225,577 research outputs found
Can observed randomness be certified to be fully intrinsic?
Randomness comes in two qualitatively different forms. Apparent randomness
can result both from ignorance or lack of control of degrees of freedom in the
system. In contrast, intrinsic randomness should not be ascribable to any such
cause. While classical systems only possess the first kind of randomness,
quantum systems are believed to exhibit some intrinsic randomness. In general,
any observed random process includes both forms of randomness. In this work, we
provide quantum processes in which all the observed randomness is fully
intrinsic. These results are derived under minimal assumptions: the validity of
the no-signalling principle and an arbitrary (but not absolute) lack of freedom
of choice. The observed randomness tends to a perfect random bit when
increasing the number of parties, thus defining an explicit process attaining
full randomness amplification.Comment: 4 pages + appendice
Postprocessing for quantum random number generators: entropy evaluation and randomness extraction
Quantum random-number generators (QRNGs) can offer a means to generate
information-theoretically provable random numbers, in principle. In practice,
unfortunately, the quantum randomness is inevitably mixed with classical
randomness due to classical noises. To distill this quantum randomness, one
needs to quantify the randomness of the source and apply a randomness
extractor. Here, we propose a generic framework for evaluating quantum
randomness of real-life QRNGs by min-entropy, and apply it to two different
existing quantum random-number systems in the literature. Moreover, we provide
a guideline of QRNG data postprocessing for which we implement two
information-theoretically provable randomness extractors: Toeplitz-hashing
extractor and Trevisan's extractor.Comment: 13 pages, 2 figure
Universal Randomness
During last two decades it has been discovered that the statistical
properties of a number of microscopically rather different random systems at
the macroscopic level are described by {\it the same} universal probability
distribution function which is called the Tracy-Widom (TW) distribution. Among
these systems we find both purely methematical problems, such as the longest
increasing subsequences in random permutations, and quite physical ones, such
as directed polymers in random media or polynuclear crystal growth. In the
extensive Introduction we discuss in simple terms these various random systems
and explain what the universal TW function is. Next, concentrating on the
example of one-dimensional directed polymers in random potential we give the
main lines of the formal proof that fluctuations of their free energy are
described the universal TW distribution. The second part of the review consist
of detailed appendices which provide necessary self-contained mathematical
background for the first part.Comment: 34 pages, 6 figure
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