Positive operator valued measures and the quantum Monty Hall problem

Zander, Claudia; Casas, M.; Plastino, A.; Plastino, A.

doi:10.1590/s0001-37652006000300003

Cited by 6 publications

(5 citation statements)

References 7 publications

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“…as elements present in the study of a quantum system (such as superpositions and projective measurements, for instance). Consequently, to this day different approaches and quantum versions of the Monty Hall problem have already been proposed [8,[11][12][13][14][15][16], and there is even a quantum algorithm developed so that two persons can play a version of the Monty Hall quantum game on a quantum computer [17]. Some of the most interesting quantum versions are those of Flitney and Abbot [11], D'Ariano et al [12] and C.-F. Li [8].…”

Section: Quantum Monty Hall Gamementioning

confidence: 99%

“…When expressed as a Monty Hall game, wining probabilities for switching doors depend on whether it is a ψ-ontic or a ψ-epistemic game [10]. Other attempts at a quantum version of the Monty Hall problem can be found in the literature, see for example [8,[11][12][13][14][15][16][17]. All these studies show that there is not a unique way to formulate a quantum version of this classical game.…”

Section: Introductionmentioning

confidence: 99%

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Quantum-Optical set-up for the Monty Hall problem

Quezada¹,

Martín-Ruiz²,

Frank³

et al. 2020

Phys. Scr.

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A quantization scheme for the Monty Hall problem is proposed inspired by an experimentallyfeasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied from a frequentist perspective by analyzing the classical expectation values of the obtained quantum probabilities. Results are examined considering both entanglement and nonentanglement between player and host, and using two different approaches: random and strategybased. A potential application to secure communications of this quantization scheme and its results is also briefly discussed.

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Section: Quantum Monty Hall Gamementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum-Optical set-up for the Monty Hall problem

Quezada¹,

Martín-Ruiz²,

Frank³

et al. 2020

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…[27][28][29] To date, the mechanics of the game have been proven useful to the study of the foundations of quantum mechanics, [30] and due to the fact that the quantization procedure of a classical game is an entirely subjective task, various quantization schemes have been developed. [31][32][33][34][35][36][37][38][39] The most relevant quantization scheme for the purposes of this paper, due to the fact that all the steps of the game are performed via unitary operators acting on a state, is the one developed by Flitney and Abbott. [32] In this work, we propose a QKD protocol based on Flitney and Abbott's quantization scheme of the Monty Hall game.…”

Section: Introductionmentioning

confidence: 99%

Quantum Key‐Distribution Protocols Based on a Quantum Version of the Monty Hall Game

Quezada

Dong

2020

Annalen der Physik

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This work illustrates a possible application of quantum game theory to the area of quantum information, in particular to quantum cryptography. The study proposed two quantum key‐distribution (QKD) protocols based on the quantum version of the Monty Hall game devised by Flitney and Abbott. Unlike most QKD protocols, in which the bits from which the key is going to be extracted are encoded in a basis choice (as in BB84), these are encoded in an operation choice. The first proposed protocol uses qutrits to describe the state of the system and the same game operators proposed by Flitney and Abbott. The motivation behind the second proposal is to simplify a possible physical implementation by adapting the formalism of the qutrit protocol to use qubits and simple logical quantum gates. In both protocols, the security relies on the violation of a Bell‐type inequality, for two qutrits and for six qubits in each case. Results show a higher ratio of violation than the E91 protocol.

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“…More broadly, the relationship between quantum theory and game theory is investigated in [10][11][12]. The Monty Hall game [13][14][15][16] has also been generalized into quantum versions [17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Quantum PBR Theorem as a Monty Hall Game

Rajan

Visser

2019

Quantum Reports

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The quantum Pusey-Barrett-Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a ψ-ontic model (system's physical state) or to a ψ-epistemic model (observer's knowledge about the system). We reformulate the PBR theorem as a Monty Hall game, and show that winning probabilities, for switching doors in the game, depend whether it is a ψ-ontic or ψ-epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved to quantum teleportation, in particular for improving reliability.

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Positive operator valued measures and the quantum Monty Hall problem

Cited by 6 publications

References 7 publications

Quantum-Optical set-up for the Monty Hall problem

Quantum-Optical set-up for the Monty Hall problem

Quantum Key‐Distribution Protocols Based on a Quantum Version of the Monty Hall Game

Quantum PBR Theorem as a Monty Hall Game

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