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

Communications in Theoretical Physics

Total versus quantum correlations in a two-mode Gaussian state

Jamal El Qars

Published Mar 2, 2021• 7 citations
Publisher

Abstract

Abstract In Li and Luo (2007 Phys. Rev. A 76 032327), the inequality ( 1 / 2 )  ≥  was identified as a fundamental postulate for a consistent theory of quantum versus classical correlations for arbitrary measures of total  and quantum  correlations in bipartite quantum states. Besides, Hayden et al (2006 Commun. Math. Phys. 265 95) have conjectured that, in some conditions within systems endowed with infinite-dimensional Hilbert spaces, quantum correlations may dominate not only half of total correlations but total correlations itself. Here, in a two-mode Gaussian state, quantifying  and  respectively by the quantum mutual information  G and the entanglement of formation (EoF)  F G , we verify that  F , R G is always less than ( 1 / 2 )  R G when  G and  F G are defined via the Rényi-2 entropy. While via the von Neumann entropy,  F , V G may even dominate 

DOI
10.1088/1572-9494/abeb60

Related papers

On conjectures of classical and quantum correlations in bipartite states

Lin Zhang, Junde Wu

In this paper, two conjectures which were proposed in Luo et al (2010 Phys. Rev. A 82 052122 ) on the correlations in a bipartite state ρ AB are studied. If the mutual information I (ρ AB ) between two quantum systems A and B before any measurement is considered as the total amount of correlations in the state ρ AB , then it can be separated into two parts: classical correlations and quantum correlations. The so-called classical correlations C (ρ AB ) in the state ρ AB are defined by the maximizing mutual information between two quantum systems A and B after von Neumann measurements on system B . We show that it is upper bounded by the von Neumann entropies of both subsystems A and B , which answered the conjecture on the classical correlation. If the quantum correlations Q (ρ AB ) in the state ρ AB are defined by Q (ρ AB ) = I (ρ AB ) − C (ρ AB ), we also show that it is upper bounded by the von Neumann entropy of subsystem B . It is also found that Q (ρ AB ) is upper bounded by the von Neumann entropy of subsystem A for a class of states.

arXiv:1105.2993•Journal of Physics A Mathematical and Theoretical•Dec 8, 2011•24 citations

Total versus quantum correlations in quantum states

Nan Li, Shunlong Luo

On the premises that total correlations in a bipartite quantum state are measured by the quantum mutual information, and that separation of total correlations into quantum and classical parts satisfies an intuitive dominance relation, we examine to what extent various entropic entanglement measures, such as the distillable entanglement, the relative entropy entanglement, the squashed entanglement, the entanglement cost, and the entanglement of formation, can be regarded as consistent measures of quantum correlations. We illustrate that the entanglement of formation often overestimates quantum correlations and thus is too big to be a genuine measure of quantum correlations. This indicates that the entanglement of formation does not quantify the quantum correlations intrinsic to a quantum state, but rather characterizes the pure entanglement needed to build the quantum state via local operations and classical communication. Furthermore, it has the consequence that, if the additive conjecture for the entanglement of formation is true (as is widely believed), then the entanglement cost, which is an operationally defined measure of entanglement with significant physical meaning, cannot be a consistent measure of quantum correlations in the sense that it may exceed total correlations. Alternatively, if the entanglement cost is dominated by total correlations, as our intuition suggests, then we can immediately disprove the additive conjecture. Both scenarios have their counterintuitive and appealing aspects, and a natural challenge arising in this context is to prove or disprove that the entanglement cost is dominated by the quantum mutual information.

