Self-Testing Quantum Random Number Generator

Lunghi, Tommaso; Brask, Jonatan Bohr; Lim, Charles Ci Wen; Lavigne, Quentin; Bowles, Joseph; Martin, Anthony; Zbinden, Hugo; Brunner, Nicolás

doi:10.1103/physrevlett.114.150501

Cited by 196 publications

(212 citation statements)

References 32 publications

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“…On the other hand, assuming the absence of local hidden variable theories, true random numbers can be obtained with "bottom up" approaches. Methods of recent introduction, evaluate the real content of entropy with an a priori characterization of the quantum system: by checking the state purity [17,25] or by checking the quantum system dimensions [26]. Our SDI protocol enables the ultra-fast generation of true random numbers.…”

mentioning

confidence: 99%

Source-Device-Independent Ultrafast Quantum Random Number Generation

Marangon¹,

Vallone²,

Villoresi³

2017

Phys. Rev. Lett.

136

126

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Secure random numbers are a fundamental element of many applications in science, statistics, cryptography and more in general in security protocols. We present a method that enables the generation of high-speed unpredictable random numbers from the quadratures of an electromagnetic field without any assumption on the input state. The method allows to eliminate the numbers that can be predict due the presence of classical and quantum side information. In particular, we introduce a procedure to estimate a bound on the conditional min-entropy based on the Entropic Uncertainty Principle for position and momentum observables of infinite dimensional quantum systems. By the above method, we experimentally demonstrated the generation of secure true random bits at a rate greater than 1 Gbit/s.Introduction -Quantum Random Number Generators (QRNG) exploits intrinsic probabilistic quantum processes to generate true random numbers. Indeed, the expression "QRNG" was first introduced for a device based on the decay of radioactive nuclei [1]. Afterwards, QRNGs exploiting the versatility of light were realized: such devices are based on optical processes such as photon welcher weg [2][3][4], photon time of arrival [5][6][7] or vacuum quadratures [8][9][10][11].Usually, the assessment of the randomness of the generated numbers is obtained by applying statistical tests on the output bits. In most of the QRNGs, passing the tests is the only method used to certify the randomness. In case of failure (attributed to hardware problem since the process is assumed to be "random"), numbers are algorithmically post-processed until the tests are passed.However, this procedure con only certifies that the numbers are identically and independently distributed (i.i.d.) with respect to those [12] applied tests. Indeed, a posteriori statistical tests cannot certify that the numbers are not known to someone possessing side information about the generator. For instance, it is not possible to eliminate hardware noise, which is a source of classical side information for an eavesdropper, Eve, who may be able to control it. Hence, a statistical test a posteriori cannot establish whether the numbers are originated by the quantum process or by the noisy hardware. Moreover, even assuming a QRNG with an ideal noiseless hardware, a statistical test cannot reveal whether the outputs arise from a a quantum measurements and then are intrinsically random. For instance, a polarization welcher weg QRNG with an optical source emitting photons in a completely mixed polarization state can be seen as the photonic version of a fair coin. The random sequence can be predicted by Eve if she knows "the coin's equations of motion" (namely she has classical side information) or if she holds a quantum system correlated with the QRNG (namely she has quantum side information).The quantity that evaluates the amount of side information on a random sequence Z is the so called conditional quantum min-entropy H min (Z|E) [13]. However, such min-entropy is generally hard to estimate....

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mentioning

confidence: 99%

Source-Device-Independent Ultrafast Quantum Random Number Generation

Marangon¹,

Vallone²,

Villoresi³

2017

Phys. Rev. Lett.

