Quantum blackjack: Advantages offered by quantum strategies in communication-limited games

Lin, Joseph X.; Formaggio, J. A.; Harrow, Aram W.; Natarajan, Anand

doi:10.1103/physreva.102.012425

Cited by 8 publications

(5 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Interestingly, in contrast to most quantum information games (see e.g. references [35,51] for exceptions) this communication scenario admits an elegant interpretation in terms of the real-life colloquial game of Battleship, as detailed in reference [52] (where the game is also independently introduced). The algebraically maximal witness value is W = 36, which corresponds to earning one point for each pair (x, y).…”

Section: Can Qutrits Outperform Qubits Assisted By Qubit-entanglement?mentioning

confidence: 99%

Entanglement in prepare-and-measure scenarios: many questions, a few answers

et al. 2022

View full text Add to dashboard Cite

Entanglement and quantum communication are paradigmatic resources in quantum information science leading to correlations between systems that have no classical analogue. Correlations due to entanglement when communication is absent have for long been studied in Bell scenarios. Correlations due to quantum communication when entanglement is absent have been studied extensively in prepare-and-measure scenarios in the last decade. Here, we set out to understand and investigate correlations in scenarios that involve both entanglement and communication, focusing on entanglement-assisted prepare-and-measure scenarios. In a recent companion paper [\href{https://arxiv.org/abs/2103.10748}{arXiv:2103.10748}], we investigated correlations based on unrestricted entanglement. Here, our focus is on scenarios with restricted entanglement. We establish several elementary relations between standard classical and quantum communication and their entanglement-assisted counterparts. In particular, while it was already known that bits or qubits assisted by two-qubit entanglement between the sender and receiver constitute a stronger resource than bare bits or qubits, we show that higher-dimensional entanglement further enhance the power of bits or qubits. We also provide a characterisation of generalised dense coding protocols, a natural subset of entanglement-assisted quantum communication protocols, finding that they can be understood as standard quantum communication protocols in real-valued Hilbert space. Though such dense coding protocols can convey up to two bits of information, we provide evidence, perhaps counter-intuitively, that resources with a small information capacity, such as a bare qutrits, can sometimes produce stronger correlations. Along the way we leave several conjectures and conclude with a list of interesting open problems.

show abstract

Section: Can Qutrits Outperform Qubits Assisted By Qubit-entanglement?mentioning

confidence: 99%

Entanglement in prepare-and-measure scenarios: many questions, a few answers

et al. 2022

View full text Add to dashboard Cite

show abstract

“…In section I, we introduced quantum effects in game theory [2][3][4][5] and the application to gambling [6][7][8][9][10][11][12][13][14][15][16]. We also mentioned what will happen when playing blackjack on a quantum computer.…”

Section: Discussionmentioning

confidence: 99%

“…They also showed that this can be improved using quantum error mitigation techniques. In blackjack, it was shown that the players can have advantages compared to the dealer, using entangled bit communication between two players by [16]. As you can see in these studies, not a few games have been examined by using quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Quantization of Blackjack: Quantum Basic Strategy and Advantage

Mura,

Wada

2020

Preprint

View full text Add to dashboard Cite

Recently, quantum computers are putting to use practically. Then casino games will be played on quantum computers shortly, as casino games have been played on classical computers. Quantum gambling theory has been studied, and it often brings non-trivial consequences that classical theory can not explain. We proposed a quantum blackjack: we devised a quantum circuit reproducing classical blackjack and found the possibility of entanglement between strategies. This circuit can be realized in the near future where quantum computers are commonplace. Furthermore, we showed the player's expectation increases compared to the classical game, using quantum basic strategy, which is a quantum version of the popularly known basic strategy of blackjack.

show abstract

“…In [17] the optimal strategy for Blackjack is discussed, where a mathematical expression is derived, providing a general solution to the player's problem of drawing additional cards, with a given hand, or not. The game is also used in [18] as a baseline for examining the advantages that quantum strategies allow in communicationlimited games. Regarding Baccarat, it has been shown in [19] that, differently from Blackjack, the "card counting" technique does not provide significant favorable strategies, both for the Trente-et-Quarante and "Nevada" variants.…”

Section: A Related Workmentioning

confidence: 99%

Optimal Decision Strategies for the Generalized Cuckoo Card Game

2024

View full text Add to dashboard Cite

Cuckoo is a popular card game, which originated in France during the 15th century and then spread throughout Europe, where it is currently well-known under distinct names and with different variants. Cuckoo is an imperfect information game-of-chance, which makes the research regarding its optimal strategies determination interesting. The rules are simple: each player receives a covered card from the dealer; starting from the player at the dealer's left, each player looks at its own card and decides whether to exchange it with the player to their left, or keep it; the dealer plays at last and, if it decides to exchange card, it draws a random one from the remaining deck; the player(s) with the lowest valued card lose(s) the round. We formulate the gameplay mathematically and provide an analysis of the optimal decision policies. Different card decks can be used for this game, e.g., the standard 52-card deck or the Italian 40-card deck. We generalize the decision model for an arbitrary number decks' cards, suites, and players. Lastly, through numerical simulations, we compare the determined optimal decision strategy against different benchmarks, showing that the strategy outperforms the random and naive policies and approaches the performance of the ideal oracle.

show abstract

Quantum blackjack: Advantages offered by quantum strategies in communication-limited games

Cited by 8 publications

References 20 publications

Entanglement in prepare-and-measure scenarios: many questions, a few answers

Entanglement in prepare-and-measure scenarios: many questions, a few answers

Quantization of Blackjack: Quantum Basic Strategy and Advantage

Optimal Decision Strategies for the Generalized Cuckoo Card Game

Contact Info

Product

Resources

About