

Title of Thesis
Application Of Gametheoretic Techniques To
Quantum Information Theory 
Author(s)
Muhammad Ramzan 
Institute/University/Department
Details Department of Physics / QuaidiAzam University,
Islamabad 
Session 2010 
Subject Physics 
Number of Pages 158 
Keywords (Extracted from title, table of contents and
abstract of thesis) Quantum, Generalization, Theoretic,
Techniques, Relationship, Equilibrium, Game, Application,
Information, Application, Reduction, Bimatrix, Unitary, Protocol,
Operators 
Abstract This work is mainly
based on quantum gametheoretic techniques and their application to
quantum information theory.Quantum game theory is an important
development in quantum computation and may have implications for
quantum information and quantum communication.The eect of quantum
memory on quantum games have been studied.Three dierent games such
as, Prisoner’s Dilemma, Battle of the Sexes and Chicken have been
analyzed in the quantum domain. By considering the restricted game
situation, it is shown that the eects of quantum memory and
decoherence become eective in a maximally entangled case.For which
the quantum player can out perform the classical player in all the
three games. It is also shown that the quantum player enjoys an
advantage over the classical player in Battle of the Sexes game for
the amplitudedamping and the depolarizing channels.The quantum
memory compensates the reduction in player’s payos due to
decoherence. It has no eect on the Nash equilibria of the three
games.
A generalization of twoplayer quantization scheme to a threeplayer
Prisoner’s Dilemma game under the eect of correlated noise is also
presented.In a restricted game scenario, it is shown the quantum
player is always better for all values of the decoherence
parameter for the entire range of memory parameter.It is seen
that for maximum degree of correlation, the game does not become
noiseless and quantum player can still outscore the classical
players for the entire range of the decoherence parameter
producing an interesting result in comparison with a twoplayer
quantum game.It is also shown that correlated noise has no eect on
the Nash equilibrium of the game.
By exploiting the threeplayer quantization scheme, we have studied
the communication aspects of a threeplayer Prisoner’s Dilemma
quantum game. It is shown that entanglement plays a dominant role in
a threeplayer quantum game.On the basis of initial state and the
measurement basis entanglement parameters, a relation among
different payos is established.It is investigated that the
strategies of the players act as information carriers in quantum
games. A relationship for the information shared among the parties
is also established.
A scheme for quantum key distribution is proposed in which a secret
key can be generated from the data coming through a partially
entanglement breaking channel.This scheme is rather deterministic
and ecient in the sense that two classical bits can be transferred
per entangled pair of qubits.Furthermore, it is important to point
out that, in this scheme, same symbol can be used for Eve’s
detection and key generation. It is also worth noting that the
eavesdropper, Eve, can be detected very easily from the disturbance
of the elements of the decoding bimatrix. We have checked for the
security of the scheme and found it secure against individual
attacks.
It is further investigated that quantum games are useful in
developing quantum cryptographic protocols.A multiparty quantum
cryptographic protocol using tripartite entangled GHZ states is
devised using gametheoretic techniques.In this protocol, two
classical bits can be transferred per entangled pair of qubits to
the communicating parties.Unitary operators applied by the sender on
a tripartite entangled state encodes a classical symbol that can be
decoded at receiver’s end with the help of a decoding matrix. In
this protocol, if Eve interferes during the transmission, she can be
detected by the disturbance of the decoding matrix. Our security
analysis shows that this protocol is also secure against
intercept/resend attacks. 
