{"id":2125,"date":"2026-04-07T09:53:59","date_gmt":"2026-04-07T07:53:59","guid":{"rendered":"https:\/\/www.milq.info\/?page_id=2125"},"modified":"2026-04-07T11:57:28","modified_gmt":"2026-04-07T09:57:28","slug":"topic1","status":"publish","type":"page","link":"https:\/\/www.milq.info\/en\/qti\/basics\/topic1\/","title":{"rendered":"Basic rules – Topic 1"},"content":{"rendered":"
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Quantum Random Number Generator<\/h1>\n

Overview Video<\/a> – Learning Material<\/a> – Exercises<\/a> – Further Information & Literature<\/a> – Quiz<\/a><\/p>\n

If you are unsure about any terms, you can always check the glossary<\/a>.<\/p>\n

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Overview Video<\/h2>\n

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Learning Material<\/h2>\n\n\t\t<\/span> <\/span> \n\t\t<\/span><\/span>\n

The generation of random numbers is an important aspect in several applications: It is important for the generation of secret keys and cryptography, for gambling machines and games of chance in general, for some numerical methods and for Quantum Key Distribution, i.e. secure communication. These applications need and rely on “real” random numbers, numbers that cannot be predicted or calculated. Even small statistical errors in secret keys generated by non-real random numbers have a negative impact on security. Today, many systems use pseudo-random number generators (pseudo-RNGs), which are deterministic, predictable and calculable due to the deterministic nature of the algorithms. True RNGs, on the other hand, also appear random and are based on complex, practically unpredictable phenomena, but are in principle still deterministic.<\/p>\n

In the context of this relevance, we are faced with a fundamental problem: classical physics is deterministic. Everything in classical physics can – theoretically – be calculated, given enough knowledge about the initial conditions. Even seemingly random experiments – such as the flip of a coin or the roll of a dice – can be calculated if you know the initial conditions (air movement, forces acting on the object, etc.). In the same way, classical computing uses deterministic algorithms and routines to generate random numbers. These are called pseudo-random number generators. Classical computers are not able to generate real random numbers; the numbers generated appear to be random, but are in principle deterministic and computable.<\/p>\n

So we need a theoretical framework that allows us to generate truly random numbers. In physics, quantum physics is the only theory with truly inherent randomness. Individual events are unpredictable and actually happen randomly. In contrast to classical physics, the effects do not appear to be random, they are random. This is proven by experimental setups that show that Bell’s Inequality does not hold (see Nobel prize in physics 2022). We will not discuss Bell’s Inequality here, that would go beyond the scope of this course. Instead, we want to emphasise and explain the random nature of quantum physics, which is summarised in the following basic rule:<\/p>\n

Basic Rule 1: Statistical Behavior<\/h3>\n

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Single events are not predictable, they are random. Only statistical predictions (for many repetitions) are possible in quantum physics.<\/p><\/blockquote>\n

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To explain the basic rule, let us discuss an example. We will build a quantum RNG, a random number generator based on quantum processes. For simplicity, we will focus on a quantum RNG that gives us a random sequence of “0” and “1” with a probability of 50% for “0” and a probability of 50% for “1”. To realise the experiment, we need two single-photon detectors, a single-photon emitter and a 50-50 beam splitter. By the way, it should be noted that single-photon detectors and emitters are not trivial tools, on the contrary, they are complex devices. However, we will not delve into the underlying technology. What is important to us is that we have two single-photon detectors, A and B, and a single-photon emitter. If detector A detects a single photon emitted by the single-photon emitter, we code this as “0”. If detector B detects a single photon, we code it as \u201c1\u201c. The 50-50 beamsplitter is placed between detector A and the single photon emitter. If the single photon is transmitted it will be detected by detector A, if it is reflected it will be detected by detector B. The probability of transmission is 50%, the probability of reflection is 50% (hence the 50-50 beam splitter).<\/p>\n

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A simplified example of a QRNG-setup is shown.<\/figcaption><\/figure>\n

With this experimental setup, the basic rule becomes clear. If we emit a single photon, we cannot predict at which detector it will be detected. It can be detected in A or B, resulting in a \u201c0\u201c or a \u201c1\u201c. Since the measurement results are not predetermined or there are no unknown circumstances, the result is random and unpredictable.<\/p>\n

If we repeat the experiment many times, say 1 million times, we can make statistical predictions. In our case, we would predict that 50% of the single photons will be detected in detector A, resulting in a “0”, and 50% will be detected in detector B, resulting in a “1”. This is only a statistical prediction, it does not mean that exactly 500,000 single photons will be detected in detector A and exactly 500,000 in detector B. It just means that with a high number of repetitions the relative frequency of detection in detector A and in detector B will likely tend towards 50%.<\/p>\n

Another interesting phenomenon of this experiment is that we never detect a photon at two detectors at the same time, i.e. we never get “0” and “1” at the same time. This indicates that individual photons are indivisible and behave like particles when measured. The photon is detected either on the transmission path (detector A) or on the reflection path (detector B). From indivisible photons we conclude that light, which is made up of many photons, is quantised.<\/p>\n

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