## News and Views

Following is a discussion about this "NEWS & VIEWS" article in Nature Vol. 464 15 April 2010 by Valerio Scarani
• The text in italics is copied from the article
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Information Science: Guaranteed Randomness

The article starts with the following text:
On page 1021 of this issue Pironio and co workers describe a method for obtaining numbers that are guaranteed to be random and private from an unknown process, provided that the numbers are certified as being derived from measurements on quantum systems.
They place the bar very high.
This also seems like an adhoc definition. I do not know the answer but it seems that a roulette based on this definition does not produce random numbers.
But in practice no such test can distinguish a sequence generated by a truly random process from one generated by a suitable deterministic algorithm that repeats itself after for example 10^23 numbers.
A computer program (its outcome) in principle is deterministic. That means you can claim that a computer can never generate random numbers because it repeats the same numbers after a certain time. However, this is only true if performance is not time dependent. If the program depends about the system clock time (and performance of the other programme's) than each time when you run your program the outcome will be different, implying no repetition and unpredictability.

The question remains what is a truly random physical process.

Moreover, in this way, whether the numbers are private cannot be checked.
What is the definition of private? I expect if you perform the same random number generator experiment at two different places (or if you repeat the experiment) the outcome should be different.
As I claimed if your programme is time dependent than you can fulfil this requirement.
Pironio and colleges take an alternative route for generating private randomness in their study, using one of the most remarkable phenomena of quantum physics: the violation of "Bell's inequalities" which has been observed in numerous different experiments in the past three decades.
The issue remains: are violations of the "Bell's inequalities" a correct criteria to distinguish between random versus non random.
To understand what Bell inequalities are first consider two quantum systems, for example two photons emitted by the same source and propagating away from one another
IMO the central issue is: what is the underlying process that causes the (simultaneous?) emission of two photons.
..only the pair of outcomes (0,1) and (1,0) are observed..
Such correlations between distant events are striking raising the question of where the connection is.
What is there so "strange" that when "A" measures a 1 at one side "B" always measures a 0 at the other side ? versus if "A" measures a 0 "B" always measures a 1 ?
The scientific is: is this always exactly 100% at all distances. Next we read:
There is surely no communication between the two photons, because the signal would need to propagate faster than light.
Accepted.
The only plausible hypothesis therefore is that the photons leave the source with a common 'List of instructions' which dictates the outcomes of each possible measurement.
First what do they mean with: 'a List of instructions'. Does this mean a computer program?
Secondly, why is so important? The only issue is that if "A" measures 1 "B" measures 0 and vice versa. There is nothing special about this. In the experiment A measures a string of zero's and one's and the question is: is the decimal value of this string a random number. The fact that B measures a composite string IMO is of no importance in a discussion of "Guaranteed randomness"
Bell inequalities are criteria that, when applied, allow this latter hypothesis to be proved false i.e. then the the observed correlations cannot arise from a pre-established list.
That being the case, it does not answer the question if random numbers are involved.
So how can random numbers be obtained using Bell inequalities.
Still it is not clear to me, in theory, how Bell inequalities can be used to obtain random numbers.
Following on from the example above, many pairs of photons are taken and the measurement procedure is repeated: two sequences of 0s and 1s are produced, one at each measurement location. If these sequences violate Bell inequalities, they are guaranteed to be private random numbers.
The question remains is each number a random number.
This sentence looks like: I generate two numbers. I perform a test bit by bit. The individual bits violate the Bell inequalities. Claim they are random. I have great problems to accept that.
There is no need to know which properties are measured or how they are measured.
This sentence more or less implies that the details of the process involved are not important. What is important that the Bell inequalities are violated.
IMO the process how you generate each number is very important, specific IMO you want to be sure that someone else can not predict the next number you will select. See also Reflection

