An Alternative Quantization Protocol for the History Dependent Parrondo Game

Quantum Multiplexers, Parrondo Games, and Proper Quantization

A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum multiplexer. This shared interest is due to the facts that an arbitrary quantum logic gate may be expressed, up to arbitrary accuracy, via a circuit consisting entirely of variations of the quantum multiplexer, and that certain one player games, the history dependent Parrondo games, can be quantized as games via a particular variation of the quantum multiplexer. However, to date all such quantizations have lacked a certain fundamental game theoretic property. The main result in this disse…

Properly Quantized History Dependent Parrondo Games, Markov Processes, and Multiplexing Circuits

In the context of quantum information theory, "quantization" of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of probability distribution with higher order randomization notions from quantum mechanics such as quantum superposition with measurement. For this to be done "properly", a faithful copy of the original construction is required to exist within the new "quantum" one, just as is required when a function is extended to a larger domain. Here procedures for extending hi…

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.

Quantum Parrondo's games under decoherence

We study the effect of quantum noise on history dependent quantum Parrondo's games by taking into account different noise channels. Our calculations show that entanglement can play a crucial role in quantum Parrondo's games. It is seen that for the maximally entangled initial state in the presence of decoherence, the quantum phases strongly influence the payoffs for various sequences of the game. The effect of amplitude damping channel leads to winning payoffs. Whereas the depolarizing and phase damping channels lead to the losing payoffs. In case of amplitude damping channel, the payoffs are …

A Personal History of the Hastings-Michalakis Proof of Hall Conductance Quantization

This is a personal history of the Hastings-Michalakis proof of quantum Hall conductance quantization.

量子化：历史与问题

Quantization: History and Problems

本文梳理了量子化从经典相空间函数到量子算符映射的历史，重点分析狄拉克方案的缺陷、格罗内沃尔德-范霍夫定理的意义，并介绍外尔量子化与几何量子化等替代方案及其与狄拉克纲领的关系。