Laboratoire d’Information Quantique, Université libre de Bruxelles (ULB), Belgium
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Abstract
Losses in the transmission channel, which increase with distance, pose a major obstacle to photonics demonstrations of quantum nonlocality and its applications. Recently, Chaturvedi, Viola, and Pawlowski (CVP) [arXiv:2211.14231] introduced a variation of standard Bell experiments with the goal of extending the range over which quantum nonlocality can be demonstrated. These experiments, which we call `routed Bell experiments’, involve two distant parties, Alice and Bob, and allow Bob to route his quantum particle along two possible paths and measure it at two distinct locations – one near and another far from the source. The premise is that a high-quality Bell violation in the short-path should constrain the possible strategies underlying the experiment, thereby weakening the conditions required to detect nonlocal correlations in the long-path. Building on this idea, CVP showed that there are certain quantum correlations in routed Bell experiments such that the outcomes of the remote measurement device cannot be classically predetermined, even when its detection efficiency is arbitrarily low. In this paper, we show that the correlations considered by CVP, though they cannot be classically predetermined, do not require the transmission of quantum systems to the remote measurement device. This leads us to define and formalize the concept of `short-range’ and `long-range’ quantum correlations in routed Bell experiments. We show that these correlations can be characterized through standard semidefinite-programming hierarchies for non-commutative polynomial optimization. We then explore the conditions under which short-range quantum correlations can be ruled out and long-range quantum nonlocality can be certified in routed Bell experiments. We point out that there exist fundamental lower-bounds on the critical detection efficiency of the distant measurement device, implying that routed Bell experiments cannot demonstrate long-range quantum nonlocality at arbitrarily large distances. However, we do find that routed Bell experiments allow for reducing the detection efficiency threshold necessary to certify long-range quantum correlations. The improvements, though, are significantly smaller than those suggested by CVP’s analysis.
Featured image: Correlations produced in a routed Bell experiment.
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► References
[1] Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, and Valerio Scarani, “Device-Independent Security of Quantum Cryptography against Collective Attacks” Phys. Rev. Lett. 98, 230501 (2007).
https://doi.org/10.1103/PhysRevLett.98.230501
[2] MOSEK ApS “Python API for Mosek. Version 10.1.28” manual.
https://docs.mosek.com/latest/pythonapi/index.html
[3] Charles H. Bennettand Gilles Brassard “Quantum cryptography: Public key distribution and coin tossing” Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing 175 (1984).
https://doi.org/10.1016/j.tcs.2014.05.025
arXiv:2003.06557
[4] Charles H. Bennett, Gilles Brassard, and David Mermin, “Quantum cryptography without Bell’s theorem” Phys. Rev. Lett. 68, 557–559 (1992).
https://doi.org/10.1103/PhysRevLett.68.557
[5] Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde, and Howard M. Wiseman, “A strong no-go theorem on the Wigner’s friend paradox” Nat. Phys. 16, 1199–1205 (2020).
https://doi.org/10.1038/s41567-020-0990-x
arXiv:1907.05607
[6] Joseph Bowles, Ivan Šupić, Daniel Cavalcanti, and Antonio Acín, “Device-independent entanglement certification of all entangled states” Phys. Rev. Lett. 121, 180503 (2018).
https://doi.org/10.1103/physrevlett.121.180503
arXiv:1801.10444
[7] Cédric Bampsand Stefano Pironio “Sum-of-squares decompositions for a family of Clauser-Horne-Shimony-Holt-like inequalities and their application to self-testing” Phys. Rev. A 91, 052111 (2015).
https://doi.org/10.1103/physreva.91.052111
arXiv:1504.06960
[8] Cyril Branciard “Detection loophole in Bell experiments: How postselection modifies the requirements to observe nonlocality” Phys. Rev. A 83, 032123 (2011).
https://doi.org/10.1103/PhysRevA.83.032123
arXiv:1010.1178
[9] Peter Brown “Github Repository for NCPOL2SDPA”.
https://github.com/peterjbrown519/ncpol2sdpa
[10] Nicolas Brunner, Edwin Peter Lobo, Jef Pauwels, Stefano Pironio, Pavel Sekatski, and Mirjam Weilenmann, In preparation.