## Letters

By S. Peronio, in Nature 15 April 2010, page 1021
The article starts with the following sentence:
Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulations of physical and biological systems.
The second part of this sentence is correct. The first part i.e. the definition of randomness, requires an explanation.
Random numbers, however, are difficult to characterize mathematically and their generation must rely on an unpredictable physical process.
Both maybe are correct. Still their is an issue: what are random numbers and or what constitutes a sequence of random numbers and or what is a random number generator. See also Reflection.
At a more fundamental level, there is no such thing as true randomness in the classical world: any classical system admits in principle a deterministic description and thus appears random to us as a consequence of a lack of knowledge about its fundamental description.
I have great objections to this sentence. Randomness has to do with unpredictability. There exists no classical world. You can only make a distinction between small and large. You can discuss the movements of the neurotransmitters in your brain and the behaviour of planets.
Quantum theory is, on the other hand, fundamentally random etc
How can a theory be random. Only physical processes can be random. There are two questions: (1) what is the definition of random and (2) how do you decide that a process is random. See also Reflection
You could rephrase this sentence as follows:
Any process described by the quantum theory is a random process
This is a simple definition but I doubt if that is true. The writers anyway do not agree. See next:
It is therefore unclear how to certify or quantify unequivocally the observed random behaviour even of a quantum process.
This sentence lacks scientific rigour. In fact if this is true how can you make any statement about randomness comparing quantum system with classical systems.
The violation of a Bell inequality guarantees that the observed output are not predetermined and that they arise from entangled quantum systems that posses intrinsic randomness.
In fact this sentence raises two questions:
1. First how do you prove/demonstrate that two entangled systems have random properties.
2. Secondly how do you prove that a system is entangled.
The answer on the second question is may be: by showing that there is a violation of the Bell inequalities. This maybe true, but that does not answer the first question.
The respective binary measurement bases x and y are chosen randomly and set by coherent qubit rotation operations before measurement.
It is conceptual wrong to select the measurement bases randomly. They should be fixed in order to clearly demonstrate that the quantum system is a random process. Introducing extra randomness makes validating difficult.
After the qubits are entangled, binary random inputs (x,y) are are fed to microwave oscillators that coherently rotate each qubit in one of two ways before measurement. Each qubit is finally measured through fluorescence that is collected by the PMTs, resulting in the binary outputs (a,b)
This is maybe the most important sentence of the whole article. However this sentence raises also one of the most important questions: Why using random inputs ? Why not measuring each photon directly ? If randomness is a function of a quantum process than you should not add aditional random parameters before measuring the output. IMO this addition is conceptual wrong. By doing that you make any proof that a quantum process is a random process extra difficult.
At the end of the article we read:
The observed CHSH violation implies that at least 42 new random bits are generated in an experiment with 99% confidence level. This is the first time that one can certify that randomness is produced in an experiment without a detailed model of the devices. We rely only on a high-level description (atoms confined to independent vacuum chambers separated by one meter)
This sentence implies how important the Bell violations are in order to generate random numbers. What I do not understand why that is and why you can not generate random numbers by a single process without a test on the Bell inequalities.

## Nature News

### Comments about the article: A truth test for randomness Quantifying just how unpredictable random numbers really are could aid quantum cryptography.

By Zeeya Merali
if the computer algorithm that generates them can be cracked, they are open to attack,
In the proposed program simulating ON OFF control this is no issue.
For these reasons, many groups are trying to produce truly random strings based on the indeterminism inherent to quantum systems. According to quantum mechanics, it is impossible to predict with certainty how a quantum particle will behave;
How do you know with certainty that indeterminism is inherent to quantum systems. Ofcourse you can claim that by definition, but that is no proof. Maybe there are also other type of processes impossible to predict. Anyway what is the definition of "impossible to predict"
Acín and his colleagues have devised a test of true randomness etc
How can you test something (i.e. randomness) when there exists no definition.
Bell calculated the maximum possible level of correlation between two particles in any classical system. Later experiments have repeatedly confirmed that entangled particles exceed this maximum limit, defying classical physics.
In a certain way what Bell did is to compare particles which which are not entangled with particles that are entangled. Compare meaning to calculate the level of correlation. He found the two being different. The question is: is that fact enough to declare the state of each individual particle as unpredictable.
They prepared a true random-number generator etc which could either be in a high or low energy level. To verify true randomness, two such ions were entangled, and the energy levels of both were measured to confirm that they were correlated beyond Bell's bound. "Violating Bell's bound confirms that the technique successfully exploits a genuine random quantum process," says Acín.
I can accept that by definition, but that is no proof that the bits generated are random bits.

## Quantum Physics

### http://arxiv.org/abs/0911.3427 Random Numbers Certified by Bell's Theorem

By: S. Pironio, A. Ac´in, S. Massar, A. Boyer de la Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning and C. Monroe
The full document starts with concepts like determinisme, clasical systems and quantum systems without a clear definition.
IMO only mathematics is deterministic meaning you can predict the outcome with 100% accuracy. If you perform a calculation (a program) based on an algorithm or a set of equations with the same initial values than the result is always the same.
The physical world is not deterministic i.e. you cannot predict its future with 100% accuracy.
As such IMO the disctinction between a classical systems versus a quantum system is rather arbitrary.
At page 1 paragragh 1 we read:
The same entangled state of the two atoms is repeatedly prepared and measured in a randomly chosen basis, and every event is recorded
It is conceptual wrong to introduce a randomly chosen basis, because this makes the validating process obscure.
At page 2 paragragh 2 we read:
Furthermore, in a device-independent scenario, where the Random Number Generator (RNG) is not trusted but viewed as a black box prepared by an adversary, no existing RNGs can establish the presence of private randomness. Indeed, one can never exclude that the numbers were generated in advance by the adversary and copied into a memory located inside the device.
If you start from a new PC, install the operating system and Excel without Internet and you enter manual the Visual Basic program as supplied and than you claim that you are not sure 100% if the system is not tampered (meaning you can not trust the results) than the discussion is closed.

