Noise-robust preparation contextuality shared between any number of observers via unsharp measurements

Hammad Anwer1, Natalie Wilson1, Ralph Silva2, Sadiq Muhammad1, Armin Tavakoli3,4,5, and Mohamed Bourennane1

1Department of Physics, Stockholm University, S-10691 Stockholm, Sweden
2Institute for Theoretical Physics, ETH Zurich, Switzerland
3Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
4Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
5Institute for Atomic and Subatomic Physics, Vienna University of Technology, 1020 Vienna, Austria

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Multiple observers who independently harvest nonclassical correlations from a single physical system share the system's ability to enable quantum correlations. We show that any number of independent observers can share the preparation contextual outcome statistics enabled by state ensembles in quantum theory. Furthermore, we show that even in the presence of any amount of white noise, there exists quantum ensembles that enable such shared preparation contextuality. The findings are experimentally realised by applying sequential unsharp measurements to an optical qubit ensemble which reveals three shared demonstrations of preparation contextuality.

When a quantum resource is measured, information is extracted from it at the price of distorting the state. Here, we aim to extract information from a quantum ensemble in such a way that classical noncontextual models cannot account for the lab observations, while simultaneously not distorting the ensemble too much to prevent us from doing such an extraction once again. We show that, in fact, one can extract contextual quantum correlations indefinitely many times from a single ensemble and we demonstrate three sequential violations of noncontextuality in an optics experiment.

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[1] C. A. Fuchs, and A. Peres, Quantum-state disturbance versus information gain: Uncertainty relations for quantum information Phys. Rev. A 53, 2038 (1996).

[2] R. Gallego, L. E. Würflinger, R. Chaves, A. Acín, M. Navascués, Nonlocality in sequential correlation scenarios, New J. Phys. 16, 033037 (2014).

[3] C. Budroni, T. Moroder, M. Kleinmann, and O. Gühne, Bounding Temporal Quantum Correlations, Phys. Rev. Lett. 111, 020403 (2013).

[4] R. Silva, N. Gisin, Y. Guryanova, and S. Popescu, Multiple Observers Can Share the Nonlocality of Half of an Entangled Pair by Using Optimal Weak Measurements, Phys. Rev. Lett. 114, 250401 (2015).

[5] A. Tavakoli, A. Cabello, Quantum predictions for an unmeasured system cannot be simulated with a finite-memory classical system, Phys. Rev. A 97, 032131 (2018).

[6] P. J. Brown and R. Colbeck Arbitrarily Many Independent Observers Can Share the Nonlocality of a Single Maximally Entangled Qubit Pair, Phys. Rev. Lett. 125, 090401 (2020).

[7] F. J. Curchod, M. Johansson, R. Augusiak, M. J. Hoban, P. Wittek, and A. Acín, Unbounded randomness certification using sequences of measurements, Phys. Rev. A 95, 020102(R) (2017).

[8] B. Coyle, M. J. Hoban, and E. Kashefi, One-Sided Device-Independent Certification of Unbounded Random Numbers, EPTCS 273, 14-26 (2018).

[9] G. Foletto, L. Calderaro, A. Tavakoli, M. Schiavon, F. Picciariello, A. Cabello, P. Villoresi, and G. Vallone, Experimental Certification of Sustained Entanglement and Nonlocality after Sequential Measurements, Phys. Rev. Applied 13, 044008 (2020).

[10] M. Schiavon, L. Calderaro, M. Pittaluga, G. Vallone, and P. Villoresi, Three-observer Bell inequality violation on a two-qubit entangled state, Quantum Sci. Technol. 2 015010 (2017).

[11] M-J. Hu, Z-Y. Zhou, X-M. Hu, C-F. Li, G-C. Guo, and Y-S. Zhang, Observation of non-locality sharing among three observers with one entangled pair via optimal weak measurement, npj Quantum Information 4, 63 (2018).

[12] A. Bera, S. Mal, A. Sen De, and U. Sen, Witnessing bipartite entanglement sequentially by multiple observers, Phys. Rev. A 98, 062304 (2018).

[13] S. Sasmal, D. Das, S. Mal, and A.S. Majumdar, Steering a single system sequentially by multiple observers, Phys. Rev. A 98, 012305 (2018).

[14] A. Shenoy H, S. Designolle, F. Hirsch, R. Silva, N. Gisin, and N. Brunner, Unbounded sequence of observers exhibiting Einstein-Podolsky-Rosen steering, Phys. Rev. A 99, 022317 (2019).

