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Quantum coin flipping, qubit measurement, and generalized
Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 2, pp. 261-281 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of Hadamard quantum coin measurement in $n$ trials, with an arbitrary number of repeated consecutive last states, is formulated in terms of Fibonacci sequences for duplicated states, Tribonacci numbers for triplicated states, and $N$-Bonacci numbers for arbitrary $N$-plicated states. The probability formulas for arbitrary positions of repeated states are derived in terms of the Lucas and Fibonacci numbers. For a generic qubit coin, the formulas are expressed by the Fibonacci and more general, $N$-Bonacci polynomials in qubit probabilities. The generating function for probabilities, the Golden Ratio limit of these probabilities, and the Shannon entropy for corresponding states are determined. Using a generalized Born rule and the universality of the $n$-qubit measurement gate, we formulate the problem in terms of generic $n$-qubit states and construct projection operators in a Hilbert space, constrained on the Fibonacci tree of the states. The results are generalized to qutrit and qudit coins described by generalized Fibonacci-$N$-Bonacci sequences.
Keywords: Fibonacci numbers, quantum coin, qubit, qudit, quantum measurement, Tribonacci numbers, $N$-Bonacci numbers.
Mots-clés : qutrit 
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O. K. Pashaev. Quantum coin flipping, qubit measurement, and generalized. Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 2, pp. 261-281. http://geodesic.mathdoc.fr/item/TMF_2021_208_2_a6/

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