Quantum randomness extraction for various levels of characterization of the devices

The amount of intrinsic randomness that can be extracted from measurement on quantum systems depends on several factors: notably, the power given to the adversary and the level of characterization of the devices of the authorized partners. After presenting a systematic introduction to these notions, in this paper we work in the class of least adversarial power, which is relevant for assessing setups operated by trusted experimentalists, and compare three levels of characterization of the devices. Many recent studies have focused on the so-called ?device-independent? level, in which a lower bound on the amount of intrinsic randomness can be certified without any characterization. The other extreme is the case when all the devices are fully characterized: this ?tomographic? level has been known for a long time. We present for this case a systematic and efficient approach to quantifying the amount of intrinsic randomness, and show that setups involving ancillas (positive-operator valued measures, pointer measurements) may not be interesting here, insofar as one may extract randomness from the ancilla rather than from the system under study. Finally, we study how much randomness can be obtained in presence of an intermediate level of characterization related to the task of ?steering?, in which Bob?s device is fully characterized while Alice?s is a black box. We obtain our results here by adapting the NPA hierarchy of semidefinite programs to the steering scenario.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?50 years of Bell?s theorem?.

[1]  Roger Colbeck,et al.  Free randomness can be amplified , 2011, Nature Physics.

[2]  M. Hall,et al.  Relaxed Bell inequalities and Kochen-Specker theorems , 2011, 1102.4467.

[3]  Nicolas Brunner,et al.  Semi-device-independent security of one-way quantum key distribution , 2011, 1103.4105.

[4]  D. J. Saunders,et al.  Experimental EPR-steering using Bell-local states , 2009, 0909.0805.

[5]  J. Skaar,et al.  Hacking commercial quantum cryptography systems by tailored bright illumination , 2010, 1008.4593.

[6]  Christian Schaffner,et al.  Robust cryptography in the noisy-quantum-storage model , 2008, Quantum Inf. Comput..

[7]  Adrian Kent,et al.  Private randomness expansion with untrusted devices , 2010, 1011.4474.

[8]  R. G. Beausoleil,et al.  Secure self-calibrating quantum random-bit generator , 2007 .

[9]  Adrian Kent,et al.  Memory attacks on device-independent quantum cryptography. , 2012, Physical review letters.

[10]  Serge Fehr,et al.  Security and Composability of Randomness Expansion from Bell Inequalities , 2011, ArXiv.

[11]  Stefano Pironio,et al.  Randomness versus nonlocality and entanglement. , 2011, Physical review letters.

[12]  Christian Kurtsiefer,et al.  A universal setup for active control of a single-photon detector. , 2013, The Review of scientific instruments.

[13]  David A. Strubbe,et al.  First-principles prediction of optical second-order harmonic generation in the endohedralN@C60compound , 2011 .

[14]  M. Curty,et al.  Measurement-device-independent quantum key distribution. , 2011, Physical review letters.

[15]  T. Symul,et al.  Real time demonstration of high bitrate quantum random number generation with coherent laser light , 2011, 1107.4438.

[16]  S. Popescu,et al.  Which states violate Bell's inequality maximally? , 1992 .

[17]  H. Weinfurter,et al.  A fast and compact quantum random number generator , 1999, quant-ph/9912118.

[18]  N. Gisin,et al.  From Bell's theorem to secure quantum key distribution. , 2005, Physical review letters.

[19]  Maassen,et al.  Generalized entropic uncertainty relations. , 1988, Physical review letters.

[20]  A. Zeilinger,et al.  Bell violation using entangled photons without the fair-sampling assumption , 2012, Nature.

[21]  Nicolas Gisin,et al.  Quantum key distribution between N partners: Optimal eavesdropping and Bell's inequalities , 2001 .

[22]  Nicolas Gisin,et al.  Imperfect measurement settings: Implications for quantum state tomography and entanglement witnesses , 2012, 1203.0911.

[23]  V. Scarani,et al.  One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering , 2011, 1109.1435.

[24]  Rodrigo Gallego,et al.  Full randomness from arbitrarily deterministic events , 2012, Nature Communications.

[25]  P. Huber,et al.  Physics performance of a low-luminosity low energy neutrino factory. , 2013, Physical review letters.

[26]  Andrew G. White,et al.  Measurement of qubits , 2001, quant-ph/0103121.

[27]  R. Renner,et al.  Uncertainty relation for smooth entropies. , 2010, Physical review letters.

[28]  Stefano Pironio,et al.  Random numbers certified by Bell’s theorem , 2009, Nature.

[29]  Jun Chen,et al.  Deterministic quantum splitter based on time-reversed Hong-Ou-Mandel interference , 2007 .

[30]  S. Pironio,et al.  Using complete measurement statistics for optimal device-independent randomness evaluation , 2013, 1309.3930.

[31]  Vadim Makarov,et al.  Optimised quantum hacking of superconducting nanowire single-photon detectors. , 2013, Optics express.

[32]  A. C. Doherty,et al.  Entanglement, einstein-podolsky-rosen correlations, bell nonlocality, and steering , 2007, 0709.0390.

[33]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

[34]  Y. S. Teo,et al.  Incomplete quantum state estimation: A comprehensive study , 2012, 1202.1713.

[35]  Stefano Pironio,et al.  Security of practical private randomness generation , 2011, 1111.6056.

[36]  A. Acín,et al.  A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations , 2008, 0803.4290.

[37]  Jean-Daniel Bancal,et al.  Device-independent entanglement quantification and related applications. , 2013, Physical review letters.

[38]  Tobias Moroder,et al.  Entanglement verification with realistic measurement devices via squashing operations , 2009, 0909.4212.

[39]  S. Massar,et al.  Device-independent state estimation based on Bell’s inequalities , 2009, 0907.2170.

[40]  S. Wehner,et al.  Publisher's Note: Bell nonlocality [Rev. Mod. Phys. 86, 419 (2014)] , 2014 .

[41]  M. Żukowski,et al.  Bell's inequalities and quantum communication complexity. , 2004, Physical review letters.

[42]  H. M. Wiseman,et al.  Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox , 2009, 0907.1109.

[43]  N. Gisin,et al.  Optical quantum random number generator , 1999, quant-ph/9907006.

[44]  V. Scarani,et al.  Device-independent security of quantum cryptography against collective attacks. , 2007, Physical review letters.

[45]  N. Gisin,et al.  Bilocal versus nonbilocal correlations in entanglement-swapping experiments , 2011, 1112.4502.

[46]  Ivan Damgård,et al.  Cryptography in the Bounded-Quantum-Storage Model , 2008, SIAM J. Comput..