Physical Review A•Sep 26, 2007•113 citations

On a conjecture of the quantum correlations

Zhang Lin, Junde Wu

In this paper, two conjectures which were proposed in [Phys. Rev. A \textbf{82}, 052122(2010)] on the correlations in a bipartite state $\rho^{AB}$ are studied. If the mutual information $I\Pa{\rho^{AB}}$ between two quantum systems $A$ and $B$ before any measurement is considered as the total amount of correlations in the state $\rho^{AB}$, then it can be separated into two parts: classical correlations and quantum correlations. The so-called classical correlations $C\Pa{\rho^{AB}}$ in the state $\rho^{AB}$, defined by the maximizing mutual information between two quantum systems $A$ and $B$ after von Neumann measurements on system $B$, we show that it is upper bounded by the von Neumann entropies of both subsystems $A$ and $B$, this answered the conjecture on the classical correlation. If the quantum correlations $Q\Pa{\rho^{AB}}$ in the state $\rho^{AB}$ is defined by $Q\Pa{\rho^{AB}}= I\Pa{\rho^{AB}} - C\Pa{\rho^{AB}}$, we show also that it is upper bounded by the von Neumann entropy of subsystem $B$. It is also obtained that $Q\Pa{\rho^{AB}}$ is upper bounded by the von Neumann entropy of subsystem $A$ for a class of states.

•May 16, 2011•0 citations

Von Neumann entropy, mutual information and total correlations of Gaussian states

Alessio Serafini, Fabrizio Illuminati, Silvio De Siena

We determine the Von Neumann entropy and the mutual information of an arbitrary bipartite Gaussian state. A comparison between mutual information and entanglement of formation for symmetric states is considered, remarking the crucial role of the symplectic eigenvalues in qualifying and quantifying correlations.

•Jul 9, 2003•1 citation

Quantifying entanglement in two-mode Gaussian states

Spyros Tserkis, Timothy C. Ralph

Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography, and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure that is straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.

arXiv:1705.03612•Physical Review A•Dec 29, 2017•78 citations

Quantum versus classical correlations in a double cavity optomechanical system

Abderrahim Lakhfif, Abdelkader Hidki, Jamal El Qars +1 more

Abstract In a bipartite quantum state, where the total correlations can be divided into classical and quantum parts, Henderson and Vedral (2001 J. Phys. A: Math. Gen. 34 6899) have conjectured that classical correlations should not be less than quantum ones. Here, we consider two symmetrical states of two driven optomechanical cavities coupled to a squeezed photon source and exposed to Markovian noise and damping. The total and quantum correlations are systematically quantified by quantum mutual information and quantum discord respectively. Interestingly, we analytically demonstrate that classical correlations in the considered two-mode Gaussian states are always superior to quantum ones, whatever the physical and environmental parameters are. Moreover, using experimentally accessible parameters, we show numerically the existence of a domination of classical correlations over quantum ones under various circumstances. Finally, we found that quantum, as well as classical correlations, have similar behaviors under the effect of thermal decoherence, squeezing and optomechanical coupling. Yet, classical correlations are more strong and robust.

