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Quantum Game Theory
Quantum game theory 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 computing. History In 1999, a professor in the math department at the University of California at San Diego named David A. Meyer first published ''Quantum Strategies'' which details a quantum version of the classical game theory game, matching pennies. In the quantum version, players are allowed access to quantum signals through the phenomenon of quantum entanglement. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategic Dominance
In game theory, strategic dominance (commonly called simply dominance) occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play. Many simple games can be solved using dominance. The opposite, intransitivity, occurs in games where one strategy may be better or worse than another strategy for one player, depending on how the player's opponents may play. Terminology When a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. The result of the comparison is one of: * B is equivalent to A: choosing B always gives the same outcome as choosing A, no matter what the other players do. * B strictly dominates A: choosing B always gives a better outcome than choosing A, no matter what the other players do. * B weakly dominates A: choosing B always gives at least as good an outcome as choosing A, no matter what the other players do, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Journal Of Theoretical Physics
The ''International Journal of Theoretical Physics'' is a peer-reviewed scientific journal of physics published by Springer Science+Business Media since 1968. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 1.708 and publishes both original research and review articles. The editor-in-chief is Heinrich Saller (Max Planck Institute for Physics). Scope and indexing The journal covers the following areas: general relativity, quantum theory with relativistic quantum field theory, quantum measurement theory, quantum geometry and quantum logic. Services abstracting and indexing this journal include Chemical Abstracts Service, Mathematical Reviews, Science Citation Index, Scopus, and Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructur . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jens Eisert
Jens Eisert, born 9 October 1970, is a German physicist, ERC fellow, and professor at the Free University of Berlin. He is known for his research in quantum information science and quantum many-body theory in condensed matter physics. He has made significant contributions to entanglement theory and the study of quantum computing, as well as to the development of protocols in the quantum technologies and to the study of complex quantum systems. Work on compressed sensing quantum state tomography he has contributed to has been influential for developing notions of benchmarking and the verification of quantum devices. The concept of a graph state has become a relevant class of multi-qubit quantum states with a number of applications in quantum computing. He has contributed to realizing a first dynamical quantum simulator, in joint work with Immanuel Bloch, Ulrich Schollwöck and others, building on his work on non-equilibrium quantum physics. In quantum many-body theory, he has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Sładkowski
Jan Sładkowski (born 1958 in Świętochłowice) is a Polish physicist. He is notable for his work on the role of exotic smoothness in cosmology, quantum game theory, and applications of thermodynamics in the theory of finance. Education He earned his PhD, under Marek Zrałek, and habilitation in theoretical physics from the University of Silesia, Katowice, Poland. He has published a number of papers on quantum field theory, mathematical physics, quantum information processing, and econophysics. Career He has held visiting posts at the Bielefeld University and at the University of Wisconsin–Madison. He presently holds the Chair of Astrophysics and Cosmology at the University of Silesia. Honors In 1999, he was a Humboldt fellow The Alexander von Humboldt Foundation (german: Alexander von Humboldt-Stiftung) is a foundation established by the German government, government of the Federal Republic of Germany and funded by the Foreign Office (Germany), Federal Foreign Office, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CHSH Game
In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics can not be reproduced by local hidden-variable theories. Experimental verification of the inequality being violated is seen as confirmation that nature cannot be described by such theories. CHSH stands for John Clauser, Michael Horne, Abner Shimony, and Richard Holt, who described it in a much-cited paper published in 1969. They derived the CHSH inequality, which, as with John Stewart Bell's original inequality, is a constraint on the statistical occurrence of "coincidences" in a Bell test which is necessarily true if there exist underlying local hidden variables, an assumption that is sometimes termed local realism. It is in fact the case that the inequality is routinely violated by modern experiments in quantum mechanics. Statement The usual form of the CHSH inequality is where ''a'' and ''a''′ are detector sett ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Refereed Game
