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 |
Files in This Item:
File | Size | Format | |
---|---|---|---|
Pashaev2021_Article_Quantum.pdf | 287.66 kB | Adobe PDF | View/Open |
CORE Recommender
SCOPUSTM
Citations
4
checked on Nov 29, 2024
WEB OF SCIENCETM
Citations
3
checked on Nov 23, 2024
Page view(s)
22,134
checked on Dec 2, 2024
Download(s)
380
checked on Dec 2, 2024
Google ScholarTM
Check
Altmetric
Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.