2002
DOI: 10.1016/s0378-4371(02)01084-1
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Quantum Parrondo's games

Abstract: Parrondo's Paradox arises when two losing games are combined to produce a winning one. A history dependent quantum Parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by general SU (2) operators to transform the game into the quantum domain. In the initial state, a superposition of qubits can be used to couple the games and produce interference leading to quite different payoffs to those in the classical case.

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Cited by 93 publications
(88 citation statements)
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“…Flitney et al have proposed a protocol for a quantum version of a history-dependent Parrondo's game. If the initial state is a superposition, payoff difference from the classical game can be acquired as a result of interference [27] . Chen et al develop a quantum version of Parrondo's game based on a quantum ratchet effect for a delta-kicked model.…”
Section: A the Main Classical Game Models And Its Quantum Counterpartmentioning
confidence: 99%
See 1 more Smart Citation
“…Flitney et al have proposed a protocol for a quantum version of a history-dependent Parrondo's game. If the initial state is a superposition, payoff difference from the classical game can be acquired as a result of interference [27] . Chen et al develop a quantum version of Parrondo's game based on a quantum ratchet effect for a delta-kicked model.…”
Section: A the Main Classical Game Models And Its Quantum Counterpartmentioning
confidence: 99%
“…The basic differences between the classical game and the quantum game are as follows [11,14,23,27,47] .…”
Section: A Basic Elements Of Classical Game and Quantum Gamementioning
confidence: 99%
“…For these games, they showed quantum Nash equilibriums different from classical ones. Furthermore, there are many results being related to games such as the Monty Hall problem by D'Ariano et al [11], Flitney and Abbott [12], and Li et al [13], Parrondo's game by Flitney et al [14], games in economics by Piotrowski and Sładkowski [15][16][17], Newcomb's paradox by Piotrowski and Sład-kowski [18], and so on.…”
Section: Pq Penny Flipmentioning
confidence: 99%
“…This can be illustrated in terms of games that lose when played individually, but win when alternated-this has been shown to be a discrete-time Brownian ratchet [9], otherwise known as a ''Parrondian game.'' Parrondo's games have significantly sparked recent interest in the areas of lattice gas automata [10], spin models [11], random walks and diffusions [12 -14], biogenesis [15], molecular transport [16,17], noise induced patterns [18], stochastic control [19,20], stochastic resonance [21], and quantum game theory [22,23]. Recently, Reimann [24] has performed an extensive review of the ratchet field.…”
mentioning
confidence: 99%