Quantum Entropy

To create an MMI system, a Random Event Generator (REG) is required, which will be influenced by the user's intent. Such a generator uses quantum effects to produce a random sequence of zeros and ones. However, the current understanding of the issue suggests that the user's intention affects not so much the random events themselves as their probability, and only a small part of the bits leaving the REG will carry a trace of this influence.

In the PEAR experiments, the signal was very weak and out of 200 "coin tosses", the result was "non-random" only in a couple. This brings us to the concept of generator’s responsiveness, that is, how easily the user's intention can change the value of the output bits. It is obvious that software pseudo-randomizers do not have such responsiveness, since the randomness in them is purely mathematical, which means it is predetermined, and so it is impossible to influence it from the outside in any way. The only changeable parameter for such a generator is the time when the number is received from the sequence. Every *true* random number generator uses a physical source of entropy to provide its inherent unpredictability.

### True Random Number Generator Physics

According to their structure, random number generators can be divided into three types: Pseudorandom (PRNG), Physical (TRNG) and Quantum (QRNG). Pseudo-random RNGs create randomness mathematically. There are such RNGs in every computer and they are an algorithm, the input of which is the so-called "seed", that is, the starting point, which can be, for example, the exact time of its launch. From this starting point, the algorithm computes a series of statistically random numbers. However, since this series of numbers is algorithmically created, all numbers in it are predetermined. That is, they are random in terms of statistics, since the probability of each of them is the same, but not random in terms of predestination. For example, if you run such a generator again with the same seed, it will produce exactly the same series of numbers as the first time. Moreover, each such RNG has a certain number of bits, after which the sequence will begin to repeat. Obviously, such RNGs are unsuitable for our experiments, since if all numbers are predetermined by the algorithm, the user's intention cannot have any effect on them.

The second type, physical RNGs (TRNGs), are typically devices that use for randomness generation some physical process that is too complex to be predictable. Such processes are no longer considered deterministic due to Chaos Theory or Uncertainty principle (for quantum RNGs).

* **Thermal noise**, also called Johnson, Nyquist or Johnson-Nyquist noise, is electronic noise created by the thermal excitation of charge carriers - usually electrons - in an electrical conductor.

* **Shot noise**, sometimes called Poisson noise due to its statistical distribution, occurs because the electrical current is made up of a very large number of discrete charges, making its flow grainy.

* **Avalanche noise** occurs in semiconductor junctions such as Zener diodes when the breakdown voltage exceeds approximately 7 volts. The strong electric field at the junction accelerates the charges until collisions set off a chain reaction that generates additional charge carriers.

* **Jitter** "noise" is not a type of noise, but tiny deviations in the rise and fall times of waveforms.

* Pure quantum systems, such as a photon passing through a beam splitter, are inherently random as described by quantum mechanics. A single photon detector in each of the two possible outputs from the beam splitter detects the photon. Each detector output is assigned to represent a 1 or a 0, which is the random output of the detection.

* **Nuclear decay noise**, obtained by measurements of the decay of radioactive material. The time of nuclear decay is determined by quantum mechanics and is considered inherently random within its expected statistical distribution.

### Quantum Entropy Devices

RNGs are considered quantum (QRNGs) when the Uncertainty Principle applies to physical processes in them and it becomes fundamentally impossible to predict the change in their parameters. For example, when the wave properties of charge carriers begin to change the result of their measurement. This happens, for example, during radioactive decay, the passage of photons through a semi-transparent mirror, or the tunneling of electrons in MOS-transistors, causing shot noise. It is believed, that flipping a bit, produced by quantum efects with intention requires much less energy, than influencing a classical physical process, so such generators should have bigger responsivity.

By the way, the PEAR experiments used the shot noise of Zener diodes, but the effect was significantly reduced by deterministic "whitening" procedure, where the data was XORed with pseudo-random entropy to eleminate statistical defects. In the Fatum project, it was decided to use a pure quantum system, which was a random number generator from the Australian National University, which measures the quantum fluctuations of virtual particles in a vacuum. The Fatum server received entropy from it through an open API.

