Quantization of Blackjack: Quantum Basic Strategy and Advantage

Quantum computers that process information by harnessing the remarkable power of quantum mechanics are increasingly being put to practical use. In the future, their impact will be felt in numerous fields, including in online casino games. This is one of the reasons why quantum gambling theory has garnered considerable attention. Studies have shown that the quantum gambling theory often yields nontrivial consequences that classical theory cannot interpret. We formulated blackjack game, which is one of the most famous card games, as a quantum game and found possible quantum entanglement between strategies. We also devised a quantum circuit reproducing classical blackjack. This circuit can be realized in the near future when quantum computers are commonplace. Furthermore, we showed that the player’s expectation increases compared to the classical game using quantum basic strategy, which is a quantum version of the popular basic strategy of blackjack.

Quantum Game of Dual-channel Supply Chain under Free-riding Behavior

Based on the perspective of the quantum game, this paper explores when the online direct sales channel takes the free-riding behavior after the retail channel provides high-quality experience and services and how the dual-channel supply chain establishes a commodity pricing strategy. The retailer’s selling price follows a decreasing function of the free-riding behavior coefficient. while the online direct selling price does an increasing function of the free-riding behavior coefficient. Under centralized decision-making, there is no quantum entanglement, so the quantum game solution is consistent with the classical game solution. Under decentralized decision-making, the optimal price and profit of the quantum game are higher than those of the classical game when the quantum entanglement degree is greater than zero. When the quantum entanglement tends to be infinite, the optimal price of the quantum game finally remains in convergence. The quantum game theory is a more optimal decision-making method than the classical game theory.

The Superiority of Quantum Strategy in 3-Player Prisoner’s Dilemma

In this paper, we extend the quantum game theory of Prisoner’s Dilemma to the N-player case. The final state of quantum game theory of N-player Prisoner’s Dilemma is derived, which can be used to investigate the payoff of each player. As demonstration, two cases (2-player and 3-player) are studied to illustrate the superiority of quantum strategy in the game theory. Specifically, the non-unique entanglement parameter is found to maximize the total payoff, which oscillates periodically. Finally, the optimal strategic set is proved to depend on the selection of initial states.

Quantum Physical Unclonable Functions: Possibilities and Impossibilities

A Physical Unclonable Function (PUF) is a device with unique behaviour that is hard to clone hence providing a secure fingerprint. A variety of PUF structures and PUF-based applications have been explored theoretically as well as being implemented in practical settings. Recently, the inherent unclonability of quantum states has been exploited to derive the quantum analogue of PUF as well as new proposals for the implementation of PUF. We present the first comprehensive study of quantum Physical Unclonable Functions (qPUFs) with quantum cryptographic tools. We formally define qPUFs, encapsulating all requirements of classical PUFs as well as introducing a new testability feature inherent to the quantum setting only. We use a quantum game-based framework to define different levels of security for qPUFs: quantum exponential unforgeability, quantum existential unforgeability and quantum selective unforgeability. We introduce a new quantum attack technique based on the universal quantum emulator algorithm of Marvin and Lloyd to prove no qPUF can provide quantum existential unforgeability. On the other hand, we prove that a large family of qPUFs (called unitary PUFs) can provide quantum selective unforgeability which is the desired level of security for most PUF-based applications.