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Related Concept Videos

Random Variables01:09

Random Variables

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A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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5.4 Gbps real time quantum random number generator with simple implementation.

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    We developed a quantum random number generation method using laser phase fluctuations. This high-speed system achieves 5.4 Gbps and passes rigorous NIST and DIEHARD randomness tests.

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    Area of Science:

    • Quantum physics
    • Information science
    • Experimental optics

    Background:

    • Random number generation is crucial for cryptography and simulations.
    • Existing methods face limitations in speed or true randomness.
    • Quantum phenomena offer a path to intrinsically secure random number generation.

    Purpose of the Study:

    • To demonstrate a practical and high-speed quantum random number generator (QRNG).
    • To validate the randomness of generated sequences using established statistical tests.
    • To develop a cost-effective QRNG using readily available components.

    Main Methods:

    • Measuring laser phase fluctuations in a simplified experimental setup.
    • Developing a theoretical model to analyze and predict randomness.
    • Implementing analog-to-digital sampling and randomness extraction on a field-programmable gate array (FPGA).

    Main Results:

    • Achieved a real-time quantum random number generation speed of 5.4 Gbps.
    • Experimental data closely matched simulation results based on the developed model.
    • Generated random bit sequences successfully passed all NIST and DIEHARD statistical tests.

    Conclusions:

    • The proposed scheme provides a high-speed, reliable source of quantum randomness.
    • The simple experimental setup and FPGA integration make the system practical for various applications.
    • The validated randomness ensures suitability for security-critical applications.