. URL https:/​/​doi.org/​10.1103/​PhysRevLett.119.120402.

[18] T. Krisnanda, C. Marletto, V. Vedral, M. Paternostro, and T. Paterek. Probing quantum features of photosynthetic organisms. npj Quant. Inf., 4: 60, 2018. URL https:/​/​doi.org/​10.1038/​s41534-018-0110-2.

[19] T. Krisnanda, G. Y. Tham, M. Paternostro, and T. Paterek. Observable quantum entanglement due to gravity. npj Quant. Inf., 6: 12, 2020. URL https:/​/​doi.org/​10.1038/​s41534-020-0243-y.

[20] V. F. Krotov. Quantum system control optimization. In Doklady Mathematics, volume 78, pages 949–952. Springer, 2008. URL https:/​/​doi.org/​10.1134/​S1064562408060380.

[21] M. H. Levitt. Spin dynamics: Basics of nuclear magnetic resonance. John Wiley and Sons, 2001.

[22] 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. URL https:/​/​doi.org/​10.1103/​PhysRevLett.119.240402.

[23] A. Mitra, K. Sivapriya, and A. Kumar. Experimental implementation of a three qubit quantum game with corrupt source using nuclear magnetic resonance quantum information processor. J. Magn. Res., 187.2 (2): 306–313, 2007. URL https:/​/​doi.org/​10.1016/​j.jmr.2007.05.013.

[24] K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral. The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys., 84: 1655, 2012. URL https:/​/​doi.org/​10.1103/​RevModPhys.84.1655.

[25] Tomoyuki Morimae, Keisuke Fujii, and Harumichi Nishimura. Power of one nonclean qubit. Physical Review A, 95 (4): 042336, 2017. URL https:/​/​doi.org/​10.1103/​PhysRevA.95.042336.

[26] M. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.

[27] H. Ollivier and W. H. Zurek. Quantum discord: A measure of the quantumness of correlations. Phys. Rev. Lett., 88 (1): 017901, 2001. URL https:/​/​doi.org/​10.1103/​PhysRevLett.88.017901.

[28] C. Peuntinger, V. Chille, L. Mista, N. Korolkova, M. Förtsch, J. Korger, C. Marquardt, and G. Leuchs. Distributing entanglement with separable states. Phys. Rev. Lett., 111 (23): 230506, 2013. URL https:/​/​doi.org/​10.1103/​PhysRevLett.111.230506.

[29] S. Qvarfort, S. Bose, and A. Serafini. Mesoscopic entanglement through central–potential interactions. J. Phys. B, 53: 235501, 2020. URL https:/​/​doi.org/​10.1088/​1361-6455/​abbe8d.

[30] A. Shukla, K. R. K. Rao, and T. S. Mahesh. Ancilla-assisted quantum state tomogarphy in multiqubit registers. Phys. Rev. A, 87: 062317, 2013. URL https:/​/​doi.org/​10.1103/​PhysRevA.87.062317.

[31] A. Streltsov, H. Kampermann, and D. Bruß. Quantum cost for sending entanglement. Phys. Rev. Lett., 108 (25): 250501, 2012. URL https:/​/​doi.org/​10.1103/​PhysRevLett.108.250501.

[32] A. Streltsov, H. Kampermann, and D. Bruß. Limits for entanglement distribution with separable states. Phys. Rev. A, 90: 032323, 2014. URL https:/​/​doi.org/​10.1103/​PhysRevA.90.032323.

[33] A. Streltsov, R. Augusiak, M. Demianowicz, and M. Lewenstein. Progress towards a unified approach to entanglement distribution. Phys. Rev. A, 92: 012335, 2015. URL https:/​/​doi.org/​10.1103/​PhysRevA.92.012335.

[34] A. Streltsov, H. Kampermann, and D. Bruß. Lectures on general quantum correlations and their applications, chapter Entanglement distribution and quantum discord. Springer International Publishing, 2017. URL https:/​/​link.springer.com/​book/​10.1007.

