Quantum-Mechanical Random-Number Generator

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Abstract
For generating the numbers 1, 2, … M in random sequence, an electronic modulo‐M counter is used, driven by the pulses from a high‐frequency pulse generator. If the pulse train is interrupted at a random time, then the counter stops at random in one of its M possible states, producing thus a random‐number modulo M. The random time is the time at which a Geiger‐Mueller tube registers an electron from a 90Sr source. The electronic circuitry is designed such that variations in the characteristics of the components do not impair the randomness. Due to the simplicity of the circuit, the degree of randomness obtainable can be discussed in detail. The randomness of the primarily generated ``basic sequence'' is limited by the finite value of the quotient (pulse‐generator frequency) / (number‐generation frequency). An extremely high degree of randomness can be realized by ``contracting'' the basic sequence, i.e., by adding (modulo M) strings of k (k=2, 3, 4, or even higher) successive numbers of the basic sequence, to form one number of the final sequence. This contraction can be achieved very easily by interrupting the pulse train only after exactly k electrons have been recorded by the Geiger‐Mueller tube. The performance of a generator was tested by recording a basic sequence of generated numbers on paper tape. For probing the long‐time reliability of the generator these recordings were made over an 18 months period, and the randomness tests were designed to discover also temporary malfunctions. In accord with the theoretical expectation, these tests did not indicate any deviation from randomness.

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