Minimum entangled state dimension required for pseudo-telepathy

Pseudo-telepathy provides an intuitive way of looking at Bell's inequalities, in which it is often obvious that feats achievable by use of quantum entanglement would be classically impossible. A two-player pseudo-telepathy game proceeds as follows: Alice and Bob are individually asked a question and they must provide an answer. They are not allowed any form of communication once the questions are asked, but they may have agreed on a common strategy prior to the execution of the game. We say that they win the game if the questions and answers fulfil a specific relation. A game exhibits pseudo-telepathy if there is a quantum strategy that makes Alice and Bob win the game for all possible questions, provided they share prior entanglement, whereas it would be impossible to win this game systematically in a classical setting. In this paper, we show that any two-player pseudo-telepathy game requires the quantum players to share an entangled quantum system of dimension at least 3x3. This is optimal for two-player games, but the most efficient pseudo-telepathy game possible, in terms of total dimension, involves three players who share a quantum system of dimension 2x2x2.Pseudo-telepathy provides an intuitive way of looking at Bell's inequalities, in which it is often obvious that feats achievable by use of quantum entanglement would be classically impossible. A two-player pseudo-telepathy game proceeds as follows: Alice and Bob are individually asked a question and they must provide an answer. They are not allowed any form of communication once the questions are asked, but they may have agreed on a common strategy prior to the execution of the game. We say that they win the game if the questions and answers fulfil a specific relation. A game exhibits pseudo-telepathy if there is a quantum strategy that makes Alice and Bob win the game for all possible questions, provided they share prior entanglement, whereas it would be impossible to win this game systematically in a classical setting. In this paper, we show that any two-player pseudo-telepathy game requires the quantum players to share an entangled quantum system of dimension at least 3x3. This is optimal for two-player games, but the most efficient pseudo-telepathy game possible, in terms of total dimension, involves three players who share a quantum system of dimension 2x2x2.

arXiv:quant-ph/0412136Dec 17, 20040 citations

Gilles Brassard A, André Allan Méthot, Alain Tapp

Pseudo-telepathy provides an intuitive way of looking at Bell's inequalities, in which it is often obvious that feats achievable by use of quantum entanglement would be classically impossible. A~two-player pseudo-telepathy game proceeds as follows: Alice and Bob are individually asked a question and they must provide an answer. They are \emph{not} allowed any form of communication once the questions are asked, but they may have agreed on a common strategy prior to the execution of the game. We~say that they \emph{win} the game if the questions and answers fulfil a specific relation. A~game exhibits \emph{pseudo-telepathy} if there is a quantum strategy that makes Alice and Bob win the game for all possible questions, provided they share prior entanglement, whereas it would be impossible to win this game systematically in a classical setting. In~this paper, we show that any two-player pseudo-telepathy game requires the quantum players to share an entangled quantum system of dimension at least~\mbox{ $3 \times 3$ }. This is optimal for two-player games, but the most efficient pseudo-telepathy game possible, in terms of total dimension, involves \emph{three} players who share a quantum system of dimension~\mbox{ $2 \times 2 \times 2$ }.Pseudo-telepathy provides an intuitive way of looking at Bell's inequalities, in which it is often obvious that feats achievable by use of quantum entanglement would be classically impossible. A~two-player pseudo-telepathy game proceeds as follows: Alice and Bob are individually asked a question and they must provide an answer. They are \emph{not} allowed any form of communication once the questions are asked, but they may have agreed on a common strategy prior to the execution of the game. We~say that they \emph{win} the game if the questions and answers fulfil a specific relation. A~game exhibits \emph{pseudo-telepathy} if there is a quantum strategy that makes Alice and Bob win the game for all possible questions, provided they share prior entanglement, whereas it would be impossible to win this game systematically in a classical setting. In~this paper, we show that any two-player pseudo-telepathy game requires the quantum players to share an entangled quantum system of dimension at least~\mbox{$3 \times 3$}. This is optimal for two-player games, but the most efficient pseudo-telepathy game possible, in terms of total dimension, involves \emph{three} players who share a quantum system of dimension~\mbox{$2 \times 2 \times 2$}.