[15] K. Mohan. A. Tavakoli, and N. Brunner, Sequential random access codes and self-testing of quantum measurement instruments, New J. Phys. 21 083034 (2019).

[16] N. Miklin, J. Borkala, and M. Pawlowski, Semi-device-independent self-testing of unsharp measurements, Phys. Rev. Research 2, 033014 (2020).

[17] H. Anwer, S. Muhammad, W. Cherifi, N. Miklin, A. Tavakoli, and M. Bourennane, Experimental Characterization of Unsharp Qubit Observables and Sequential Measurement Incompatibility via Quantum Random Access Codes, Phys. Rev. Lett. 125, 080403 (2020).

[18] G. Foletto, L. Calderaro, G. Vallone, and P. Villoresi, Experimental demonstration of sequential quantum random access codes, Phys. Rev. Research 2, 033205 (2020).

[19] R. W. Spekkens, Contextuality for preparations, transformations, and unsharp measurements Phys. Rev. A 71, 052108 (2005).

[20] R. W. Spekkens, Negativity and Contextuality are Equivalent Notions of Nonclassicality, Phys. Rev. Lett. 101, 020401 (2008).

[21] R. W. Spekkens, D. H. Buzacott, A. J. Keehn, B. Toner, and G. J. Pryde, Preparation Contextuality Powers Parity-Oblivious Multiplexing Phys. Rev. Lett. 102, 010401 (2009).

[22] M. S. Leifer, and O. J. E. Maroney, Maximally Epistemic Interpretations of the Quantum State and Contextuality, Phys. Rev. Lett. 110, 120401 (2013).

[23] M. Banik, S. S. Bhattacharya, A. Mukherjee, A. Roy, A. Ambainis, and A. Rai, Limited preparation contextuality in quantum theory and its relation to the Cirel'son bound, Phys. Rev. A 92, 030103(R) (2015).

[24] S. Ghorai, A. K. Pan, Optimal quantum preparation contextuality in an n-bit parity-oblivious multiplexing task Phys. Rev. A 98, 032110 (2018).

[25] A. Tavakoli and R. Uola, Measurement incompatibility and steering are necessary and sufficient for operational contextuality, Phys. Rev. Research 2, 013011 (2020).

[26] D. Saha, and A. Chaturvedi, Preparation contextuality: the ground of quantum communication advantage, Phys. Rev. A 100, 022108 (2019).

[27] A. Tavakoli, E. Zambrini Cruzeiro, R. Uola, and A. A. Abbott, Bounding and Simulating Contextual Correlations in Quantum Theory, PRX Quantum 2, 020334 (2021).

[28] A. Chaturvedi, M. Farkas, and V. Wright, Characterising and bounding the set of quantum behaviours in contextuality scenarios, Quantum 5, 484 (2021).

[29] A. Hameedi, A. Tavakoli, B. Marques, and M. Bourennane, Communication games reveal preparation contextuality, Phys. Rev. Lett. 119, 220402 (2017).

[30] M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, An experimental test of noncontextuality without unphysical idealizations, Nature Communications 7, 11780 (2016).

[31] S. Kochen, and E. P. Specker, The Problem of Hidden Variables in Quantum Mechanics, Indiana University Mathematics Journal, 17, 59 (1967).

[32] N. Harrigan, and R. W. Spekkens, Einstein, Incompleteness, and the Epistemic View of Quantum States, Found Phys (2010) 40, 125 (2010).

[33] A. Ambainis, A. Nayak, A. Ta-Shma, U. Vazirani, Dense quantum coding and a lower bound for 1-way quantum automata, Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC'99), 376-383 (1999).

[34] A. Tavakoli, A. Hameedi, B. Marques, and M. Bourennane, Quantum random access codes using single d-Level systems, Phys. Rev. Lett. 114, 170502 (2015).

[35] A. Chailloux, I. Kerenidis, S. Kundu, and J. Sikora, Optimal bounds for parity-oblivious random access codes, New J. Phys. 18, 045003 (2016).

[36] One could alternatively consider the Bobs' measurement devices inducing the noise. However, this is less detrimental than noisy preparations. The reason is that if Alice's preparations are noisy the correlations due to all Bobs' measurements are weaker, whereas if instead one (or many) of the Bobs sometimes fail to perform the intended measurement, the state relayed to the next Bob retains a higher degree of coherence and leads to him observering stronger correlations.

