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A Single Entangled System Is an Unbounded Source of Nonlocal Correlations and of Certified Random Numbers
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12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC) - License:
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- Publication Date: 2018-03-14
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Florian J. Curchod, Markus Johansson, Remigiusz Augusiak, Matty J. Hoban, Peter Wittek, and Antonio Acín. A Single Entangled System Is an Unbounded Source of Nonlocal Correlations and of Certified Random Numbers. In 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 73, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.TQC.2017.1
https://doi.org/10.4230/LIPIcs.TQC.2017.1
Abstract
The outcomes of local measurements made on entangled systems can be certified to be random provided that the generated statistics violate a Bell inequality. This way of producing randomness relies only on a minimal set of assumptions because it is independent of the internal functioning of the devices generating the random outcomes. In this context it is crucial to understand both qualitatively and quantitatively how the three fundamental quantities – entanglement, non-locality and randomness – relate to each other. To explore these relationships, we consider the case where repeated (non projective) measurements are made on the physical systems, each measurement being made on the post-measurement state of the previous measurement. In this work, we focus on the following questions: Given a single entangled system, how many nonlocal correlations in a sequence can we obtain? And from this single entangled system, how many certified random numbers is it possible to generate? In the standard scenario with a single measurement in the sequence, it is possible to generate non-local correlations between two distant observers only and the amount of random numbers is very limited. Here we show that we can overcome these limitations and obtain any amount of certified random numbers from a single entangled pair of qubit in a pure state by making sequences of measurements on it. Moreover, the state can be arbitrarily weakly entangled. In addition, this certification is achieved by near-maximal violation of a particular Bell inequality for each measurement in the sequence. We also present numerical results giving insight on the resistance to imperfections and on the importance of the strength of the measurements in our scheme.
Keywords
- Randomness certification
- Nonlocality
- Entanglement
- Sequences of measurements
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References
- Antonio Acín, Serge Massar, and Stefano Pironio. Randomness versus nonlocality and entanglement. Phys. Rev. Lett., 108:100402, Mar 2012. URL: http://dx.doi.org/10.1103/PhysRevLett.108.100402.
- Antonio Acín, Stefano Pironio, Tamás Vértesi, and Peter Wittek. Optimal randomness certification from one entangled bit. Phys. Rev. A, 93(4):040102, April 2016. URL: http://dx.doi.org/10.1103/PhysRevA.93.040102.
- Jean-Daniel Bancal, Lana Sheridan, and Valerio Scarani. More randomness from the same data. New J. Phys., 16(3):033011, 2014. URL: http://dx.doi.org/10.1088/1367-2630/16/3/033011.
-
John S. Bell. On the Einstein Podolsky Rosen paradox. Physics, 1:195, 1964.
- Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner. Bell nonlocality. Rev. Mod. Phys., 86:419-478, Apr 2014. URL: http://dx.doi.org/10.1103/RevModPhys.86.419.
-
Orest Bucicovschi and Jiří Lebl. On the continuity and regularity of convex extensions. J. Convex Anal., 20(4):1113-1126, 2013.
-
Roger Colbeck. Quantum and Relativistic Protocols for Secure Multi-Party Computation. PhD thesis, University of Cambridge, 2006.
- Roger Colbeck and Renato Renner. Free randomness can be amplified. Nat. Phys., 8(6):450-454, May 2012. URL: http://dx.doi.org/10.1038/nphys2300.
- Florian J. Curchod, Markus Johansson, Remigiusz Augusiak, Matty J. Hoban, Peter Wittek, and Antonio Acín. Unbounded randomness certification using sequences of measurements. Phys. Rev. A, 95(2), feb 2017. URL: http://dx.doi.org/10.1103/physreva.95.020102.
- Giacomo Mauro D'Ariano, Paoloplacido Lo Presti, and Paolo Perinotti. Classical randomness in quantum measurements. J. Phys. A: Math. Gen., 38(26):5979, 2005. URL: http://dx.doi.org/10.1088/0305-4470/38/26/010.
