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

Abstract

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.

Quantum version of a generalized Monty Hall game and its possible applications to quantum secure communications

“…Furthermore, if P ns + P s = 1, then $ B max = 1. This (18) that, the more doors are included in the superposition of Bob's strategy (more b j,0 = 0), the closer the curve is going to be to the case where $ B max is reached.…”

“…In our previous work [18], we proposed two quantum keydistribution protocols based on the quantum version of the regular Monty Hall game developed by Flitney and Abbott [27]. Since the regular Monty Hall game mechanics and parameters only allow the game to be played by two parties, the formalism in Flitney and Abbott's work could not be used to develop a multi-party quantum protocol.…”

“…Applications of quantum game theory have already been found in the study of quantum coherence [15] and quantum mechanics foundations [16], in a quantum-like description of markets and economics [17] and in the development of quantum key-distribution protocols [18]. Furthermore, in 1999 Eisert et al conjectured that "survival games" might be played by nature at a molecular level [19] and in 2014, Bohl et al concluded that classical game theory can correctly model some of the behaviors of viruses, genes and proteins [20], suggesting that smaller molecules can be considered as players in a quantum game.…”

Bell‐GHZ Measurement‐Device‐Independent Quantum Key Distribution

“…[ 4–10 ] Furthermore, maximally entangled states, such as the Greenberger–Horne–Zeilinger (GHZ) state and the W state, have been used for quantum secure direct communications (QSDC), [ 11,12 ] quantum dialogue (QD), [ 13,14 ] and two‐parties QKD protocols. [ 15–18 ]…”

“…[4][5][6][7][8][9][10] Furthermore, maximally entangled states, such as the Greenberger-Horne-Zeilinger (GHZ) state and the W state, have been used for quantum secure direct communications (QSDC), [11,12] quantum dialogue (QD), [13,14] and two-parties QKD protocols. [15][16][17][18] There are many approaches to QKD, which can be classified into at least four groups: A direct approach that is hard to DOI: 10.1002/andp.202100116 implement because of the high characterization of sources, channels, and measurement devices. [19,20] A quantum-teleportation approach becomes impractical due to the currently available technology.…”