[35] J. Teles, E. R. DeAzevero, J. C. C. Freitas, R. S. Sarthour, I. S. Oliveira, and T. J. Bonagamba. Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei. Phil. Trans. R. Soc. A, 370: 4770, 2012. URL https:/​/​royalsocietypublishing.org/​doi/​10.1098/​rsta.2011.0365. https:/​/​doi.org/​10.1098/​rsta.2011.0365.

[36] V. Vedral and M. B. Plenio. Entanglement measures and purification procedures. Phys. Rev. A, 57: 1619, 1998. URL https:/​/​doi.org/​10.1103/​PhysRevA.57.1619.

[37] V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight. Quantifying entanglement. Phys. Rev. Lett., 78: 2275, 1997. URL https:/​/​doi.org/​10.1103/​PhysRevLett.78.2275.

[38] G. Vidal and R. F. Werner. Computable measure of entanglement. Phys. Rev. A, 65: 032314, 2002. URL https:/​/​doi.org/​10.1103/​PhysRevA.65.032314.

[39] C. E. Vollmer, D. Schulze, T. Eberle, V. Händchen, J. Fiurášek, and R. Schnabel. Experimental entanglement distribution by separable states. Phys. Rev. Lett., 111 (23): 230505, 2013. URL https:/​/​doi.org/​10.1103/​PhysRevLett.111.230505.

[40] X.-D. Yang, A.-M. Wang, X.-S. Ma, F. Xu, H. You, and W.-Q. Niu. Experimental creation of entanglement using separable states. Chin. Phys. Lett., 22 (2): 279, 2005. URL https:/​/​doi.org/​10.1088/​0256-307x/​22/​2/​004.

[41] M. Zuppardo, T. Krisnanda, T. Paterek, S. Bandyopadhyay, A. Banerjee, P. Deb, S. Halder, K. Modi, and M. Paternostro. Excessive distribution of quantum entanglement. Phys. Rev. A, 93: 012305, 2016. URL https:/​/​doi.org/​10.1103/​PhysRevA.93.012305.

Cited by

[1] Jonathan A. Jones, "Controlling NMR spin systems for quantum computation", Progress in Nuclear Magnetic Resonance Spectroscopy 140-141, 49 (2024).

[2] 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).

[3] M. Kemal Döner and André Großardt, "Is Gravitational Entanglement Evidence for the Quantization of Spacetime?", Foundations of Physics 52 5, 101 (2022).

[4] 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).

[5] Ray Ganardi, Ekta Panwar, Mahasweta Pandit, Bianka Woloncewicz, and Tomasz Paterek, "Quantitative Nonclassicality of Mediated Interactions", PRX Quantum 5 1, 010318 (2024).

[6] Kavita Dorai and Arvind, "NMR Quantum Information Processing: Indian Contributions and Perspectives", Journal of the Indian Institute of Science 103 2, 569 (2023).

[7] Lin-Qing Chen, Flaminia Giacomini, and Carlo Rovelli, "Quantum States of Fields for Quantum Split Sources", Quantum 7, 958 (2023).

[8] André Großardt, "Three little paradoxes: Making sense of semiclassical gravity", AVS Quantum Science 4 1, 010502 (2022).

[9] Bruno F. E. Matarèse, Andrej Rusin, Colin Seymour, and Carmel Mothersill, "Quantum Biology and the Potential Role of Entanglement and Tunneling in Non-Targeted Effects of Ionizing Radiation: A Review and Proposed Model", International Journal of Molecular Sciences 24 22, 16464 (2023).

[10] B. Sharmila, V. R. Krithika, Soham Pal, T. S. Mahesh, S. Lakshmibala, and V. Balakrishnan, "Tomographic entanglement indicators from NMR experiments", The Journal of Chemical Physics 156 15, 154102 (2022).

[11] Marios Christodoulou, Andrea Di Biagio, Markus Aspelmeyer, Časlav Brukner, Carlo Rovelli, and Richard Howl, "Locally Mediated Entanglement in Linearized Quantum Gravity", Physical Review Letters 130 10, 100202 (2023).