The experiment consists of a violation of the CHSH inequality with a random choice of measurement inputs, where every event is measured.
The same comment about "random choice" as previous.

At page 19 there is a paragraph called: "D.2 Generation of measurement settings".

The measurement settings were chosen by combining several online random number generators that use: radioactive decay as a source of randomness; atmospheric noise as a source of randomness ; and randomness derived from remote computer and network activity
Why all of those different sources ? Why is all this important ? (Are "we" hiding something) If your quantum system, composed of entangled particles, shows random physical behaviour than you should:
• First measure these parameters in the most direct straight forward method without adding extra sources of randomness
• Secondly establish that the parameters show random behaviour in a simple and straight forward manner.

At page 20 there is a paragraph called: "D.4 Statistical tests".

As the strings we consider contain several thousands of bits, only the tests statistically relevant for such small strings were performed. Specifically the tests called “Frequency”, “Block frequency”, “Runs”, “DFT”, “Serial” and “Approximate Entropy” were reprogrammed from  (sections 2.1, 2.2, 2.3, 2.6, 2.11, 2.12 )
The same tests were also performed on the proposed "ON OFF" process simulated by the Excel program written in Visual Basic. See Description and operation, sheet "NIST"
The result of these statistical tests are described by a p-value, which is the probability that a perfect random number generator would have produced a sequence less random than the sequence that was tested, given the kind of non-randomness assessed by the test. A p-value of 1 therefore means that the sequence tested appears to have been generated by a perfectly random process, while a p-value of 0 implies that the sequence appear to be completely non-random 
The problem with the document is that no such extreme examples are supplied with the "Nist" document to support this claim.

### Reflection

A central issue of both articles is:
1. What are random numbers (A sequence of). What means randomness.
2. How are random numbers generated.
What is wrong with the following definition:
The output of a process is random (i.e. either 0 or 1) if you can repeat it n times and if the output of time n+1 is independent of time n (and all the previous times). That means the chance of finding a 0 or a 1 is 50%.
This definition is in line with the operation of a roulette. However also simpler processes can be considered.
The next question to be asked is: can such a process be simulated on a computer.
IMO it can. The process suggested is what is called an ON OFF process. For a description of the program and a copy of the program in EXCEL go here:
ON OFF The importance of this program is that you will generate a number independent of any human influence when or wherever you use this. The number generated is impossible to predict because it depends on the PC performance
IMO the opinion of both articles is that if you want to generate (private) random numbers you have to used a process based on quantum mechanics i.e. the process must involve entanglement. To demonstrate that the process must violate the Bell's inequality theorem. If that is the case than the process is capable to generate random numbers. The details of the process are not important. There is also the claim that it is difficult to define random mathematically.
I have great problems with this whole reasoning.
IMO the most important part is the process involved. In fact it should be a combination of clear and not clear. If you consider a roulette the basics are clear and simple but if you perform one experiment (using the rules in regulation), to explain the actual outcome of that experiment, is impossible. The only thing you can say is that every time that you perform an experiment the chance of finding a certain number is the same.
IMO the fact that a process involves quantum mechanics is not a guarantee that it produces a random number.
• The half-life time of a radioactive element is not a random number.
• The experiment called "Schrödinger’s cat paradox" can not be used to generate random numbers.
• The same with the two slit experiment with single photons. Here the interference between the two slits causes a disruption.
A the other side certain other experiments could be used to generate random numbers.
• The outcome of the measurement of the polarization angle of a photon IMO in principle can be used to generate random bits and random numbers, but than you have to demonstrate that the outcome of one experiment is independent of the previous experiment.
• IMO the experiment with only one slit with single photons can be used. Here the outcome is a string like: L,R,R,L,L,R,L,R with R meaning detected at the right side.

### Reflection part 2

At a more fundamental level I have a great problem with the simplicity to define classical systems as deterministic versus quantum systems as indeterministic. Or to rephrase this as classical systems are predictable versus quantum systems are unpredictable.

The issue is what means randomness, what defines a state, when measured, as being random state. (The measuring process itself can also effect this state). Part of the answer is that it is difficult mathematical. That maybe the case. However that means that you cannot use Bell's violation as the decisive factor to decide if something is random or not, because Bell's violation is inprincipe a mathematical operation.

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Created: 20 April 2010