- Gonzalo de la Torre, Matty J. Hoban, Chirag Dhara, Giuseppe Prettico, and Antonio Acín. Maximally nonlocal theories cannot be maximally random. Phys. Rev. Lett., 114(16):160502, 2015. URL: http://dx.doi.org/10.1103/physrevlett.114.160502.
- Rodrigo Gallego, Lluis Masanes, Gonzalo De La Torre, Chirag Dhara, Leandro Aolita, and Antonio Acín. Full randomness from arbitrarily deterministic events. Nat. Commun., 4:2654, 2013. URL: http://dx.doi.org/10.1038/ncomms3654.
- Rodrigo Gallego, Lars Erik Würflinger, Rafael Chaves, Antonio Acín, and Miguel Navascués. Nonlocality in sequential correlation scenarios. New J. Phys., 16(3):033037, 2014. URL: http://dx.doi.org/10.1088/1367-2630/16/3/033037.
- Meng-Jun Hu, Zhi-Yuan Zhou, Xiao-Min Hu, Chuan-Feng Li, Guang-Can Guo, and Yong-Sheng Zhang. Experimental sharing of nonlocality among multiple observers with one entangled pair via optimal weak measurements. arXiv:1609.01863, Sep 2016. URL: http://arxiv.org/abs/1609.01863.
- Lluis Masanes, Antonio Acín, and Nicolas Gisin. General properties of nonsignaling theories. Phys. Rev. A, 73(1):012112, Jan 2006. URL: http://dx.doi.org/10.1103/physreva.73.012112.
- Olmo Nieto-Silleras, Stefano Pironio, and Jonathan Silman. Using complete measurement statistics for optimal device-independent randomness evaluation. New J. Phys., 16(1):013035, 2014. URL: http://dx.doi.org/10.1088/1367-2630/16/1/013035.
- Stefano Pironio, Antonio Acín, Serge Massar, Antoine Boyer de la Giroday, Dzmitry N. Matsukevich, Peter Maunz, Steven Matthew Olmschenk, David Hayes, Le Luo, T. Andrew Manning, and Christopher R. Monroe. Random numbers certified by bell’s theorem. Nature, 464(7291):1021-1024, 2010. URL: http://dx.doi.org/10.1038/nature09008.
- Sandu Popescu. Bell’s inequalities and density matrices: Revealing "hidden" nonlocality. Phys. Rev. Lett., 74(14):2619-2622, Apr 1995. URL: http://dx.doi.org/10.1103/physrevlett.74.2619.
- Sandu Popescu and Daniel Rohrlich. Quantum nonlocality as an axiom. Found. Phys., 24(3):379-385, 1994. URL: http://dx.doi.org/10.1007/BF02058098.
-
Tyrrell Rockafellar. Convex Analysis. Princeton Press, 1970.
- Matteo Schiavon, Luca Calderaro, Mirko Pittaluga, Giuseppe Vallone, and Paolo Villoresi. Three-observer bell inequality violation on a two-qubit entangled state. Quantum Science and Technology, 2(1):015010, mar 2017. URL: http://dx.doi.org/10.1088/2058-9565/aa62be.
- Ralph Silva, Nicolas Gisin, Yelena Guryanova, and Sandu Popescu. Multiple observers can share the nonlocality of half of an entangled pair by using optimal weak measurements. Phys. Rev. Lett., 114(25):250401, 2015. URL: http://dx.doi.org/10.1103/physrevlett.114.250401.
- Umesh Vazirani and Thomas Vidick. Certifiable quantum dice. Phil. Trans. R. Soc. A., 370(1971):3432-3448, Jun 2012. URL: http://dx.doi.org/10.1098/rsta.2011.0336.
- Peter Wittek. Algorithm 950: Ncpol2sdpa - sparse semidefinite programming relaxations for polynomial optimization problems of noncommuting variables. ACM Trans. Math. Softw., 41(3):21:1-21:12, 2015. URL: http://dx.doi.org/10.1145/2699464.
- Makoto Yamashita, Katsuki Fujisawa, and Masakazu Kojima. Implementation and evaluation of SDPA 6.0 (semidefinite programming algorithm 6.0). Optimization Methods and Software, 18(4):491-505, 2003. URL: http://dx.doi.org/10.1080/1055678031000118482.