相关论文: Quantum PBR Theorem as a Monty Hall Game
Response to a poll can be manipulated by means of a series of leading questions. We show that such phenomena cannot be explained by use of classical probability theory, whereas quantum probability theory admits a possibility of offering an…
Quantum pseudo-telepathy games, such as the Mermin-Peres magic square and the doily game, theoretically allow players to win with unit probability when using entangled quantum strategies. We quantitatively characterize the quantum advantage…
The basic Monty Hall problem is explored to introduce into the fundamental concepts of the game theory and to give a complete Bayesian and a (noncooperative) game-theoretic analysis of the situation. Simple combinatorial arguments are used…
We study a quantum version of a penny flip game played using control parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this game by introducing auxiliary spins which can be used to alter the behaviour of the system.…
Although quantum systems are generally described by quantum state vectors, we show that in certain cases their measurement processes can be reformulated as probabilistic equations expressed in terms of probabilistic state vectors. These…
Quantum Phase Transition (QPT) is a phase transition between different quantum states by adjusting some control parameters. Based on the Principle of Hamilton Dynamics (PHD) and the Principle of Lagrangian Dynamics (PLD), a general QPT…
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…
In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear subspaces of a Hilbert space, the assignment of truth values to quantum propositions (i.e., experimentally verifiable propositions relating to…
A probabilistic framework is developed that gives a unifying perspective on both the classical and the quantum games. We suggest exploiting peculiar probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to construct quantum…
We propose a new approach to solve the classical Monty Hall problem in its general form. The solution is based on basic tools of probability theory, by defining three elementary events which decompose the sample space into a partition. The…
We analyze the quantum penny flip game using geometric algebra and so determine all possible unitary transformations which enable the player Q to implement a winning strategy. Geometric algebra provides a clear visual picture of the quantum…
The box-ball system is studied from the viewpoint of combinatorics of words and tableaux. Each state of the box-ball system can be transformed into a pair of tableaux $(P,Q)$ by the Robinson-Schensted-Knuth correspondence. In the language…
Game versions of the Monty Hall Problem are discussed. The focus is on the principle of eliminating the dominated strategies, both in the zero-sum and noncooperative formulations.
We study the quantum moment problem: Given a conditional probability distribution together with some polynomial constraints, does there exist a quantum state rho and a collection of measurement operators such that (i) the probability of…
In Ref. [1] one of the authors proposed postulates for axiomatizing Quantum Mechanics as a "fair operational framework", namely regarding the theory as a set of rules that allow the experimenter to predict future events on the basis of…
Bell theorems of many-body nonlocality and contextuality serve as a benchmark for proving quantum advantage in that a quantum computer outperforms a classical computer for a certain problem. In practice, however, near-term quantum devices…
Recent works have shown that defining a behavioural equivalence that matches the observational properties of a quantum-capable, concurrent, non-deterministic system is a surprisingly difficult task. We explore coalgebras over distributions…
We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These…
QBism is an interpretation of quantum theory which views quantum mechanics as standard probability theory supplemented with a few extra normative constraints. The fundamental gambit is to represent states and measurements, as well as time…
This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There…