Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/11391
Title: Quantum coin flipping, qubit measurement, and generalized Fibonacci numbers
Authors: Pashaev, Oktay
Keywords: Fibonacci numbers
Quantum measurement
Tribonacci numbers
N-Bonacci numbers
Publisher: Pleiades Publishing
Abstract: 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 FibonacciN-Bonacci sequences.
URI: https://doi.org/10.1134/S0040577921080079
https://hdl.handle.net/11147/11391
ISSN: 0040-5779
1573-9333
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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