Game-theoretic discussion of quantum state estimation and cloning

Lee, Chiu Fan; Johnson, Neil F.

doi:10.1016/j.physleta.2003.10.019

Cited by 16 publications

(16 citation statements)

References 18 publications

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“…That is, a viewpoint that is motivated by the geometrical perspective that Clifford's geometric algebra provides. Such situations take place in the area of quantum communication and particularly in quantum cryptography [59][60][61]. Phase structure for Alice in quantum PD game using EPR setting.…”

Section: Discussionmentioning

confidence: 99%

Analyzing Three-Player Quantum Games in an EPR Type Setup

2011

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We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. The quantum games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting. In this setting, the players' strategy sets remain identical to the ones in the mixed-strategy version of the classical game that is obtained as a proper subset of the corresponding quantum game. Using GA we investigate the outcome of a realization of the game by players sharing GHZ state, W state, and a mixture of GHZ and W states. As a specific example, we study the game of three-player Prisoners' Dilemma.

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Section: Discussionmentioning

confidence: 99%

Analyzing Three-Player Quantum Games in an EPR Type Setup

2011

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“…Table 3. The payoffs of the three players for γ = 0, δ = π/2 and γ = π/2, δ = 0, for different Alice's operations, as obtained from equation (8). The payoffs of the three players for γ = δ = 0 and γ = δ = π/2, for different Alice's operations, as obtained from equation (8).…”

Section: Discussionmentioning

confidence: 99%

“…U A (0, 0, 0) U A (π/3, π/2, π/2) U A (π/2, π/2, π/2) U A (π, π, π) TABLE III: The payoffs of the three players for γ = 0, δ = π/2 and γ = π/2, δ = 0, for different Alice's operations, as obtained from equation (8).…”

Section: Figure Captionmentioning

confidence: 99%

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Communication aspects of a three-player Prisoner's Dilemma quantum game

Ramzan

Khan

2008

J. Phys. A: Math. Theor.

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We present a quantization scheme for a three-player Prisoner's Dilemma game. It is shown that entanglement plays a dominant role in the three-player quantum game. Four different types of payoffs are identified on the basis of different combinations of initial state and measurement basis entanglement parameters. A relation among these different payoffs is also established. We also study the communication aspects of the three-player game.By exploiting different combinations of initial state and measurement basis entanglement parameters, we establish a relationship for the information shared among the parties. It is seen that the strategies of the players act as carriers of information in quantum games.

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“…In this case one can analyse the impact of quantum information processing on classical scenarios. On the other hand quantum games can be also used to analyse typical quantum situations like state estimation and cloning [24].…”

Section: Progress In Quantum Algorithmsmentioning

confidence: 99%

Models of quantum computation and quantum programming languages

Miszczak¹

2011

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.

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Game-theoretic discussion of quantum state estimation and cloning

Abstract: We present a game-theoretic perspective on the problems of quantum state estimation and quantum cloning. This enables us to show why the focus on universal machines and the different measures of success, as employed in previous works, are in fact legitimite. *

Cited by 16 publications

References 18 publications

Analyzing Three-Player Quantum Games in an EPR Type Setup

Analyzing Three-Player Quantum Games in an EPR Type Setup

Communication aspects of a three-player Prisoner's Dilemma quantum game

Models of quantum computation and quantum programming languages

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