Quantum Information and ComputationJul 1, 200518 citations

The Impossibility of Pseudo-Telepathy Without Quantum Entanglement

Viktor Galliard, Stefan Wolf, Alain Tapp

Imagine that Alice and Bob, unable to communicate, are both given a 16-bit string such that the strings are either equal, or they differ in exactly 8 positions. Both parties are then supposed to output a 4-bit string in such a way that these short strings are equal if and only if the original longer strings given to them were equal as well. It is known that this task can be fulfilled without failure and without communication if Alice and Bob share 4 maximally entangled quantum bits. We show that, on the other hand, they CANNOT win the same game with certainty if they only share classical bits, even if it is an unlimited number. This means that for fulfilling this particular distributed task, quantum entanglement can completely replace communication. This phenomenon has been called pseudo-telepathy. The results of this paper complete the analysis of the first proposed game of this type between two players.Imagine that Alice and Bob, unable to communicate, are both given a 16-bit string such that the strings are either equal, or they differ in exactly 8 positions. Both parties are then supposed to output a 4-bit string in such a way that these short strings are equal if and only if the original longer strings given to them were equal as well. It is known that this task can be fulfilled without failure and without communication if Alice and Bob share 4 maximally entangled quantum bits. We show that, on the other hand, they CANNOT win the same game with certainty if they only share classical bits, even if it is an unlimited number. This means that for fulfilling this particular distributed task, quantum entanglement can completely replace communication. This phenomenon has been called pseudo-telepathy. The results of this paper complete the analysis of the first proposed game of this type between two players.

arXiv:quant-ph/0211011Nov 4, 200220 citations

Two Party Pseudo Telepathy Games

Indranil Chakrabarty

In this work we have introduced two party pseudo telepathy games with respective winning conditions. One cannot win these games deterministically by any kind of classical protocols. Interestingly we find out that in quantum world, these winning conditions can be achieved if the players share an entangled state. We also introduced a game which is impossible to win if the players are form classical world, (both probabilistically and deterministically) yet there exists a perfect quantum strategy by following which, one can attain the winning condition of the game.In this work we have introduced two party pseudo telepathy games with respective winning conditions. One cannot win these games deterministically by any kind of classical protocols. Interestingly we find out that in quantum world, these winning conditions can be achieved if the players share an entangled state. We also introduced a game which is impossible to win if the players are form classical world, (both probabilistically and deterministically) yet there exists a perfect quantum strategy by following which, one can attain the winning condition of the game.

Dec 28, 20061 citation

Noise and the Mermin-GHZ Game

Ivan Fialík

A pseudo-telepathy game is a game for two or more players for which there is no classical winning strategy, but there is a winning strategy based on sharing quantum entanglement by the players. Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game, quantum players are almost certain to make errors even though they use a winning strategy. After introducing a model for pseudo-telepathy games, we investigate the impact of several basic noisy quantum channels on the quantum winning strategy for the Mermin-GHZ game. The question of how strong the noise can be so that quantum players would still be better than classical ones is also dealt with.A pseudo-telepathy game is a game for two or more players for which there is no classical winning strategy, but there is a winning strategy based on sharing quantum entanglement by the players. Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game, quantum players are almost certain to make errors even though they use a winning strategy. After introducing a model for pseudo-telepathy games, we investigate the impact of several basic noisy quantum channels on the quantum winning strategy for the Mermin-GHZ game. The question of how strong the noise can be so that quantum players would still be better than classical ones is also dealt with.

Electronic Notes in Theoretical Computer ScienceSep 1, 20091 citation

Extending and Characterizing Quantum Magic Games

Arkhipov, Alex

The Mermin-Peres magic square game is a cooperative two-player nonlocal game in which shared quantum entanglement allows the players to win with certainty, while players limited to classical operations cannot do so, a phenomenon dubbed "quantum pseudo-telepathy". The game has a referee separately ask each player to color a subset of a 3x3 grid. The referee checks that their colorings satisfy certain parity constraints that can't all be simultaneously realized. We define a generalization of these games to be played on an arbitrary arrangement of intersecting sets of elements. We characterize exactly which of these games exhibit quantum pseudo-telepathy, and give quantum winning strategies for those that do. In doing so, we show that it suffices for the players to share three Bell pairs of entanglement even for games on arbitrarily large arrangements. Moreover, it suffices for Alice and Bob to use measurements from the three-qubit Pauli group. The proof technique uses a novel connection of Mermin-style games to graph planarity.The Mermin-Peres magic square game is a cooperative two-player nonlocal game in which shared quantum entanglement allows the players to win with certainty, while players limited to classical operations cannot do so, a phenomenon dubbed "quantum pseudo-telepathy". The game has a referee separately ask each player to color a subset of a 3x3 grid. The referee checks that their colorings satisfy certain parity constraints that can't all be simultaneously realized. We define a generalization of these games to be played on an arbitrary arrangement of intersecting sets of elements. We characterize exactly which of these games exhibit quantum pseudo-telepathy, and give quantum winning strategies for those that do. In doing so, we show that it suffices for the players to share three Bell pairs of entanglement even for games on arbitrarily large arrangements. Moreover, it suffices for Alice and Bob to use measurements from the three-qubit Pauli group. The proof technique uses a novel connection of Mermin-style games to graph planarity.

arXiv:1209.3819Sep 18, 201221 citations

3 \times 3

}. This is optimal for two-player games, but the most efficient pseudo-telepathy game possible, in terms of total dimension, involves \emph{three} players who share a quantum system of dimension~\mbox{

2 \times 2 \times 2