Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2407.21730 · Physical Review A

Linking quantum discord with Bayesian game theory

Adam Lowe

Published Oct 25, 2024• 1 citation
arXivHTMLPDF

Abstract

Witnessing quantum correlation in real, practical experimental setups is a key focus for the development of near-future quantum technologies. While there are several experimental protocols for witnessing entanglement, detecting quantum discord remains far more elusive. A recently proposed quantum discord witness offers an experimentally accessible setup which allows the quantum discord to be witnessed through a nonlinear combination of correlation functions. Interestingly, the experimental setup can be mapped to Bayesian game theory allowing for an extended generalization of the proposed witness. Subsequently, it is shown that there is a direct link between the expected payoff in Bayesian game theory and the previously proposed quantum discord witness by uniting these two concepts through the established CHSH game.

DOI
10.1103/physreva.110.042429

Related papers

Quantum advantage beyond entanglement in Bayesian game theory

Adam Lowe

Abstract Quantum discord has been utilised in order to find quantum advantage in an extension of the Clauser, Horne, Shimony, and Holt game. By writing the game explicitly as a Bayesian game, the resulting game is modified such the payoff’s are different. Crucially, restrictions are imposed on the measurements that Alice and Bob can perform. By imposing these restrictions, it is found that there exists quantum advantage beyond entanglement for a given quantum state. This is shown by decomposing the expected payoff into a classical and quantum term. By optimising over the expected payoff, the classical limit is surpassed for the given state in the restricted measurement space. This gives an operational framework in order to witness and determine the quantum discord for specific states, whilst demonstrating the importance of measurement in quantum advantage.

arXiv:2306.05090•Journal of Physics A Mathematical and Theoretical•Jan 8, 2024•3 citations

Determining quantum correlation through Nash equilibria in constant-sum games

Adam Lowe

Quantum game theory has emerged as a promising candidate to further the understanding of quantum correlations. Motivated by this, it is demonstrated that pure strategy Nash equilibria can be utilized as a mechanism to witness and determine quantum correlation. By combining quantum theory with Bayesian game theory, a constant-sum game is designed in which the players are competing against each other and crucially gain at the other player’s expense. Subsequently, it is found that mixed strategy Nash equilibria are only necessary when considering quantum correlation for the designed game. This reveals that a Bayesian game-theoretic framework yields a sufficient condition for detecting quantum effects.

arXiv:2410.15401•APL Quantum•Mar 1, 2025•2 citations

Witnessing the quantum discord of all the unknown states

Sixia Yu, Chengjie Zhang, Qing Chen +1 more

Like entanglement, quantum discord quantifies the quantum correlations. Unlike entanglement, whose detection is extremely difficult, the quantum discord of an arbitrary bipartite state allows itself to be detected perfectly by a single observable, the quantum discord witness. In particular, we report a single observable whose expectation value provides a necessary and sufficient condition for the vanishing quantum discord of an arbitrary bipartite unknown state with four copies. A quantum circuit is designed to measure the quantum discord witness by using only local qubit-measurements.

arXiv:1102.4710•Feb 23, 2011•8 citations

How to observe and quantify quantum-discord states via correlations

Matthew A. Hunt, Igor V. Lerner, I. V. Yurkevich +1 more

Quantum correlations between parts of a composite system most clearly reveal themselves through entanglement. Designing, maintaining, and controlling entangled systems is very demanding, which raises the stakes for understanding the efficacy of entanglement-free, yet quantum correlations, exemplified by quantum discord. Discord is defined via conditional mutual entropies of parts of a composite system and its direct measurement is hardly possible even via full tomographic characterization of the system state. Here we design a simple protocol to detect and quantify quantum discord in an unentangled bipartite system. Our protocol relies on a characteristic of discord that can be extracted from repeated direct measurements of certain correlations between subsystems of the bipartite system. The proposed protocol opens a way of extending experimental studies of discord to electronic systems, but can also be implemented in quantum-optical systems.

arXiv:1901.11514•Physical Review A•Aug 16, 2019•14 citations

Quantum discord in quantum random access codes and its connection to dimension witnesses

Yao Yao, Hong-Wei Li, Xu‐Bo Zou +6 more

We exploit quantum discord (and geometric discord) to detect quantum correlations present in a well-known communication model called quantum random access codes (QRACs), which has a variety of applications in quantum information theory. In spite of the fact that there is no entanglement between the two parts involved in this model, analytical derivation shows that the quantum discord is nonzero and highlights that quantum discord might be regarded as a figure of merit to characterize the quantum feature of QRACs, since this model has no classical counterparts. To gain further insight, we also investigate the dynamical behavior of quantum discord under some specific state rotations. In the two-state case, the connection between quantum discord and dimension witness is graphically discussed and intriguingly, our results illustrate that these two quantities are monotonically related to each other. For state encodings in the real $|0\ensuremath{\rangle}\ensuremath{-}|1\ensuremath{\rangle}$ plane, we derive an explicit analytical expression of the geometric discord and find that geometric discord reaches the maximal value for the optimal encoding strategy. However, for arbitrary state encodings in the Bloch sphere, our numerical simulations reveal that maximal geometric discord could not coincide with optimal $2\ensuremath{\rightarrow}1$ QRAC.

