Bit of Quantum

Peter Nimbe, Benjamin Asubam Weyori, Adebayo Felix Adekoya

Abstract Bit rotation is an operation similar to shift except that the bits that fall off at one end are put back to the other end. In left rotation, the bits that fall off at left end are put back at right end. In right rotation, the bits that fall off at the right end are put back at the left end. Applications of bit rotation include; registers, cryptography, computing with a single bit string circularly shifted to the right or left based on some position but no work has been done with respect to shifting the bits one position at a time generating emergent bit strings equal to the number of bits-1 from the incident bit string, and then recombining or extracting bit(s) from each of the bit strings or words to form back the incident bit string. In this article, the authors present a new approach of rotating classical bit strings known as CRotate. A quantum approach to bit rotation known as QRotate is presented as well. The quantum perspective uses the concept of bit swapping by avenue of the quantum swap gate in jsqubits. Models and algorithms are duly presented.

Alex Wilkins

Edgard Elbaz

Rubens Viana Ramos, Fábio Alencar Mendonça

Quantum protocols for bit commitment have been proposed and it is largely accepted that unconditionally secure quantum bit commitment is not possible; however, it can be more secure than classical bit commitment. In despite of its usefulness, quantum bit commitment protocols have not been experimentally implemented. The main reason is the fact that all proposed quantum bit commitment protocols require quantum memory. In this work, we show a quantum bit commitment protocol that does not require quantum memory and can be implemented with present technology.

Adrian Kent

A bit string commitment protocol securely commits N classical bits so that the recipient can extract only M<N bits of information about the string. Classical reasoning suggests that bit string commitment implies bit commitment and hence, given the Mayers-Lo-Chau theorem, that nonrelativistic quantum bit string commitment is impossible. Not so: there exist nonrelativistic quantum bit string commitment protocols, with security parameters epsilon and M, that allow A to commit N=N(M,epsilon) bits to B so that A's probability of successfully cheating when revealing any bit and B's probability of extracting more than N'=N-M bits of information about the N bit string before revelation are both less than epsilon. With a restrictive definition of security against A, N can be taken to be O(exp(CN')) for a positive constant C. I briefly discuss possible applications.