Quantum game theory

Quantum game theory, concisely put, is an extension of classical game theory to the quantum domain. It differs from classical game theory in three primary ways:
#Superposed initial states,
#Quantum Entanglement of initial states,
#Superposition of strategies to be used on the initial states.

This theory is based on the physics of information much like Quantum Cryptography.

Superposed initial states

The information transfer that occurs during a game can be viewed as a physical process.In the simplest case of a classical game between two players with two strategies each, both the players can use a bit (a '0' or a '1') to convey their choice of strategy. A popular example of such a game is the Prisoners' Dilemma, where each of the convicts can either "confess" or "defect" to having committed the crime. In the quantum version of the game, the bit is replaced by the qubit, which is, simply put, a quantum superposition of two or more base states. In the case of a two-strategy game this can be physically implemented by the use of an entity like the electron which has a superposed spin state, with the base states being +1/2(plus half) and -1/2(minus half). Each of the spin states can be used to represent each of the two strategies available to the players. When a measurement is made on the electron, it collapses to one of the base states, thus conveying the strategy used by the player.

Entangled initial states

The set of qubits which are initially provided to each of the players (to be used to convey their choice of strategy) may be entangled. For instance, an entangled pair of qubits implies that an operation performed on one of the qubits, affects the other qubit as well, thus altering the expected pay-offs of the game.

Superposition of strategies to be used on initial states

The job of a player in a game is to choose a strategy. In terms of bits this means that the player has to choose between 'flipping' the bit to its opposite state or leaving its current state untouched. When extended to the quantum domain this implies that the player can "rotate" the qubit to a new state, thus changing the probability amplitudes of each of the base states. Such operations on the qubits are required to be unitary transformations on the initial state of the qubit. This is different from the classical procedure of assigning different probabilities to the act of selecting each of the strategies.

Multiplayer games

Introducing quantum information into multiplayer games allows a new type of equilibrium strategy which is not found in traditional games. The entanglement of players's choices can have the effect of a contract by preventing players from profiting from betrayal. [citation|url=http://prola.aps.org/abstract/PRA/v64/i3/e030301|title=Multiplayer quantum games|author=Simon C. Benjamin and Patrick M. Hayden|date=13 August 2001|DOI=10.1103/PhysRevA.64.030301]

ee also

* Adrian P. Flitney
* Jan Sładkowski
* Jens Eisert
* Azhar Iqbal

References

External links

* [http://www.nature.com/nature/journal/v445/n7124/full/445144a.html Quantum Games: States of Play, "Nature" (2007), Navroz Patel]
* [http://www.sciencenews.org/pages/sn_arc99/11_20_99/bob2.htm Article in Science News Magazine]
* [http://www.nature.com/news/1999/991021/pf/991021-3_pf.html Article in Nature Magazine]
* [http://physicsweb.org/articles/world/15/10/7 Article on PhysicsWeb]
* [http://xstructure.inr.ac.ru/x-bin/revtheme3.py?level=1&index1=-85152&skip=0 Review Articles on arxiv.org]