Parrondo's paradox in quantum walks with deterministic aperiodic sequence of coins

2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Zbigniew Walczak ◽  
Jarosław H. Bauer
Keyword(s):  
Quantum Walks ◽  
Parrondo’S Paradox

QUANTUM PARRONDO'S GAMES CONSTRUCTED BY QUANTUM RANDOM WALKS

2013 ◽  
Vol 12 (04) ◽  
pp. 1350024 ◽  
Author(s):  
MIN LI ◽  
YONG-SHENG ZHANG ◽  
GUANG-CAN GUO
Keyword(s):  
Random Walks ◽  
Discrete Time ◽  
Quantum Walks ◽  
Quantum Random Walks ◽  
Parrondo’S Paradox ◽  
Time Quantum

We construct a Parrondo's game using discrete-time quantum walks (DTQWs). Two losing games are represented by two different coin operators. By mixing the two coin operators UA(αA, βA, γA) and UB(αB, βB, γB), we may win the game. Here, we mix the two games in position instead of time. With a number of selections of the parameters, we can win the game with sequences ABB, ABBB, etc. If we set βA = 45°, γA = 0, αB = 0, βB = 88°, we find game 1 with [Formula: see text], [Formula: see text] will win and get the most profit. If we set αA = 0, βA = 45°, αB = 0, βB = 88° and game 2 with [Formula: see text], [Formula: see text] will win most. Game 1 is equivalent to game 2 with changes in sequences and steps. But at large enough steps, the game will lose at last. Parrondo's paradox does not exist in classical situation with our model.

scholarly journals Implementing Parrondo’s paradox with two-coin quantum walks

2018 ◽  
Vol 5 (2) ◽  
pp. 171599 ◽  
Author(s):  
Jishnu Rajendran ◽  
Colin Benjamin
Keyword(s):  
Random Walks ◽  
Shift Operator ◽  
Biological Systems ◽  
Quantum Walks ◽  
Initial State ◽  
Apparent Paradox ◽  
Parrondo’S Paradox ◽  
The Asymmetry

Parrondo’s paradox is ubiquitous in games, ratchets and random walks. The apparent paradox, devised by J. M. R. Parrondo, that two losing games A and B can produce a winning outcome has been adapted in many physical and biological systems to explain their working. However, proposals on demonstrating Parrondo’s paradox using quantum walks failed for a large number of steps. In this work, we show that instead of a single coin if we consider a two-coin initial state which may or may not be entangled, we can observe a genuine Parrondo’s paradox with quantum walks. Furthermore, we focus on reasons for this and pin down the asymmetry in initial two-coin state or asymmetry in shift operator, either of which is necessary for observing a genuine Parrondo’s paradox. We extend our work to a three-coin initial state too with similar results. The implications of our work for observing quantum ratchet-like behaviour using quantum walks are also discussed.

scholarly journals Experimental Realization of Parrondo's Paradox in 1D Quantum Walks

2020 ◽  
Vol 3 (6) ◽  
pp. 1900127 ◽  
Author(s):  
Munsif Jan ◽  
Qin‐Qin Wang ◽  
Xiao‐Ye Xu ◽  
Wei‐Wei Pan ◽  
Zhe Chen ◽  
...  
Keyword(s):  
Quantum Walks ◽  
Experimental Realization ◽  
Parrondo’S Paradox

scholarly journals Parrondo's paradox in quantum walks with time-dependent coin operators

2020 ◽  
Vol 102 (4) ◽  
Author(s):  
Marcelo A. Pires ◽  
Sílvio M. Duarte Queirós
Keyword(s):  
Quantum Walks ◽  
Time Dependent ◽  
Parrondo’S Paradox

scholarly journals Quantum walks defined by digraphs and generalized Hermitian adjacency matrices

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Sho Kubota ◽  
Etsuo Segawa ◽  
Tetsuji Taniguchi
Keyword(s):  
Quantum Walks ◽  
Adjacency Matrices

scholarly journals Parameterization of quantum walks on cycles

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Shuji Kuriki ◽  
Md Sams Afif Nirjhor ◽  
Hiromichi Ohno
Keyword(s):  
Quantum Walks

scholarly journals Chiral Floquet Systems and Quantum Walks at Half-Period

2021 ◽  
Author(s):  
C. Cedzich ◽  
T. Geib ◽  
A. H. Werner ◽  
R. F. Werner
Keyword(s):  
Quantum Walks ◽  
Half Period
Sign in / Sign up

Export Citation Format

Share Document