[11] Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner, “Bell nonlocality” Rev. Mod. Phys. 86, 419–478 (2014).
https://doi.org/10.1103/revmodphys.86.419
arXiv:1303.2849
[12] Paul Busch “Unsharp reality and joint measurements for spin observables” Phys. Rev. D 33, 2253 (1986).
https://doi.org/10.1103/physrevd.33.2253
[13] John F. Clauserand Michael A. Horne “Experimental consequences of objective local theories” Phys. Rev. D 10, 526–535 (1974).
https://doi.org/10.1103/PhysRevD.10.526
[14] Boris C. Cirel’son “Quantum generalizations of Bell’s inequality” Lett. Math. Phys. 4, 93–100 (1980).
https://doi.org/10.1007/bf00417500
[15] Adan Cabelloand Jan-Åke Larsson “Minimum detection efficiency for a loophole-free atom-photon Bell experiment” Phys. Rev. Lett. 98, 220402 (2007).
https://doi.org/10.1103/physrevlett.98.220402
[16] Anubhav Chaturvedi, Giuseppe Viola, and Marcin Pawłowski, “Extending loophole-free nonlocal correlations to arbitrarily large distances” (2022).
arXiv:2211.14231v1
[17] Anubhav Chaturvedi, Giuseppe Viola, and Marcin Pawłowski, “Extending loophole-free nonlocal correlations to arbitrarily large distances” npj Quantum Information 10, 7 (2024).
https://doi.org/10.1038/s41534-023-00799-1
arXiv:2211.14231v2
[18] Philippe H. Eberhard “Background level and counter efficiencies required for a loophole-free Einstein-Podolsky-Rosen experiment” Phys. Rev. A 47, R747–R750 (1993).
https://doi.org/10.1103/PhysRevA.47.R747
[19] Anupam Gargand N David Mermin “Detector inefficiencies in the Einstein-Podolsky-Rosen experiment” Phys. Rev. D 35, 3831 (1987).
https://doi.org/10.1103/physrevd.35.3831
[20] Otfried Gühneand Géza Tóth “Entanglement detection” Phys. Reps. 474, 1–75 (2009).
https://doi.org/10.1016/j.physrep.2009.02.004
arXiv:0811.2803
[21] Teiko Heinosaari, Takayuki Miyadera, and Mário Ziman, “An invitation to quantum incompatibility” J. Phys. A Math. Theor. 49, 123001 (2016).
https://doi.org/10.1088/1751-8113/49/12/123001
arXiv:1511.07548
[22] Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen, “MIP*=RE” (2022).
arXiv:2001.04383
[23] Pekka Lahti “Coexistence and joint measurability in quantum mechanics” Int. J. Theor. Phys 42, 893–906 (2003).
https://doi.org/10.1023/A:1025406103210
[24] Jan-Åke Larsson “Bell’s inequality and detector inefficiency” Phys. Rev. A 57, 3304 (1998).
https://doi.org/10.1103/physreva.57.3304
[25] Edwin Peter Loboand Stefano Pironio (2024) In preparation.
[26] Michele Masini, Marie Ioannou, Nicolas Brunner, Stefano Pironio, and Pavel Sekatski, “Joint-measurability and quantum communication with untrusted devices” (2024).
arXiv:2403.14785
[27] Serge Massarand Stefano Pironio “Violation of local realism versus detection efficiency” Phys. Rev. A 68, 062109 (2003).
https://doi.org/10.1103/PhysRevA.68.062109
[28] Dominic Mayersand Andrew Yao “Self testing quantum apparatus” Quantum Information and Computation 4, 273–286 (2004).
https://doi.org/10.26421/qic4.4-3
[29] Miguel Navascués, Stefano Pironio, and Antonio Acín, “Bounding the Set of Quantum Correlations” Phys. Rev. Lett. 98, 010401 (2007).
https://doi.org/10.1103/PhysRevLett.98.010401
[30] Miguel Navascués, Stefano Pironio, and Antonio Acín, “A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations” New J. Phys. 10, 073013 (2008).
https://doi.org/10.1088/1367-2630/10/7/073013
arXiv:0803.4290
[31] Jef Pauwels, Stefano Pironio, Emmanuel Zambrini Cruzeiro, and Armin Tavakoli, “Adaptive Advantage in Entanglement-Assisted Communications” Phys. Rev. Lett. 129, 120504 (2022).
https://doi.org/10.1103/PhysRevLett.129.120504
arXiv:2203.05372
[32] Philip M. Pearle “Hidden-Variable Example Based upon Data Rejection” Phys. Rev. D 2, 1418–1425 (1970).
https://doi.org/10.1103/physrevd.2.1418
[33] Stefano Pironio, Antonio Acín, Serge Massar, A Boyer de La Giroday, Dzmitry N Matsukevich, Peter Maunz, Steven Olmschenk, David Hayes, Le Luo, and T Andrew Manning, “Random numbers certified by Bell’s theorem” Nature 464, 1021–1024 (2010).
https://doi.org/10.1038/nature09008
arXiv:0911.3427
[34] Stefano Pironio, Miguel Navascués, and Antonio Acin, “Convergent relaxations of polynomial optimization problems with noncommuting variables” SIOPT 20, 2157–2180 (2010).
https://doi.org/10.1137/090760155
arXiv:0903.4368
[35] Matthew F. Pusey “Verifying the quantumness of a channel with an untrusted device” JOSA B 32, A56 (2015).
https://doi.org/10.1364/josab.32.000a56
arXiv:1502.03010
[36] Gilles Pütz, Anthony Martin, Nicolas Gisin, Djeylan Aktas, Bruno Fedrici, and Sébastien Tanzilli, “Quantum nonlocality with arbitrary limited detection efficiency” Phys. Rev. Lett. 116, 010401 (2016).