Quantum refereed game in quantum information processing is a class of games in the general theory of quantum games. It is played between two players, Alice and Bob, and arbitrated by a referee. The referee outputs the pay-off for the players after interacting with them for a fixed number of rounds, while exchanging quantum information. Definition An n-turn quantum referee performs n rounds of interaction with the player Alice and Bob. Each interaction involves receiving some quantum states from Alice and Bob, processing the quantum states together with the "left-over" state from the previous interaction, producing some output state, and sending part of the output state to the players. At the end of the n rounds, the referee processes the final state received from the players and decides the pay-off for Alice and Bob. The role of the referee is to pass along qubits to players Alice and Bob. It is the referee's job to entangle the qubits, which is argued to be essential in quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Pseudo-telepathy
Quantum pseudo-telepathy is the fact that in certain Bayesian games with asymmetric information, players who have access to a shared physical system in an entangled quantum state, and who are able to execute strategies that are contingent upon measurements performed on the entangled physical system, are able to achieve higher expected payoffs in equilibrium than can be achieved in any mixed-strategy Nash equilibrium of the same game by players without access to the entangled quantum system. In their 1999 paper, Gilles Brassard, Richard Cleve and Alain Tapp demonstrated that quantum pseudo-telepathy allows players in some games to achieve outcomes that would otherwise only be possible if participants were allowed to communicate during the game. This phenomenon came to be referred to ''as quantum pseudo-telepathy'', with the prefix ''pseudo'' referring to the fact that quantum pseudo-telepathy does not involve the exchange of information between any parties. Instead, quantum pse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Tic-tac-toe
Quantum tic-tac-toe is a " quantum generalization" of tic-tac-toe in which the players' moves are "superpositions" of plays in the classical game. The game was invented by Allan Goff of Novatia Labs, who describes it as "a way of introducing quantum physics without mathematics", and offering "a conceptual foundation for understanding the meaning of quantum mechanics". Background The motivation to invent quantum tic-tac-toe was to explore what it means to be in two places at once. In classical physics, a single object cannot be in two places at once. In quantum physics, however, the mathematics used to describe quantum systems seems to imply that before being subjected to quantum measurement (or "observed") certain quantum particles can be in multiple places at once. (The textbook example of this is the double-slit experiment.) How the universe can be like this is rather counterintuitive. There is a disconnect between the mathematics and our mental images of reality, a discon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimax Theorem
In the mathematical area of game theory, a minimax theorem is a theorem providing conditions that guarantee that the max–min inequality is also an equality. The first theorem in this sense is von Neumann's minimax theorem from 1928, which was considered the starting point of game theory. Since then, several generalizations and alternative versions of von Neumann's original theorem have appeared in the literature. Zero-sum games The minimax theorem was first proven and published in 1928 by John von Neumann, who is quoted as saying "''As far as I can see, there could be no theory of games ... without that theorem ... I thought there was nothing worth publishing until the Minimax Theorem was proved''". Formally, von Neumann's minimax theorem states: Let X \subset \mathbb^n and Y \subset \mathbb^m be compact convex sets. If f: X \times Y \rightarrow \mathbb is a continuous function that is concave-convex, i.e. : f(\cdot,y): X \to \mathbb is concave for fixed y, and : f(x,\cdo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Measurement
In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. The predictions that quantum physics makes are in general probabilistic. The mathematical tools for making predictions about what measurement outcomes may occur were developed during the 20th century and make use of linear algebra and functional analysis. Quantum physics has proven to be an empirical success and to have wide-ranging applicability. However, on a more philosophical level, debates continue about the meaning of the measurement concept. Mathematical formalism "Observables" as self-adjoint operators In quantum mechanics, each physical system is associated with a Hilbert space, each element of which represents a possible state of the physical system. The approach codified by John von Neumann represents a measurement upon a physical system by a self-adjoint operator on that Hilbert space termed an "observable". These observables play the role of measurab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess
Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to distinguish it from related games, such as xiangqi (Chinese chess) and shogi (Japanese chess). The recorded history of chess goes back at least to the emergence of a similar game, chaturanga, in seventh-century India. The rules of chess as we know them today emerged in Europe at the end of the 15th century, with standardization and universal acceptance by the end of the 19th century. Today, chess is one of the world's most popular games, played by millions of people worldwide. Chess is an abstract strategy game that involves no hidden information and no use of dice or cards. It is played on a chessboard with 64 squares arranged in an eight-by-eight grid. At the start, each player controls sixteen pieces: one king, one queen, two rooks, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
