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arXiv:2205.00088 · The European Physical Journal Special Topics

Classical optical analogue of quantum discord

Jacob M. Leamer, Wenlei Zhang, Nicholas J. Savino, Ravi K. Saripalli, Sanjaya Lohani, Ryan T. Glasser, Denys I. Bondar

Published Sep 18, 2023• 3 citations
arXivHTMLPDF
DOI
10.1140/epjs/s11734-023-00988-1

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Quantum entanglement plays a key role in quantum information and quantum computation and thus attracts much attention in many branches of physics both in theory and in experiment. But recent studies revealed that some separable states (non-entangled state) may speed up certain tasks over their classical counterparts and may also possess certain kinds of quantum correlations. For example, geometric quantum discord, which is a more general quantum correlation measure than entanglement, can be nonzero for some separable states. From a practical point of view, it is proposed that the geometric quantum discord be responsible for the power of many quantum information processing tasks. In order to capture such correlations, Ollivier and Zurek introduced quantum discord, which measures the discrepancy between two natural yet different quantum analogues of two classically equivalent expressions of mutual information. However, the calculation of quantum discord is based on numerical maximization procedure, and there are few analytical expressions even for a two-qubit state. In order to obtain the analytical results of quantum discord, a geometric measure of quantum discord which measures the quantum correlations through the minimum Hilbert-Schmidt distance between the given state and zero discord state is introduced. Geometric quantum discord is defined as an effective measure of quantum correlation, and the geometric quantum discord through the minimal distance between the quantum state and the set of zero-discord states in a bipartite quantum system can be worked out. In this paper, by using the geometric quantum discord measurement method, the geometric quantum discord in Tavis-Cummings model is investigated, and the influences of the initial state purity, entanglement degree, dipole-dipole coupling intensity between two atoms, and field in the Fock state on the evolution characteristic of geometric quantum discord are analyzed. The results show that the geometric quantum discord appears periodically. It initially decreases to a minimum value, and then turns out to be increased for different initial states. The rigorous analysis and numerical results reveal that when we take a suitable initial state, the geometric quantum discord of two atoms can be kept in correlation. When the atoms are in the different initial states, the quantum properties of the system are significant. The photon number of the field can lead the quantum discord to be weakened. Geometric quantum discord can be increased by increasing the cavity photon number and the dipole-dipole coupling intensity. Geometric quantum discord can be enhanced obviously by increasing the strength of the dipole-dipole coupling interaction. The conclusions may conduce to the understanding of quantum correlation for the other systems from the view of geometric quantum discord.

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A behavioral quantum strategy is shown to replicate the payoff of a classical mixed strategy in an extensive-form game with imperfect recall, using only local measurements on a separable quantum state with nonzero discord. Classical behavioral strategies, constrained by memory loss, cannot achieve this coordination. When reinterpreted as a two-player game, the same construction yields a Nash equilibrium in behavioral quantum strategies. This result offers a quantum analogue of Kuhn’s Theorem: quantum discord substitutes for strategic memory, enabling coordination in settings where classical agents fail. These findings highlight discord as a minimal yet sufficient quantum resource for restoring equilibrium behavior under imperfect recall.
Optically coupled optomechanical oscillators has turned out to be a versatile experimental resource for exploring optomechanical synchronizations and correlations. In this work, we investigate the phenomena of quantum synchronization and quantum correlations in two optically coupled optomechanical oscillators with two different topologies. In one case the oscillators are coupled with optical photons in a reversible manner, termed as bidirectional coupling, while in the other photons are allowed to enter to the other oscillator but not allowed to exchanged back in the opposite direction, termed as unidirectional coupling. Our results shows that irrespective of these configurations, when synchronization builds up, the two oscillators also become quantum mechanically correlated with a finite degree of Gaussian quantum discord. However, we find that depending on these topologies, both synchronization and quantum discord behave in a very distinctive manner. For instance, in bidirectionally coupled optomechanical oscillators, we find both quantum synchronization and discord exhibit a tongue like pattern which is the quantum analogue of an Arnold tongue. Whereas, in the unidirectionally coupled oscillators, we observe a novel blockade like behavior for quantum phase synchronization, also known as the quantum synchronization blockade, while quantum discord being failed to map such an anomalous behavior.
Quantum entanglement plays a key role in quantum information and quantum computation and thus attracts much attention in many branches of physics both in theory and in experiment. But recent studies revealed that some separable states (non-entangled state) may speed up certain tasks over their classical counterparts and may also possess certain kinds of quantum correlations. For example, geometric quantum discord, which is a more general quantum correlation measure than entanglement, can be nonzero for some separable states. From a practical point of view, it is proposed that the geometric quantum discord be responsible for the power of many quantum information processing tasks. In order to capture such correlations, Ollivier and Zurek introduced quantum discord, which measures the discrepancy between two natural yet different quantum analogues of two classically equivalent expressions of mutual information. However, the calculation of quantum discord is based on numerical maximization procedure, and there are few analytical expressions even for a two-qubit state. In order to obtain the analytical results of quantum discord, a geometric measure of quantum discord which measures the quantum correlations through the minimum Hilbert-Schmidt distance between the given state and zero discord state is introduced. Geometric quantum discord is defined as an effective measure of quantum correlation, and the geometric quantum discord through the minimal distance between the quantum state and the set of zero-discord states in a bipartite quantum system can be worked out. In this paper, by using the geometric quantum discord measurement method, the geometric quantum discord in Tavis-Cummings model is investigated, and the influences of the initial state purity, entanglement degree, dipole-dipole coupling intensity between two atoms, and field in the Fock state on the evolution characteristic of geometric quantum discord are analyzed. The results show that the geometric quantum discord appears periodically. It initially decreases to a minimum value, and then turns out to be increased for different initial states. The rigorous analysis and numerical results reveal that when we take a suitable initial state, the geometric quantum discord of two atoms can be kept in correlation. When the atoms are in the different initial states, the quantum properties of the system are significant. The photon number of the field can lead the quantum discord to be weakened. Geometric quantum discord can be increased by increasing the cavity photon number and the dipole-dipole coupling intensity. Geometric quantum discord can be enhanced obviously by increasing the strength of the dipole-dipole coupling interaction. The conclusions may conduce to the understanding of quantum correlation for the other systems from the view of geometric quantum discord.