[37] A. Kumari and A. K. Pan, Sharing nonlocality and nontrivial preparation contextuality using the same family of Bell expressions, Phys. Rev. A 100, 062130 (2019).

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[10] Ya-Li Mao, Zheng-Da Li, Anna Steffinlongo, Bixiang Guo, Biyao Liu, Shufeng Xu, Nicolas Gisin, Armin Tavakoli, and Jingyun Fan, "Recycling nonlocality in quantum star networks", Physical Review Research 5 1, 013104 (2023).

[11] Meng Yan, Hao-Zhan Zou, and Xiang Zhan, "Qubit measurements for testing contextuality through the violation of Liang-Spekkens-Wiseman-Yu-Oh inequality", New Journal of Physics 25 8, 083032 (2023).

[12] Zinuo Cai and Changliang Ren, "Full network nonlocality sharing in extended bilocal scenario via weak measurements with the optimal pointer", Journal of Physics A: Mathematical and Theoretical 57 19, 195305 (2024).

[13] Jaskaran Singh, Rajendra Singh Bhati, and Arvind, "Revealing quantum contextuality using a single measurement device", Physical Review A 107 1, 012201 (2023).

[14] Xin-Hong Han, Hui-Chao Qu, Xuan Fan, Ya Xiao, and Yong-Jian Gu, "Manipulating the quantum steering direction with sequential unsharp measurements", Physical Review A 106 4, 042416 (2022).

[15] Shufen Dong, Zinuo Cai, Chunfeng Wu, and Changliang Ren, "Sharing quantum steering via standard projective measurements", Physical Review A 110 1, 012203 (2024).

[16] Shuming Cheng, Lijun Liu, Travis J. Baker, and Michael J. W. Hall, "Recycling qubits for the generation of Bell nonlocality between independent sequential observers", Physical Review A 105 2, 022411 (2022).

[17] Debarshi Das, Arkaprabha Ghosal, Ananda G. Maity, Som Kanjilal, and Arup Roy, "Ability of unbounded pairs of observers to achieve quantum advantage in random access codes with a single pair of qubits", Physical Review A 104 6, L060602 (2021).

[18] Costantino Budroni, Adán Cabello, Otfried Gühne, Matthias Kleinmann, and Jan-Åke Larsson, "Kochen-Specker contextuality", Reviews of Modern Physics 94 4, 045007 (2022).

[19] Karthik Mohan, Armin Tavakoli, and Nicolas Brunner, "Sequential random access codes and self-testing of quantum measurement instruments", New Journal of Physics 21 8, 083034 (2019).

[20] Asmita Kumari and A. K. Pan, "Sharing nonlocality and nontrivial preparation contextuality using the same family of Bell expressions", Physical Review A 100 6, 062130 (2019).

[21] Hammad Anwer, Sadiq Muhammad, Walid Cherifi, Nikolai Miklin, Armin Tavakoli, and Mohamed Bourennane, "Experimental Characterization of Unsharp Qubit Observables and Sequential Measurement Incompatibility via Quantum Random Access Codes", Physical Review Letters 125 8, 080403 (2020).

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[23] Ananda G. Maity, Debarshi Das, Arkaprabha Ghosal, Arup Roy, and A. S. Majumdar, "Detection of genuine tripartite entanglement by multiple sequential observers", Physical Review A 101 4, 042340 (2020).

[24] Shashank Gupta, Ananda G. Maity, Debarshi Das, Arup Roy, and A. S. Majumdar, "Genuine Einstein-Podolsky-Rosen steering of three-qubit states by multiple sequential observers", Physical Review A 103 2, 022421 (2021).

[25] Armin Tavakoli, Emmanuel Zambrini Cruzeiro, Roope Uola, and Alastair A. Abbott, "Bounding and Simulating Contextual Correlations in Quantum Theory", PRX Quantum 2 2, 020334 (2021).

[26] Gautam Sharma, Sk Sazim, and Shiladitya Mal, "Role of fine-grained uncertainty in determining the limit of preparation contextuality", Physical Review A 104 3, 032424 (2021).

[27] Shihui Wei, Fenzhuo Guo, Fei Gao, and Qiaoyan Wen, "Certification of three black boxes with unsharp measurements using 3 → 1 sequential quantum random access codes", New Journal of Physics 23 5, 053014 (2021).

[28] Gautam Sharma, Sk Sazim, and Shiladitya Mal, "Role of fine-grained uncertainty in determining the limit of preparation contextuality", arXiv:1905.09695, (2019).

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