Quantum version of the Monty Hall problem

@article{Flitney2002QuantumVO,
  title={Quantum version of the Monty Hall problem},
  author={Adrian P. Flitney and Derek Abbott},
  journal={Physical Review A},
  year={2002},
  volume={65},
  pages={062318}
}
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 that obtained with a classical mixed strategy. However, if the initial state involves entanglement of the qutrits 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 Version of a Generalized Monty Hall Game and Its Possible Applications to Quantum Secure Communications
TLDR
This work proposes a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free, and not fixed on its regular values, and extends its quantum scheme to include multiple independent players.
Advantage of a quantum player over a classical one in 2 × 2 quantum games
  • A. Flitney, D. Abbott
  • Physics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2003
We study a general 2 × 2 symmetric entangled quantum game. When one player has access only to classical strategies, while the other can use the full range of quantum strategies, there are ‘miracle’
The quantum Monty Hall problem
We consider a variation of the Monty Hall problem and we present a quantum version of it in which the quiz show master does not know where the prize is and can accidentally reveal it. We prove that
A ug 2 00 4 Advantage of a quantum player over a classical one in 2 x 2 quantum games
We study a general 2×2 symmetric, entangled, quantum game. When one player has access only to classical strategies while the other can use the full range of quantum strategies, there are 'miracle'
Multiplayer quantum Minority game with decoherence
A quantum version of the Minority game for an arbitrary number of agents is studied. When the number of agents is odd, quantizing the game produces no advantage to the players, however, for an even
Quantum Game Simulator, Using the Circuit Model of Quantum
TLDR
A general two-player quantum game simulator that can simulate any two- player quantum game described by a 2x2 payoff matrix (two strategy games) and applies the simulator to two well known quantum games, the Battle of Sexes and the Chicken game.
Quantum-Optical set-up for the Monty Hall problem
TLDR
A quantization scheme for the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game and considering both entanglement and non-entanglement between player and host.
...
...

References

Quantum Computation and Quantum Information
TLDR
This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.