Journal of Physics B Atomic Molecular and Optical Physics•Apr 24, 2022•11 citations
Abstract In Li and Luo (2007 Phys. Rev. A 76 032327), the inequality ( 1 / 2 )  ≥  was identified as a fundamental postulate for a consistent theory of quantum versus classical correlations for arbitrary measures of total  and quantum  correlations in bipartite quantum states. Besides, Hayden et al (2006 Commun. Math. Phys. 265 95) have conjectured that, in some conditions within systems endowed with infinite-dimensional Hilbert spaces, quantum correlations may dominate not only half of total correlations but total correlations itself. Here, in a two-mode Gaussian state, quantifying  and  respectively by the quantum mutual information  G and the entanglement of formation (EoF)  F G , we verify that  F , R G is always less than ( 1 / 2 )  R G when  G and  F G are defined via the Rényi-2 entropy. While via the von Neumann entropy,  F , V G may even dominate 
In this paper, two conjectures which were proposed in Luo et al (2010 Phys. Rev. A 82 052122 ) on the correlations in a bipartite state ρ AB are studied. If the mutual information I (ρ AB ) between two quantum systems A and B before any measurement is considered as the total amount of correlations in the state ρ AB , then it can be separated into two parts: classical correlations and quantum correlations. The so-called classical correlations C (ρ AB ) in the state ρ AB are defined by the maximizing mutual information between two quantum systems A and B after von Neumann measurements on system B . We show that it is upper bounded by the von Neumann entropies of both subsystems A and B , which answered the conjecture on the classical correlation. If the quantum correlations Q (ρ AB ) in the state ρ AB are defined by Q (ρ AB ) = I (ρ AB ) − C (ρ AB ), we also show that it is upper bounded by the von Neumann entropy of subsystem B . It is also found that Q (ρ AB ) is upper bounded by the von Neumann entropy of subsystem A for a class of states.
On the premises that total correlations in a bipartite quantum state are measured by the quantum mutual information, and that separation of total correlations into quantum and classical parts satisfies an intuitive dominance relation, we examine to what extent various entropic entanglement measures, such as the distillable entanglement, the relative entropy entanglement, the squashed entanglement, the entanglement cost, and the entanglement of formation, can be regarded as consistent measures of quantum correlations. We illustrate that the entanglement of formation often overestimates quantum correlations and thus is too big to be a genuine measure of quantum correlations. This indicates that the entanglement of formation does not quantify the quantum correlations intrinsic to a quantum state, but rather characterizes the pure entanglement needed to build the quantum state via local operations and classical communication. Furthermore, it has the consequence that, if the additive conjecture for the entanglement of formation is true (as is widely believed), then the entanglement cost, which is an operationally defined measure of entanglement with significant physical meaning, cannot be a consistent measure of quantum correlations in the sense that it may exceed total correlations. Alternatively, if the entanglement cost is dominated by total correlations, as our intuition suggests, then we can immediately disprove the additive conjecture. Both scenarios have their counterintuitive and appealing aspects, and a natural challenge arising in this context is to prove or disprove that the entanglement cost is dominated by the quantum mutual information.
In this paper, two conjectures which were proposed in [Phys. Rev. A \textbf{82}, 052122(2010)] on the correlations in a bipartite state ρAB\rho^{AB}ρAB are studied. If the mutual information $I\Pa{\rho^{AB}}$ between two quantum systems AAA and BBB before any measurement is considered as the total amount of correlations in the state ρAB\rho^{AB}ρAB, then it can be separated into two parts: classical correlations and quantum correlations. The so-called classical correlations $C\Pa{\rho^{AB}}$ in the state ρAB\rho^{AB}ρAB, defined by the maximizing mutual information between two quantum systems AAA and BBB after von Neumann measurements on system BBB, we show that it is upper bounded by the von Neumann entropies of both subsystems AAA and BBB, this answered the conjecture on the classical correlation. If the quantum correlations $Q\Pa{\rho^{AB}}$ in the state ρAB\rho^{AB}ρAB is defined by $Q\Pa{\rho^{AB}}= I\Pa{\rho^{AB}} - C\Pa{\rho^{AB}}$, we show also that it is upper bounded by the von Neumann entropy of subsystem BBB. It is also obtained that $Q\Pa{\rho^{AB}}$ is upper bounded by the von Neumann entropy of subsystem AAA for a class of states.
Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography, and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure that is straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.
Abstract In a bipartite quantum state, where the total correlations can be divided into classical and quantum parts, Henderson and Vedral (2001 J. Phys. A: Math. Gen. 34 6899) have conjectured that classical correlations should not be less than quantum ones. Here, we consider two symmetrical states of two driven optomechanical cavities coupled to a squeezed photon source and exposed to Markovian noise and damping. The total and quantum correlations are systematically quantified by quantum mutual information and quantum discord respectively. Interestingly, we analytically demonstrate that classical correlations in the considered two-mode Gaussian states are always superior to quantum ones, whatever the physical and environmental parameters are. Moreover, using experimentally accessible parameters, we show numerically the existence of a domination of classical correlations over quantum ones under various circumstances. Finally, we found that quantum, as well as classical correlations, have similar behaviors under the effect of thermal decoherence, squeezing and optomechanical coupling. Yet, classical correlations are more strong and robust.