arXiv:1207.1275•Physical Review A•Dec 13, 2012•13 citations

Quantum Games and Quantum Discord

Ahmad Ahsan Nawaz, A. H. Toor

We quantize prisoners dilemma and chicken game by our generalized quantization scheme to explore the role of quantum discord in quantum games. In order to establish this connection we use Werner-like state as an initial state of the game. In this quantization scheme measurement can be performed in entangled as well as in product basis. For the measurement in entangled basis the dilemma in both the games can be resolved by separable states with non-zero quantum discord. Similarly for product basis measurement the payoffs are quantum mechanical only for nonzero values of quantum discord.

arXiv:1012.1428•Dec 7, 2010•2 citations
Witnessing quantum correlation in real, practical experimental setups is a key focus for the development of near-future quantum technologies. While there are several experimental protocols for witnessing entanglement, detecting quantum discord remains far more elusive. A recently proposed quantum discord witness offers an experimentally accessible setup which allows the quantum discord to be witnessed through a nonlinear combination of correlation functions. Interestingly, the experimental setup can be mapped to Bayesian game theory allowing for an extended generalization of the proposed witness. Subsequently, it is shown that there is a direct link between the expected payoff in Bayesian game theory and the previously proposed quantum discord witness by uniting these two concepts through the established CHSH game.
Abstract Quantum discord has been utilised in order to find quantum advantage in an extension of the Clauser, Horne, Shimony, and Holt game. By writing the game explicitly as a Bayesian game, the resulting game is modified such the payoff’s are different. Crucially, restrictions are imposed on the measurements that Alice and Bob can perform. By imposing these restrictions, it is found that there exists quantum advantage beyond entanglement for a given quantum state. This is shown by decomposing the expected payoff into a classical and quantum term. By optimising over the expected payoff, the classical limit is surpassed for the given state in the restricted measurement space. This gives an operational framework in order to witness and determine the quantum discord for specific states, whilst demonstrating the importance of measurement in quantum advantage.
Quantum game theory has emerged as a promising candidate to further the understanding of quantum correlations. Motivated by this, it is demonstrated that pure strategy Nash equilibria can be utilized as a mechanism to witness and determine quantum correlation. By combining quantum theory with Bayesian game theory, a constant-sum game is designed in which the players are competing against each other and crucially gain at the other player’s expense. Subsequently, it is found that mixed strategy Nash equilibria are only necessary when considering quantum correlation for the designed game. This reveals that a Bayesian game-theoretic framework yields a sufficient condition for detecting quantum effects.
Like entanglement, quantum discord quantifies the quantum correlations. Unlike entanglement, whose detection is extremely difficult, the quantum discord of an arbitrary bipartite state allows itself to be detected perfectly by a single observable, the quantum discord witness. In particular, we report a single observable whose expectation value provides a necessary and sufficient condition for the vanishing quantum discord of an arbitrary bipartite unknown state with four copies. A quantum circuit is designed to measure the quantum discord witness by using only local qubit-measurements.
Quantum correlations between parts of a composite system most clearly reveal themselves through entanglement. Designing, maintaining, and controlling entangled systems is very demanding, which raises the stakes for understanding the efficacy of entanglement-free, yet quantum correlations, exemplified by quantum discord. Discord is defined via conditional mutual entropies of parts of a composite system and its direct measurement is hardly possible even via full tomographic characterization of the system state. Here we design a simple protocol to detect and quantify quantum discord in an unentangled bipartite system. Our protocol relies on a characteristic of discord that can be extracted from repeated direct measurements of certain correlations between subsystems of the bipartite system. The proposed protocol opens a way of extending experimental studies of discord to electronic systems, but can also be implemented in quantum-optical systems.
We exploit quantum discord (and geometric discord) to detect quantum correlations present in a well-known communication model called quantum random access codes (QRACs), which has a variety of applications in quantum information theory. In spite of the fact that there is no entanglement between the two parts involved in this model, analytical derivation shows that the quantum discord is nonzero and highlights that quantum discord might be regarded as a figure of merit to characterize the quantum feature of QRACs, since this model has no classical counterparts. To gain further insight, we also investigate the dynamical behavior of quantum discord under some specific state rotations. In the two-state case, the connection between quantum discord and dimension witness is graphically discussed and intriguingly, our results illustrate that these two quantities are monotonically related to each other. For state encodings in the real $|0\ensuremath{\rangle}\ensuremath{-}|1\ensuremath{\rangle}$ plane, we derive an explicit analytical expression of the geometric discord and find that geometric discord reaches the maximal value for the optimal encoding strategy. However, for arbitrary state encodings in the Bloch sphere, our numerical simulations reveal that maximal geometric discord could not coincide with optimal $2\ensuremath{\rightarrow}1$ QRAC.
We quantize prisoners dilemma and chicken game by our generalized quantization scheme to explore the role of quantum discord in quantum games. In order to establish this connection we use Werner-like state as an initial state of the game. In this quantization scheme measurement can be performed in entangled as well as in product basis. For the measurement in entangled basis the dilemma in both the games can be resolved by separable states with non-zero quantum discord. Similarly for product basis measurement the payoffs are quantum mechanical only for nonzero values of quantum discord.