Testing randomness of series generated in an optical Bell’s experiment (original) (raw)
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Assessing randomness with the aid of quantum state measurement
American Journal of Physics
Randomness is a valuable resource in science, cryptography, engineering, and information technology. Quantum-mechanical sources of randomness are attractive because of the indeterminism of individual quantum processes. Here we consider the production of random bits from polarization measurements on photons. We first present a pedagogical discussion of how the quantum randomness inherent in such measurements is connected to quantum coherence, and how it can be quantified in terms of the quantum state and an associated entropy value known as min-entropy. We then explore these concepts by performing a series of single-photon experiments that are suitable for the undergraduate laboratory. We prepare photons in different nonentangled and entangled states, and measure these states tomographically. We use the information about the quantum state to determine, in terms of the min-entropy, the minimum amount of randomness produced from a given photon state by different bit-generating measurements. This is helpful in assessing the presence of quantum randomness and in ensuring the quality and security of the random-bit source.
Randomness of imperfectly entangled states
arXiv: Quantum Physics, 2019
The generation of series of random numbers is an important and difficult problem. Appropriate measurements on entangled states have been proposed as the definitive solution, based on the impossibility of exploiting quantum non locality to get faster than light signaling. There is a controversy regarding what is preferable to produce series with utilizable randomness in practice, high or low entanglement. We prepare biphotons with three different levels of entanglement, easy entangled, marginally entangled and no entangled. Randomness is evaluated, independently of the quantum non locality argument, through a battery of standard statistical tests, Hurst exponent, Kolmogorov complexity, Takens dimension of embedding, and Augmented Dickey Fuller and Kwiatkowski Phillips Schmidt Shin tests to check stationarity. The no entangled case is found to produce the smallest rate of not random series, and the marginal case the largest. Although the entangled case has a larger rate of not random ...
Kolmogorov complexity of sequences of random numbers generated in Bell's experiments
Physical Review A
Quantum states are the ultimate touchstone to produce sequences of random numbers. Spatially spread entangled states allow the generation of correlated random sequences in remote locations. The impossibility of observing a quantum state, without disturbing it, ensures that the messages encoded using these sequences cannot be eavesdropped. This is the basis of Quantum Key Distribution. It is then of crucial importance knowing whether the sequences generated in the practice by spatially spread entangled states are truly random, or not. Yet, that knowledge is not immediate. One of the obstacles is the very definition of randomness. "Statistical" randomness is related with the frequency of occurrence of strings of data. "Algorithmic" randomness is related with compressibility of the sequence, what is given by Kolmogorov complexity. Sequences generated by entangled pairs of photons are analyzed, focusing on estimations of their complexity. Standard tests of statistical randomness are also applied. PACS: 03.67.Dd Quantum cryptography and communication security. 05.45.Tp Time series analysis. 03.65.Ud Entanglement and quantum non-locality (EPR paradox, Bell's inequalities, etc.).
How Random Is Quantum Randomness? An Experimental Approach
2009
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness-recently proved to be theoretically incomputable-and some well-known computable sources of pseudo-randomness. Incomputability is a necessary, but not sufficient "symptom" of "true randomness."
New Journal of Physics, 2015
What is the most efficient way to generate random numbers device-independently using a photon pair source based on spontaneous parametric down conversion? We consider this question by comparing two implementations of a detection-loophole-free Bell test. In particular, we study in detail a scenario where a source is used to herald path-entangled states, i.e. entanglement between two spatial modes sharing a single photon and where non-locality is revealed using photon counting preceded by small displacement operations. We start by giving a theoretical description of such a measurement. We then show how to optimize the Bell-CHSH violation through a non-perturbative calculation, taking the main experimental imperfections into account. We finally bound the amount of randomness that can be extracted and compare it to the one obtained with the conventional scenario using photon pairs entangled e.g. in polarization and analyzed through photon counting. While the former requires higher overall detection efficiencies, it is far more efficient in terms of the entropy per experimental run and under reasonable assumptions, it provides higher random bit rates.
Effects of Reduced Measurement Independence on Bell-Based Randomness Expansion
Physical Review Letters, 2012
With the advent of quantum information, the violation of a Bell inequality is used as evidence of the absence of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One of the key assumptions of Bell's Theorem is the existence of experimental "free will", meaning that measurement settings can be chosen at random and independently by each party. The relaxation of this assumption potentially shifts the balance of power towards an eavesdropper. We consider a no-signalling model with reduced "free will" and bound the adversary's capabilities in the task of randomness expansion.
Device-independent randomness certification using multiple copies of entangled states
arXiv (Cornell University), 2022
We demonstrate to what extent many copies of maximally entangled two-qubit states enable for generating a greater amount of certified randomness than that can be certified from a single copy. Although it appears that greater the dimension of the system implies a higher amount of randomness, the non-triviality lies in the deviceindependent simultaneous certification of generated randomness from many copies of entangled states. This is because, most of the two-outcome Bell inequalities (viz., Clauser-Horne-Shimony-Holt, Elegant, or Chain Bell inequality) are optimized for a single copy of two-qubit entangled state. Thus, such Bell inequalities can certify neither many copies of entangled states nor a higher amount of randomness. In this work, we suitably invoke a family of n-settings Bell inequalities which is optimized for n/2 copies of maximally entangled two-qubit states, thereby, possess the ability to certify more randomness from many copies of two-qubit entangled state.
Practical random number generation protocol for entanglement-based quantum key distribution
2008
A simple protocol which takes advantage of the inherent random times of detections in single photon counting modules is presented for random active basis choices when using entanglement-based protocols for Quantum Key Distribution (QKD). It may also be applicable to the BB84 protocol in certain cases. The scheme presented uses the single photon detectors already present on a QKD setup, working on the same rate as the system is capable of detecting, and is, therefore, not limited by the output rates of quantum random number generators. This protocol only requires small hardware modifications making it an attractive solution. We perform a proof-of-principle experiment employing a spontaneous parametric down-conversion process in a χ (2) non-linear crystal to demonstrate the feasibility of our scheme, and show that the generated sequence passes randomness tests.