arXiv subjects

Derek Abbott

Publications and source records attributed to Derek Abbott.

101 records · Page 6Linked to original sources

arXiv2004

Quantum two and three person duels

In game theory, a popular model of a struggle for survival among three competing agents is a truel, or three person generalization of a duel. Adopting the ideas recently developed in quantum game theory, we present a quantum scheme for the problems of duels and truels. In the classical case, the outcome is sensitive to the precise rules under which the truel is performed and can be counter intuitive. These aspects carry over into our quantum scheme, but interference amongst the players' strategies can arise, leading to game equilibria different from the classical case.

quant-ph↗

arXiv2003

Quantum random walks with history dependence

We introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying the history dependence. By mixing the biased random walk with an unbiased one, the direction of the bias can be reversed leading to a new quantum version of Parrondo's paradox.

quant-ph↗

arXiv2003

Minimal Brownian Ratchet: An Exactly Solvable Model

We develop an exactly-solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations we obtain the steady-state probabilities. Generally the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space we find the null-curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null-curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force. We also indicate the off-balance behavior with biased random noise.

cond-mat.stat-mech↗

arXiv2003

Dreams versus Reality: Plenary Debate Session on Quantum Computing

This is a transcript of a debate on quantum computing that took place at 6:00pm, Wednesday, 4th June 2003, La Fonda Hotel, Santa Fe, USA. Transcript editor: Derek Abbott. Pro Team: Carlton M. Caves, Daniel Lidar, Howard Brandt, Alex Hamilton. Con Team: David Ferry, Julio Gea-Banacloche, Sergey Bezrukov, Laszlo Kish.

quant-ph↗

arXiv2002

An introduction to quantum game theory

The application of the methods of quantum mechanics to game theory provides us with the ability to achieve results not otherwise possible. Both linear superpositions of actions and entanglement between the players' moves can be exploited. We provide an introduction to quantum game theory and review the current status of the subject.

quant-ph↗

arXiv2002

Parameter identification using the Hilbert transform

Many physical systems can be adequately modelled using a second order approximation. The problem of plant identification reduces to the problem of estimating the position of a single pair of complex conjugate poles. One approach to the problem is to apply the method of least squares to the time domain data. This type of computation is best carried out in "batch" mode and applies to an entire data set. Another approach would be to design an adaptive filter and to use autoregressive, AR, techniques. This would be well suited to continuous real-time data and could track slow changes on the underlying plant. I this paper we present a very fast but approximate technique for the estimation of the position of a single pair of complex conjugate poles, using the Hilbert transform to reconstruct the analytic signal.

physics.data-an↗

arXiv2002

A semi-quantum version of the game of Life

A version of John Conway's game of Life is presented where the normal binary values of the cells are replaced by oscillators which can represent a superposition of states. The original game of Life is reproduced in the classical limit, but in general additional properties not seen in the original game are present that display some of the effects of a quantum mechanical Life. In particular, interference effects are seen.

quant-ph↗

arXiv2002

The physical basis for Parrondo's games

Several authors have implied that the original inspiration for Parrondo's games was a physical system called a ``flashing Brownian ratchet''. The relationship seems to be intuitively clear but, surprisingly, has not yet been established with rigor. In this paper, we apply standard finite-difference methods of numerical analysis to the Fokker-Planck equation. We derive a set of finite difference equations and show that they have the same form as Parrondo's games. Parrondo's games, are in effect, a particular way of sampling a Fokker-Planck equation. Physical Brownian ratchets have been constructed and have worked. It is hoped that the finite element method presented here will be useful in the simulation and design of flashing Brownian ratchets.

cond-mat.stat-mech↗

arXiv2002

Quantum version of the Monty Hall problem

A version of the Monty Hall problem is presented where the players are permitted to select quantum strategies. If the initial state involves no entanglement the Nash equilibrium in the quantum game offers the players nothing more than can be obtained with a classical mixed strategy. However, if the initial state involves entanglement of the qubits of the two players, it is advantageous for one player to have access to a quantum strategy while the other does not. Where both players have access to quantum strategies there is no Nash equilibrium in pure strategies, however, there is a Nash equilibrium in quantum mixed strategies that gives the same average payoff as the classical game.

quant-ph↗

arXiv2002

Quantum Parrondo's Games

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.

quant-ph↗

arXiv2000

New paradoxical games based on Brownian ratchets

Based on Brownian ratchets, a counter-intuitive phenomenon has recently emerged -- namely, that two losing games can yield, when combined, a paradoxical tendency to win. A restriction of this phenomenon is that the rules depend on the current capital of the player. Here we present new games where all the rules depend only on the history of the game and not on the capital. This new history-dependent structure significantly increases the parameter space for which the effect operates.

cond-mat.stat-mech↗