https://doi.org/10.1103/physrevlett.116.010401
arXiv:1509.07139
[37] Tristan Le Roy-Deloison, Edwin Peter Lobo, Jef Pauwels, and Stefano Pironio, “Device-independent quantum key distribution based on routed Bell tests” (2024).
arXiv:2404.01202
[38] Ivan Šupićand Joseph Bowles “Self-testing of quantum systems: a review” Quantum 4, 337 (2020).
https://doi.org/10.22331/q-2020-09-30-337
arXiv:1904.10042
[39] William Slofstra “Tsirelson’s problem and an embedding theorem for groups arising from non-local games” JAMS 33, 1–56 (2019).
https://doi.org/10.1090/jams/929
arXiv:1606.03140
[40] Peter W. Shorand John Preskill “Simple Proof of Security of the BB84 Quantum Key Distribution Protocol” Phys. Rev. Lett. 85, 441–444 (2000).
https://doi.org/10.1103/PhysRevLett.85.441
[41] Marco Tomamichel, Serge Fehr, Jędrzej Kaniewski, and Stephanie Wehner, “One-sided device-independent QKD and position-based cryptography from monogamy games” Advances in Cryptology–EUROCRYPT 2013: 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26-30, 2013. Proceedings 32 609–625 (2013).
https://doi.org/10.1007/978-3-642-38348-9_36
[42] Benjamin Tonerand Frank Verstraete “Monogamy of Bell correlations and Tsirelson’s bound” (2006).
[43] Roope Uola, Tobias Moroder, and Otfried Gühne, “Joint Measurability of Generalized Measurements Implies Classicality” Phys. Rev. Lett. 113, 160403 (2014).
https://doi.org/10.1103/PhysRevLett.113.160403
arXiv:1407.2224
[44] Johannes Wilms, Yann Disser, Gernot Alber, and Ian C. Percival, “Local realism, detection efficiencies, and probability polytopes” Phys. Rev. A 78, 032116 (2008).
https://doi.org/10.1103/physreva.78.032116
arXiv:0808.2126
[45] Peter Wittek “Algorithm 950: Ncpol2sdpa—Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables” ACM Trans. Math. Softw. 41 (2015).
https://doi.org/10.1145/2699464
arXiv:1308.6029
[46] Erik Woodhead “Quantum cloning bound and application to quantum key distribution” Phys. Rev. A 88, 012331 (2013).
https://doi.org/10.1103/physreva.88.012331
arXiv:1303.4821
[47] Erik Woodhead “Imperfections and self testing in prepare-and-measure quantum key distribution” thesis (2014).
https://dipot.ulb.ac.be/dspace/bitstream/2013/209185/1/23388d86-c59c-449c-b88a-1e97a45f1ad8.txt
[48] Erik Woodhead, Stefano Pironio, and Jonathan Silman, “Partially deterministic polytopes” In preparation.
[49] Sixia Yuand Nai-le Liu “Entanglement Detection by Local Orthogonal Observables” Phys. Rev. Lett. 95, 150504 (2005).
https://doi.org/10.1103/PhysRevLett.95.150504
[50] Víctor Zapatero, Tim van Leent, Rotem Arnon-Friedman, Wen-Zhao Liu, Qiang Zhang, Harald Weinfurter, and Marcos Curty, “Advances in device-independent quantum key distribution” Npj Quantum Inf. 9, 10 (2023).
https://doi.org/10.1038/s41534-023-00684-x
arXiv:2208.12842
Cited by
[1] Tristan Le Roy-Deloison, Edwin Peter Lobo, Jef Pauwels, and Stefano Pironio, “Device-independent quantum key distribution based on routed Bell tests”, arXiv:2404.01202, (2024).
[2] Luis Villegas-Aguilar, Emanuele Polino, Farzad Ghafari, Marco Túlio Quintino, Kiarn T. Laverick, Ian R. Berkman, Sven Rogge, Lynden K. Shalm, Nora Tischler, Eric G. Cavalcanti, Sergei Slussarenko, and Geoff J. Pryde, “Nonlocality activation in a photonic quantum network”, Nature Communications 15, 3112 (2024).
[3] Anubhav Chaturvedi, Giuseppe Viola, and Marcin Pawłowski, “Extending loophole-free nonlocal correlations to arbitrarily large distances”, npj Quantum Information 10, 7 (2024).
[4] Michele Masini, Marie Ioannou, Nicolas Brunner, Stefano Pironio, and Pavel Sekatski, “Joint-measurability and quantum communication with untrusted devices”, arXiv:2403.14785, (2024).
The above citations are from SAO/NASA ADS (last updated successfully 2024-05-02 12:43:35). The list may be incomplete as not all publishers provide suitable and complete citation data.
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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.
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