However, such a system also has flaws. Since there is only one source of entropy, and there are many users, their intentions can interfere with each other if they affect the REG at the same time. Not to mention that if the source of entropy breaks down, the whole system will stop working, which happened in January 2019 during the fires in Australia. After that the developers of Randonautica began to consider alternative entropy sources that could be built directly into the user's smartphone.

As a result, two new experimental REGs were developed by Randonautica enthusiasts: CamRNG, which used thermal and shot noise from individual sensors in the smartphone's camera matrix, resulting from the fact that photons are emitted by a light source at random times, and Temporal, which gets physical entropy from the processor cycle counter. However, in addition to the insufficiently high rate of entropy production, a serious problem with these REGs is the dependence on the phone model and its operating system. To partially solve this problem, a server version of CamRNG was created.

Also worth mentioning is a line of experimental REG devices designed by Scott Wilber. These devices are called the Mind Enabled Devices (MED) and are often used in Fatum Project's internal research. The uniqueness of such devices lies in the fact that they are specially designed to work with MMI and are a chip with many ring oscillators that produce jitter from thermal and quantum shot noise. Further, the noise from different generators is combined by the XOR logical operation, which allows eliminating statistical defects without deterministic post-processing, which is important, since such post-processing is often used in hardware RNGs and reduces the MMI effect. In addition, the MED has a built-in bias amplification algorithm to amplify the signal, which we will discuss next. It is believed that such devices are the most advanced REGs and can be accessed by anyone involved in the development of Randonautica research initiatives.

### Post-Processing the Noise

A serious problem of physical RNGs is that, unlike pseudo-random noise, physical noise has significant statistical defects. Simply put, this means that sometimes it behaves randomly, and sometimes not. Therefore, in order to make it statistically random, the physical RNG uses a "whitening" procedure, which is also called unbiasing algorithms.

Whitening is usually done by passing statistically imperfect true random numbers through a cryptographic hash function such as SHA-1 or by combining them with pseudo-random numbers through a logical XOR operation.

In the Psyleron QRNG, which was used in the experiments of the PEAR laboratory to eliminate defects, the shot noise was subjected to a logical XOR operation, combined with a pseudo-random noise stream, which reduced the influence of quantum processes on the output data by at least a factor of two.

Most often, in order to increase the amount of output entropy, physical noise is simply fed as a seed to a pseudo-random RNG, thus making its result unpredictable. At the same time, the amount of quantum entropy does not increase, and its influence on each specific bit becomes extremely small.

## Comscire PQ128MS

PQ128MS was designed in such a way as to achieve the maximum influence of quantum processes on each bit of the output data and completely get rid of pseudo-random algorithms during correction of statistical defects. It is currenntly used as a new primary source of the Entropy at Randonautica server.

The device is based on ring oscillators. These are closed circuits made of an odd number of transistor inverters that change the signal entering them to the opposite. The signal in such an oscillator oscillates between two voltage levels. Since tunnel leakage occurs in the transistors included in the inverters, Shot noise occurs, which causes jitter in the time of voltage drops and rises. Thus, by reading the signal at regular intervals, certain bit states can be obtained from this jitter.

In the PQ128MS, the circular oscillator has three outputs with an equal number of elements between them, which allows us to get three different signals from it, which are then combined with a logical XOR operation. This triples the probability of sampling a ring oscillator output signal exactly during a transition when the shot noise-induced jitter makes the measurement quantum mechanically indeterminate. Thus, despite the significant influence of thermal noise, quantum Shot Noise creates a contribution that is quite capable of changing the value of the output bit. Further, the entropy from hundreds of such oscillators is combined into a single output using the logical XOR operation, which makes it possible to eliminate statistical defects without using pseudo-random entropy. Thus, all the bits involved in the XOR operation are the product of quantum entropy, which means that its contribution to the result becomes maximum. And finally, outputs from three such generators are XORed together for better reliability.

(read more technically accurate info about the PQ devices in this paper)