[12] 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).

[13] André Großardt and M Kemal Döner, "Lessons and complications from gravitationally induced entanglement", Journal of Physics: Conference Series 2533 1, 012022 (2023).

[14] Akira Matsumura, "Role of matter coherence in entanglement due to gravity", Quantum 6, 832 (2022).

[15] S. Lakshmibala and V. Balakrishnan, SpringerBriefs in Physics 83 (2022) ISBN:978-3-031-19413-9.

[16] Vasileios Fragkos, Michael Kopp, and Igor Pikovski, "On inference of quantization from gravitationally induced entanglement", AVS Quantum Science 4 4, 045601 (2022).

[17] Onur Hosten, "Constraints on probing quantum coherence to infer gravitational entanglement", Physical Review Research 4 1, 013023 (2022).

[18] Tanjung Krisnanda, Su-Yong Lee, Changsuk Noh, Jaewan Kim, Alexander Streltsov, Timothy C H Liew, and Tomasz Paterek, "Correlations and energy in mediated dynamics", New Journal of Physics 24 12, 123025 (2022).

[19] André Großardt, "Self-gravitational dephasing of quasiclassical Stern-Gerlach trajectories", Physical Review D 109 2, L021904 (2024).

[20] Laszlo Gyongyosi and Sandor Imre, "Circuit Depth Reduction for Gate-Model Quantum Computers", Scientific Reports 10, 11229 (2020).

[21] Laszlo Gyongyosi and Sandor Imre, "Scalable distributed gate-model quantum computers", Scientific Reports 11, 5172 (2021).

[22] Richard Howl, Vlatko Vedral, Devang Naik, Marios Christodoulou, Carlo Rovelli, and Aditya Iyer, "Non-Gaussianity as a signature of a quantum theory of gravity", arXiv:2004.01189, (2020).

[23] Laszlo Gyongyosi and Sandor Imre, "Entanglement accessibility measures for the quantum Internet", Quantum Information Processing 19 4, 115 (2020).

[24] Laszlo Gyongyosi, "Quantum State Optimization and Computational Pathway Evaluation for Gate-Model Quantum Computers", Scientific Reports 10, 4543 (2020).

[25] Laszlo Gyongyosi and Sandor Imre, "Theory of Noise-Scaled Stability Bounds and Entanglement Rate Maximization in the Quantum Internet", Scientific Reports 10, 2745 (2020).

[26] Tanjung Krisnanda, "Distribution of quantum entanglement: Principles and applications", arXiv:2003.08657, (2020).

[27] Laszlo Gyongyosi, "Dynamics of entangled networks of the quantum Internet", Scientific Reports 10, 12909 (2020).

[28] Laszlo Gyongyosi, "Unsupervised Quantum Gate Control for Gate-Model Quantum Computers", Scientific Reports 10, 10701 (2020).

[29] Laszlo Gyongyosi and Sandor Imre, "Entanglement concentration service for the quantum Internet", Quantum Information Processing 19 8, 221 (2020).

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

[31] Laszlo Gyongyosi and Sandor Imre, "Routing space exploration for scalable routing in the quantum Internet", Scientific Reports 10, 11874 (2020).

[32] Laszlo Gyongyosi, "Objective function estimation for solving optimization problems in gate-model quantum computers", Scientific Reports 10, 14220 (2020).

[33] Laszlo Gyongyosi, "Decoherence dynamics estimation for superconducting gate-model quantum computers", Quantum Information Processing 19 10, 369 (2020).

[34] B. Sharmila, "Signatures of nonclassical effects in tomograms", arXiv:2009.09798, (2020).

[35] Laszlo Gyongyosi and Sandor Imre, "Resource prioritization and balancing for the quantum internet", Scientific Reports 10, 22390 (2020).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-24 20:16:39) and SAO/NASA ADS (last updated successfully 2024-05-24 20:16:39). The list may be incomplete as not all publishers provide suitable and complete citation data.