136

126

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“…Last year, Bowles et al proposed a new scheme based on a prepare-and-measure setup [21] and experimentally realized it [22]. This protocol (BQB14 for abbreviation) seems like SDI protocol, but requires the assumptions that the preparation and measurement devices are independent and the quantum system has bounded dimension.…”

Section: Introductionmentioning

confidence: 99%

More randomness from a prepare-and-measure scenario with independent devices

Han

Yin

et al. 2016

Phys. Rev. A

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How to generate genuine quantum randomness from untrusted devices is an important problem in quantum information processing. Inspired by the previous work on self-testing quantum random number generator [Phys. Rev. Lett. 114, 150501], we present a new method to generate quantum randomness from a prepare-and-measure scenario with independent devices. In existing protocols, the quantum randomness only depends on a witness value (e.g., CHSH value ), which is calculated with the observed probabilities. Differently, here all the observed probabilities are directly used to calculate the min-entropy in our method. Through numerical simulation, we find that the minentropy of our proposed scheme is higher than the previous work, when a typical untrusted BB84 setup is used. Consequently, thanks to the proposed method, more genuine quantum random numbers may be obtained than before.

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“…Device-independence is a very valuable property in physical implementations of various quantum schemes. Typical examples of its usefulness include the transmission of information safely using untrusted devices, and easy monitoring of the overall performance of vulnerable quantum devices [11][12][13][14].We consider in this paper the setting of a Bell experiment, i.e., two spatially separated parties sharing a quantum state and performing local measurements on their subsystems. The corresponding statistics of the measurement outcomes is called a Bell correlation.…”

mentioning

confidence: 99%

“…However, sometimes we still want to draw nontrivial conclusions on the quantum properties of the involved system. This sounds like a challenging, or even impossible task, but it has been shown to be possible in many cases [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. These kinds of tasks are called device-independent as their application assumes only the correctness of quantum mechanics as a valid description of nature, and is independent of the internal workings of the devices used.…”

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confidence: 99%

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Device-independent characterizations of a shared quantum state independent of any Bell inequalities

Wei

Sikora

2017

Phys. Rev. A

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In a Bell experiment two parties share a quantum state and perform local measurements on their subsystems separately, and the statistics of the measurement outcomes are recorded as a Bell correlation. For any Bell correlation, it turns out that a quantum state with minimal size that is able to produce this correlation can always be pure. In this work, we first exhibit two deviceindependent characterizations for the pure state that Alice and Bob share using only the correlation data. Specifically, we give two conditions that the Schmidt coefficients must satisfy, which can be tight, and have various applications in quantum tasks. First, one of the characterizations allows us to bound the entanglement between Alice and Bob using Renyi entropies and also to bound the underlying Hilbert space dimension. Second, when the Hilbert space dimension bound is tight, the shared pure quantum state has to be maximally entangled. Third, the second characterization gives a sufficient condition that a Bell correlation cannot be generated by particular quantum states. We also show that our results can be generalized to the case of shared mixed states.Introduction.-In the study of quantum physics, frequently the internal workings of a quantum device are not exactly known. For example, it is often the case that we do not have sufficient knowledge of the internal physical structure, or the precision of the quantum controls is very limited, or even the devices we are using cannot be trusted. In these cases, it could be that the only reliable information available is the measurement statistics from observing the quantum system. However, sometimes we still want to draw nontrivial conclusions on the quantum properties of the involved system. This sounds like a challenging, or even impossible task, but it has been shown to be possible in many cases [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. These kinds of tasks are called device-independent as their application assumes only the correctness of quantum mechanics as a valid description of nature, and is independent of the internal workings of the devices used. Device-independence is a very valuable property in physical implementations of various quantum schemes. Typical examples of its usefulness include the transmission of information safely using untrusted devices, and easy monitoring of the overall performance of vulnerable quantum devices [11][12][13][14].We consider in this paper the setting of a Bell experiment, i.e., two spatially separated parties sharing a quantum state and performing local measurements on their subsystems. The corresponding statistics of the measurement outcomes is called a Bell correlation. It has been shown that the dimension and the entanglement of the underlying quantum state can be quantified in a device-independent way using only the Bell correlation data [5,[8][9][10]. In fact, some quantum states can even be pinned down completely by their violations of particular Bell inequalities, but this is only known to be possible for some special cases [1][2][...

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Self-Testing Quantum Random Number Generator

Cited by 196 publications

References 32 publications

Source-Device-Independent Ultrafast Quantum Random Number Generation

Source-Device-Independent Ultrafast Quantum Random Number Generation

More randomness from a prepare-and-measure scenario with independent devices

Device-independent characterizations of a shared quantum state independent of any Bell inequalities

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