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

Analytical expression of quantum discord for rank-2 two-qubit states

Zhu, X., Fei, S., Li-Jost, X.

Published Jan 1, 2018• 3 citations
OpenAlex

Abstract

Quantum correlations characterized by quantum entanglement and quantum discord play important roles in many quantum information processing. We study the relations among the entanglement of formation, concurrence, tangle, linear entropy-based classical correlation and von Neumann entropy-based classical correlation . We present analytical formulae of linear entropy-based classical correlation for arbitrary $$d\otimes 2$$ quantum states and von Neumann entropy-based classical correlation for arbitrary $$2\otimes 2$$ rank-2 quantum states. From the von Neumann entropy-based classical correlation, we derive an explicit formula of quantum discord for arbitrary rank-2 two-qubit quantum states.

Related papers

Quantum Discord for d⊗2 Systems

Zhihao Ma, Zhihua Chen, F. F. Fanchini +1 more

We present an analytical solution for classical correlation, defined in terms of linear entropy, in an arbitrary system when the second subsystem is measured. We show that the optimal measurements used in the maximization of the classical correlation in terms of linear entropy, when used to calculate the quantum discord in terms of von Neumann entropy, result in a tight upper bound for arbitrary d⊗2 systems. This bound agrees with all known analytical results about quantum discord in terms of von Neumann entropy and, when comparing it with the numerical results for 10(6) two-qubit random density matrices, we obtain an average deviation of order 10(-4). Furthermore, our results give a way to calculate the quantum discord for arbitrary n-qubit GHZ and W states evolving under the action of the amplitude damping noisy channel.

arXiv:1509.01410•Scientific Reports•Jun 3, 2015•28 citations

Quantum discord of two-qubit rank-2 states

Mingjun Shi, Wei Yang, Feng-Jian Jiang +1 more

Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. In this paper, we discuss thoroughly the case of two-qubit rank-two states. An analytical expression for the quantum discord is obtained by means of Koashi-Winter relation. A geometric picture is demonstrated by means of quantum steering ellipsoid. We point out that in this case the optimal measurement is indeed the von Neumann measurement, which is usually used in the study of quantum discord. However, for some two-qubit states with the rank larger than two, we find that three-element POVM measurement is more optimal. It means that more careful attention should be paid in the discussion of quantum discord.

arXiv:1107.2246•Journal of Physics A Mathematical and Theoretical•Sep 22, 2011•62 citations

Monogamy properties of quantum and classical correlations

Gian Luca Giorgi

In contrast with entanglement, as measured by concurrence, in general, quantum discord does not possess the property of monogamy; that is, there is no tradeoff between the quantum discord shared by a pair of subsystems and the quantum discord that both of them can share with a third party. Here, we show that, as far as monogamy is considered, quantum discord of pure states is equivalent to the entanglement of formation. This result allows one to analytically prove that none of the pure three-qubit states belonging to the subclass of $W$ states is monogamous. A suitable physical interpretation of the meaning of the correlation information as a quantifier of monogamy for the total information is also given. Finally, we prove that, for rank 2 two-qubit states, discord and classical correlations are bounded from above by single-qubit von Neumann entropies.

arXiv:1109.1696•Physical Review A•Nov 2, 2011•122 citations

Quantum discord for a two-parameter class of states in 2⊗dquantum systems

Mazhar Ali

Quantum discord witnesses the nonclassicality of quantum states even when there is no entanglement in these quantum states. This type of quantum correlation also has some interesting and significant applications in quantum information processing. Quantum discord has been evaluated explicitly only for a certain class of two-qubit states. We extend the previous studies to 2⊗ d quantum systems and derive analytical expressions for quantum discord, classical correlation and entanglement for a two-parameter class of states for d ⩾ 3. We compare quantum discord, classical correlation and entanglement for qubit–qutrit systems to demonstrate that different measures of quantum correlation are not identical and conceptually different.

arXiv:1008.4013•Journal of Physics A Mathematical and Theoretical•Nov 15, 2010•40 citations

Quantum discord for two-qubit X states

Mazhar Ali, A. R. P. Rau, G. Alber

Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. In general, this correlation is different from entanglement, and quantum discord may be nonzero even for certain separable states. Even in the simple case of bipartite quantum systems, this different kind of quantum correlation has interesting and significant applications in quantum information processing. So far, quantum discord has been calculated explicitly only for a rather limited set of two-qubit quantum states and expressions for more general quantum states are not known. In this article, we derive explicit expressions for quantum discord for a larger class of two-qubit states, namely, a seven-parameter family of so called $X$ states that have been of interest in a variety of contexts in the field. We also study the relation between quantum discord, classical correlation, and entanglement for a number of two-qubit states to demonstrate that they are independent measures of correlation with no simple relative ordering between them.

arXiv:1002.3429•Physical Review A•Apr 12, 2010•835 citations

Quantum and classical correlations for a two-qubitXstructure density matrix

Bang-Fu Ding, Xiao-Yun Wang, Heping Zhao

We derive explicit expressions for quantum discord and classical correlation for an X structure density matrix. Based on the characteristics of the expressions, the quantum discord and the classical correlation are easily obtained and compared under different initial conditions using a novel analytical method. We explain the relationships among quantum discord, classical correlation, and entanglement, and further find that the quantum discord is not always larger than the entanglement measured by concurrence in a general two-qubit X state. The new method, which is different from previous approaches, has certain guiding significance for analysing quantum discord and classical correlation of a two-qubit X state, such as a mixed state.

