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Certified quantum random numbers based on single-photon entanglement

Nicolò Leone, Stefano Azzini, Sonia Mazzucchi, Valter Moretti, Lorenzo Pavesi

Published Apr 9, 2021• 3 citations
OpenAlex

Abstract

Random number generators are employed for stochastic simulations and cryptography. Besides the quality of randomness, a crucial aspect for applications is security, namely the monitoring of the lower bound on the entropy produced by the generator in any context, even fraudulent ones. In this regard, quantum entanglement represents an ideal resource, because it provides non-classical correlations between intrinsically random outcomes. However, entanglement-based certified random numbers generators are particularly challenging from a practical point of view. Here, we demonstrate a new certified quantum random number generator based on momentum-polarization entangled single photon states. The use of single particle entanglement allows employing an attenuated laser source and a simple setup where only linear optical components are utilized. A semi-device independent modeling of the photonic quantum random number generator certifies a minimum entropy of $(2.5 \pm 0.5)\%$, corresponding to a generation rate of 4.4 kHz. Modeling the generation stage of the setup permits to increase the certified minimum entropy to $(30.1 \pm 0.5)\%$, implying a generation rate of 52.7 kHz, at the expenses of an increased level of trust on the system.

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International Journal of Mathematical Sciences and Computing•Aug 8, 2021•4 citations
Random number generators are employed for stochastic simulations and
cryptography. Besides the quality of randomness, a crucial aspect for
applications is security, namely the monitoring of the lower bound on the
entropy produced by the generator in any context, even fraudulent ones. In this
regard, quantum entanglement represents an ideal resource, because it provides
non-classical correlations between intrinsically random outcomes. However,
entanglement-based certified random numbers generators are particularly
challenging from a practical point of view. Here, we demonstrate a new
certified quantum random number generator based on momentum-polarization
entangled single photon states. The use of single particle entanglement allows
employing an attenuated laser source and a simple setup where only linear
optical components are utilized. A semi-device independent modeling of the
photonic quantum random number generator certifies a minimum entropy of (2.5±0.5)%(2.5 \pm 0.5)\%(2.5±0.5)%, corresponding to a generation rate of 4.4 kHz. Modeling the
generation stage of the setup permits to increase the certified minimum entropy
to (30.1±0.5)%(30.1 \pm 0.5)\%(30.1±0.5)%, implying a generation rate of 52.7 kHz, at the expenses
of an increased level of trust on the system.
Quantum entanglement represents an ideal resource to guarantee the security of random numbers employed in many scientific and cryptographic applications. However, entanglement-based certified random number generators are particularly challenging to implement. Here, we demonstrate a certified quantum random number generator based on momentum-polarization entangled single-photon states. The use of single-photon entanglement allows an attenuated laser source to be employed and a simple setup where only linear optical components are utilized. For the latter, a semi-device-independent modeling of the photonic quantum random number generator is developed, which certifies a minimum entropy of $(2.5\ifmmode\pm\else\textpm\fi{}0.5)\mathrm{%}$, corresponding to a generation rate of 4.4 kHz. At the expenses of a higher level of trust in the system, the certified minimum entropy can be increased to $(30.1\ifmmode\pm\else\textpm\fi{}0.5)\mathrm{%}$, implying a generation rate of 52.7 kHz. Our results show that a simple optical implementation combined with an accurate modeling provide an entanglement-based high-security quantum random number generator using imperfect devices.
Single-photon entanglement is a peculiar type of entanglement in which two or more degrees of freedom of a single photon are correlated quantum-mechanically. Here, we demonstrate a photonic integrated chip able to generate and manipulate single-photon path-entangled states, using a commercial red LED as light source. A Bell test, in the Clauser, Horne, Shimony, and Holt (CHSH) form, is performed to confirm the presence of entanglement, resulting in a maximum value of the CHSH correlation parameter equal to 2.605±0.004. This allows us to use it as an integrated semi-device independent quantum random number generator able to produce certified random numbers. The certification scheme is based on a Bell’s inequality violation and on a partial characterization of the experimental setup, without the need of introducing any further assumptions either on the input state or on the particular form of the measurement observables. In the end a min-entropy of 33% is demonstrated.
Self-testing and semi-device independent protocols are becoming the preferred choice for quantum technologies, being able to certify their quantum nature with few assumptions and simple experimental implementations. In particular, for quantum random number generators, the possibility of monitoring, in real time, the entropy of the source only by measuring the input/output statistics is a characteristic that no other classical system could provide. The cost of this possibility is not necessarily increased complexity and reduced performance. Indeed, here we show that with a simple optical setup consisting of commercially available components, a high bit generation rate can be achieved. We manage to certify 145.5 MHz of quantum random bit generation rate.
One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. First, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to give lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. Our results demonstrate the first experiment that certifies nearly two bits of randomness from binary measurements of two parties [1], [2]. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation Theorem. Second, we present an efficient and practical method for certifying quantum randomness using generalized measurements. Indeed, we have derived a method for self-testing the presence of POVMs. We present the certification of more than one bit of min-entropy from a single POVM on one of the qubits of an entangled state using a variant of the elegant Bell inequality. We also obtain more than one bit of randomness in a prepare and measure scenario of a similar structure with a POVM on a single qubit [3]. We provide numerical simulations to demonstrate the effectiveness of our randomness certification and expansion.
Self-testing and semi-device independent protocols are becoming the preferred choice for quantum technologies, being able to certify their quantum nature with few assumptions and simple experimental implementations. In particular, for quantum random number generators, the possibility of monitoring, in real time, the entropy of the source only by measuring the input/output statistics is a characteristic that no other classical system could provide. The cost of this possibility is not necessarily increased complexity and reduced performance. Indeed, here we show that with a simple optical setup consisting of commercially available components, a high bit generation rate can be achieved. We manage to certify 145.5 MHz of quantum random bit generation rate.
Random numbers play an important role in many areas, for example, encryption, cryptography, static analysis, simulations.It is also a fundamental resource in science and engineering.There are algorithmically generated numbers that are similar to random distributions, but are not actually random, called pseudo random number generators.In many cases the tasks to be solved are based on the unpredictability of random numbers, which cannot be guaranteed in the case of pseudo random number generators, true randomness is required.In such situations, we use real random number generators whose source of randomness is unpredictable random events.Quantum Random Number Generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements.Our goal is to generate fast random numbers at a lower cost.At the same time, a high level of randomness is essential.Through quantum mechanics, we can obtain true numbers using the unpredictable behavior of a photon, which is the basis of many modern cryptographic protocols.It is essential to trust cryptographic random number generators to generate only true random numbers.This is why certification methods are needed which will check both the operation of the device and the quality of the random bits generated.We present the improved novel quantum random number generator, which is based the on time of arrival QRNG.It uses the simple version of the detectors with few requirements.The novel QRNG produces more than one random bit per each photon detection.It is rather efficient and has a high level of randomness.Self-testing as well as device independent quantum random number generation methods are analyzed.The advantages and disadvantages of both methods are identified.The model of a novel semi self-testing certification method for quantum random number generators (QRNG) is offered in the paper.This method combines different types of certification approaches and is rather secure and efficient.Finally, the novel certification method is integrated into the model of the new quantum random number generator.The paper analyzes its security and efficiency.