Łukasz Pawela

Decoherence effects in the quantum qubit flip game using Markovian approximation

We are considering a quantum version of the penny flip game, whose implementation is influenced by the environment that causes decoherence of the system. In order to model the decoherence, we assume Markovian approximation of open quantum system dynamics. We focus our attention on the phase damping, amplitude damping and amplitude raising channels. Our results show that the Pauli strategy is no longer a Nash equilibrium under decoherence. We attempt to optimize the players’ control pulses in the aforementioned setup to allow them to achieve higher probability of winning the game compared with the Pauli strategy.

Quantum Prisoner’s Dilemma game on hypergraph networks

We study the possible advantages of adopting quantum strategies in multi-player evolutionary games. We base our study on the three-player Prisoner’s Dilemma (PD) game. In order to model the simultaneous interaction between three agents we use hypergraphs and hypergraph networks. In particular, we study two types of networks: a random network and a SF-like network. The obtained results show that in the case of a three-player game on a hypergraph network, quantum strategies are not necessarily stochastically stable strategies. In some cases, the defection strategy can be as good as a quantum one.

Cooperative quantum Parrondo’s games

Abstract Coordination and cooperation are among the most important issues of game theory. Recently, the attention turned to game theory on graphs and social networks. Encouraged by interesting results obtained in quantum evolutionary game analysis, we study cooperative Parrondo’s games in a quantum setup. The game is modeled using multidimensional quantum random walks with biased coins. We use the GHZ and W entangled states as the initial state of the coins. Our analysis shows that an apparent paradox in cooperative quantum games and some interesting phenomena can be observed.

General Model for an Entanglement-Enhanced Composed Quantum Game on a Two-Dimensional Lattice

We introduce a method of analyzing entanglement-enhanced quantum games on regular lattices of agents. Our method is valid for setups with periodic and non-periodic boundary conditions. To demonstrate our approach we study two different types games, namely the Prisoners dilemma game and a cooperative Parrondos game. In both cases we obtain results showing, that entanglement is a crucial resource necessary for the agents to achieve positive capital gain.

Distinguishability of generic quantum states

Properties of random mixed states of dimension

Quantum control with spectral constraints

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Enhancing Pseudo-Telepathy in the Magic Square Game

distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large

Almost all quantum channels are equidistant

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Quantum games on evolving random networks

, due to the concentration of measure, the trace distance between two random states tends to a fixed number

Quantum control robust with respect to coupling with an external environment

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