Chinese Physics B•Oct 1, 2011•15 citations
Quantum correlations characterized by quantum entanglement and quantum discord play important roles in many quantum information processing. We study the relations among the entanglement of formation, concurrence, tangle, linear entropy-based classical correlation and von Neumann entropy-based classical correlation . We present analytical formulae of linear entropy-based classical correlation for arbitrary d⊗2d\otimes 2d⊗2 quantum states and von Neumann entropy-based classical correlation for arbitrary 2⊗22\otimes 22⊗2 rank-2 quantum states. From the von Neumann entropy-based classical correlation, we derive an explicit formula of quantum discord for arbitrary rank-2 two-qubit quantum states.
We present an analytical solution for classical correlation, defined in terms of linear entropy, in an arbitrary system when the second subsystem is measured. We show that the optimal measurements used in the maximization of the classical correlation in terms of linear entropy, when used to calculate the quantum discord in terms of von Neumann entropy, result in a tight upper bound for arbitrary d⊗2 systems. This bound agrees with all known analytical results about quantum discord in terms of von Neumann entropy and, when comparing it with the numerical results for 10(6) two-qubit random density matrices, we obtain an average deviation of order 10(-4). Furthermore, our results give a way to calculate the quantum discord for arbitrary n-qubit GHZ and W states evolving under the action of the amplitude damping noisy channel.
Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. In this paper, we discuss thoroughly the case of two-qubit rank-two states. An analytical expression for the quantum discord is obtained by means of Koashi-Winter relation. A geometric picture is demonstrated by means of quantum steering ellipsoid. We point out that in this case the optimal measurement is indeed the von Neumann measurement, which is usually used in the study of quantum discord. However, for some two-qubit states with the rank larger than two, we find that three-element POVM measurement is more optimal. It means that more careful attention should be paid in the discussion of quantum discord.
In contrast with entanglement, as measured by concurrence, in general, quantum discord does not possess the property of monogamy; that is, there is no tradeoff between the quantum discord shared by a pair of subsystems and the quantum discord that both of them can share with a third party. Here, we show that, as far as monogamy is considered, quantum discord of pure states is equivalent to the entanglement of formation. This result allows one to analytically prove that none of the pure three-qubit states belonging to the subclass of WWW states is monogamous. A suitable physical interpretation of the meaning of the correlation information as a quantifier of monogamy for the total information is also given. Finally, we prove that, for rank 2 two-qubit states, discord and classical correlations are bounded from above by single-qubit von Neumann entropies.
Quantum discord witnesses the nonclassicality of quantum states even when there is no entanglement in these quantum states. This type of quantum correlation also has some interesting and significant applications in quantum information processing. Quantum discord has been evaluated explicitly only for a certain class of two-qubit states. We extend the previous studies to 2⊗ d quantum systems and derive analytical expressions for quantum discord, classical correlation and entanglement for a two-parameter class of states for d ⩾ 3. We compare quantum discord, classical correlation and entanglement for qubit–qutrit systems to demonstrate that different measures of quantum correlation are not identical and conceptually different.
Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. In general, this correlation is different from entanglement, and quantum discord may be nonzero even for certain separable states. Even in the simple case of bipartite quantum systems, this different kind of quantum correlation has interesting and significant applications in quantum information processing. So far, quantum discord has been calculated explicitly only for a rather limited set of two-qubit quantum states and expressions for more general quantum states are not known. In this article, we derive explicit expressions for quantum discord for a larger class of two-qubit states, namely, a seven-parameter family of so called XXX states that have been of interest in a variety of contexts in the field. We also study the relation between quantum discord, classical correlation, and entanglement for a number of two-qubit states to demonstrate that they are independent measures of correlation with no simple relative ordering between them.
We derive explicit expressions for quantum discord and classical correlation for an X structure density matrix. Based on the characteristics of the expressions, the quantum discord and the classical correlation are easily obtained and compared under different initial conditions using a novel analytical method. We explain the relationships among quantum discord, classical correlation, and entanglement, and further find that the quantum discord is not always larger than the entanglement measured by concurrence in a general two-qubit X state. The new method, which is different from previous approaches, has certain guiding significance for analysing quantum discord and classical correlation of a two-qubit X state, such as a mixed state.