Construction of Generalized Quantum Boolean Functions

PANG Shanqi; ZHANG Qingjuan; LIN Xiao

doi:10.1049/cje.2019.03.001

Volume 28 Issue 3

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PANG Shanqi, ZHANG Qingjuan, LIN Xiao, “Construction of Generalized Quantum Boolean Functions,” Chinese Journal of Electronics, vol. 28, no. 3, pp. 508-513, 2019, doi: 10.1049/cje.2019.03.001

Citation:

PANG Shanqi, ZHANG Qingjuan, LIN Xiao, “Construction of Generalized Quantum Boolean Functions,” Chinese Journal of Electronics, vol. 28, no. 3, pp. 508-513, 2019, doi: 10.1049/cje.2019.03.001

PANG Shanqi, ZHANG Qingjuan, LIN Xiao, “Construction of Generalized Quantum Boolean Functions,” Chinese Journal of Electronics, vol. 28, no. 3, pp. 508-513, 2019, doi: 10.1049/cje.2019.03.001

Citation:

PANG Shanqi, ZHANG Qingjuan, LIN Xiao, “Construction of Generalized Quantum Boolean Functions,” Chinese Journal of Electronics, vol. 28, no. 3, pp. 508-513, 2019, doi: 10.1049/cje.2019.03.001

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Construction of Generalized Quantum Boolean Functions

doi: 10.1049/cje.2019.03.001

1.
College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China;
2.
Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Xinxiang 453007, China

Funds: This work is supported by the National Natural Science Foundation of China (No.11571094).

Received Date: 2017-12-25
Publish Date: 2019-05-10

Abstract

Abstract

The existing construction methods of Quantum Boolean functions (QBFs) are extended and simplified. All QBFs with one qubit and all local QBFs with any qubits are constructed. And we propose the concept of Generalized quantum Boolean functions (GQBFs). We find all GQBFs with one qutrit and all kinds of local GQBFs with any qutrits. The number of each of the four kinds of functions above is uncountably infinitely many. By using diagonal matrices, we obtain uncountably infinitely many non-local QBFs with any qubits and GQBFs with any qutrits. Infinitely many families of GQBFs with any qudits are obtained from the properties of projection matrices of known saturated orthogonal arrays.
- Quantum information,
- Matrix image of orthogonal array,
- Quantum Boolean functions,
- Generalized quantum Boolean functions

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References(20)

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