Quantum strategies for simple two-player XOR games
- PDF / 1,452,916 Bytes
- 22 Pages / 439.37 x 666.142 pts Page_size
- 19 Downloads / 182 Views
Quantum strategies for simple two‑player XOR games Ricardo Faleiro1 Received: 4 November 2019 / Accepted: 3 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The non-local game scenario provides a powerful framework to study the limitations of classical and quantum correlations, by studying the upper bounds of the wining probabilities those correlations offer in cooperation games where communication between players is prohibited. Building upon results presented in the seminal work of Cleve et al. (in: 19th IEEE annual conference on computational complexity, 2004), a straightforward construction to compute the Tsirelson bounds for simple two-player XOR games is presented. The construction is applied explicitly to some examples, including the Entanglement Assisted Orientation in Space (EAOS) game of Brukner et al. (Int J Quant Inf 4(2):365–370), proving for the first time that their proposed quantum strategy is in fact the optimal, as it reaches the Tsirelson bound. Keywords Non-local game · XOR game · Tsirelson inequality · EAOS game
1 Introduction Non-signaling games are cooperation multiplayer games where the players do not know all the information they could know in order to play the game in an ideal manner—they only know explicitly the information that was given to them by a neutral party, appropriately entitled as the Referee. This is usually imposed by a constraint called the No Signaling Condition, where communication either classical or quantum is not allowed between the players (physically one could think that the players are spacelike separated from one another). This type of game is called non-local when players using strategies that exploit the non-locality of quantum mechanics, i.e
* Ricardo Faleiro [email protected] 1
Instituto de Telecomunicações and Departamento de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais, 1049‑001 Lisboa, Portugal
13
Vol.:(0123456789)
229 Page 2 of 22 R. Faleiro
quantum strategies, can reach higher probabilities to win than players restricted to using classical strategies. A short and concise overview on non-local games can be found in [3]. Such games always evolve according to the following stages1, – The Referee sends to each player a specific input, usually referred to as a question (q); – Each player only receives its own question and since they can’t communicate with one another they are ignorant of the others’. Then each player will produce an output i.e an answer (a) based on a previously agreed common strategy and send them to the Referee; – The Referee will check the players’ answers against the questions and see if they are “correct” i.e if they respect the winning condition specified in the rules of the game; Also, depending on whether the questions and/or answers used in the game are classical or quantum information, we say the game is a classical non-local game or quantum non-local game, respectively. This work deals with classical non-local games, which means that the questions a
Data Loading...
