Von Neumann Normalisation and Symptoms of Randomness: An Application to Sequences of Quantum Random Bits
نویسندگان
چکیده
Due to imperfections in measurement and hardware, the flow of bits generated by a quantum random number generator (QRNG) contains bias and correlation, two symptoms of non-randomness. There is no algorithmic method to eliminate correlation as this amounts to guaranteeing incomputability. However, bias can be mitigated: QRNGs use normalisation techniques such as von Neumann’s method—the first and simplest technique for reducing bias—and other more efficient modifications. In this paper we study von Neumann un-biasing normalisation for an ideal QRNG operating ‘to infinity’, i.e. producing an infinite bitsequence. We show that, surprisingly, von Neumann un-biasing normalisation can both increase or decrease the (algorithmic) randomness of the generated sequences. The impact this has on the quality of incomputability of sequences of bits from QRNGs is discussed. A successful application of von Neumann normalisation—in fact, any un-biasing transformation—does exactly what it promises, un-biasing, one (among infinitely many) symptoms of randomness; it will not produce ‘true’ randomness, a mathematically vacuous concept.
منابع مشابه
Von Neumann Normalisation of a Quantum Random Number Generator
In this paper we study von Neumann un-biasing normalisation for ideal and real quantum random number generators, operating on finite strings or infinite bit sequences. In the ideal cases one can obtain the desired un-biasing. This relies critically on the independence of the source, a notion we rigorously define for our model. In real cases, affected by imperfections in measurement and hardware...
متن کاملReiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras
متن کامل
Simulatings POVMs on EPR pairs with six bits of expected communication
We present a classical protocol for simulating correlations obtained by bipartite POVMs on an EPR pair. The protocol uses shared random variables (also known as local hidden variables) augmented by six bits of expected communication. Entanglement simulation was first introduced by Maudlin in a 1992 paper published in a philosophical journal [7] and was revived independently by Brassard, Cleve a...
متن کاملEECS 495 : Randomized Algorithms Assignment
Randomized algorithm analyses normally assume access to a sequence of unbiased truly random bits. Unfortunately, it is not always easy to generate random bits with this property. Sources of randomness often are biased in one way or another. Is it possible to use an biased source of randomness to produce an unbiased sequence of random bits? To word it more formally, suppose we are given a biased...
متن کاملA quantum random number generator certified by value indefiniteness
In this paper we propose a quantum random number generator (QRNG) which utilises an entangled photon pair in a Bell singlet state, and is certified explicitly by value indefiniteness. While “true randomness” is a mathematical impossibility, the certification by value indefiniteness ensures the quantum random bits are incomputable in the strongest sense. This is the first QRNG setup in which a p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011