We found an universal local unitary (orthogonal) transformation which transforms any centrosymmetric (CS) density matrix ρ_{CS} into the X density matrix ρ_X: H\otimes Hρ_{CS}H\otimes H=ρ_X, where H is the Hadamard transformation. Because quantum discord is invariant under the local unitary transformations, this remarkable property allows to get the discord of general two-qubit CS states in the analytical form using the corresponding well-known formulas for the X states. Examples of systems with CS density matrices provided from the recent literature, including XXZ spin model with the Dzyaloshinsky-Moriya interaction, a gas of spin-carrying particles in closed nanopore, and a family of pseudopure states.
For the first time, we compute the quantum discord in bipartite systems containing up to nine qubits. An analytical expression is obtained for the discord in a bipartite system with three qubits. The dependence of the discord on the temperature and the structural parameter of the model is studied.
Radhakrishnan \emph{et.al} [Phys. Rev. Lett. \textbf{124}, 110401 (2020)] proposed quantum discord to multipartite systems and derived explicit formulae for any states. These results are significant in capturing quantum correlations for multi-qubit systems. In this paper, we evaluate the geometric measure of multipartite quantum discord and obtain results for a large family of multi-qubit states. %Intriguingly, our results demonstrate that for the family of states, multipartite geometric discord decreases exponentially as the number of parties increases while multipartite quantum discord not,t…
Two-qubit X-state is a large class of quantum states which plays an important role in the quantification and dynamical study of quantum correlations. However, the corresponding quantification of quantum discord is still missing for bona fide discord measures, like original quantum discord, Bures distance of discord, and relative entropy of discord. In this paper, we consider the calculation of Bures distance of discord, which is a kind of correlation satisfying all criteria of a discord measure, for two-qubit X-states. Firstly, we derive an explicit expression for Bures distance of discord for…
We present a reliable algorithm to evaluate quantum discord for general two--qubit states, amending and extending an approach recently put forward for the subclass of X--states. A closed expression for the discord of arbitrary states of two qubits cannot be obtained, as the optimization problem for the conditional entropy requires the solution to a pair of transcendental equations in the state parameters. We apply our algorithm to run a numerical comparison between quantum discord and an alternative, computable measure of non-classical correlations, namely the geometric discord. We identify th…
We investigate the exact dynamics of trace distance discord by considering two qubits under dephasing whose states belong to a class of $X$ states beyond Bell diagonal form. The necessary condition for the occurrence of freezing trace distance discord is found and compared with that of entropic discord. For an illustration, we consider two interacting qubits coupled to independent reservoirs and demonstrate these dynamical properties of trace distance discord. It is interesting to find that the freezing trace distance discord exists even for $X$ states without maximally mixed marginals and can…
We consider the geometric global quantum discord (GGQD) of two-qubit systems. By analyzing the symmetry of geometric global quantum discord we give an approach for deriving analytical formulae of the extremum problem which lies at the core of computing the GGQD for arbitrary two-qubit states. Furthermore, formulae of GGQD of arbitrary two-qubit states and some concrete examples are presented.
Quantum discord is an effective measure of quantum correlation introduced by Olliver and Zurek. We evaluate analytically the quantum discord for a large family of non-X-states. Exact solutions of the quantum discord are obtained of the four parametric space for non-X-states. Dynamic behavior of the quantum discord is also explored under the action of the Kraus operator.
The exact solutions of the super quantum discord are derived for general two qubit X states in terms of a one-variable function. Several exact solutions of the super quantum discord are given for the general X-state over nontrivial regions of a seven dimensional manifold. It is shown that the super quantum discord of the X state may increase or decreases under the phase damping channel.
The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A particular attention is devoted to two special classes of three-qubit $X$ states. They include three-qubit states of ${\rm W}$, ${\rm GHZ}$ and Bell type. We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems.
The difference of quantum mutual information for bipartite system of qubits and minimum taken with respect to local unitary transformation group is introduced as a characteristic of quantum correlations.The two qubits example (and specifically the two qubits X state) is studied in some details.
We investigate the dynamics of quantum discord and entanglement for a class of mixed qubit-qutrit states assuming that only the qutrit is under the action of a dephasing channel. We demonstrate that even though the entanglement in the qubit-qutrit state disappears in a finite time interval, partial coherence left in the system enables quantum discord to remain invariant throughout the whole time evolution.
Global quantum discord (GQD), proposed by Rulli and Sarandy [Phys. Rev. A \textbf{84}, 042109 (2011)], is a generalization of quantum discord to multipartite states. In this paper, we provide an equivalent expression for GQD, and obtain the analytical expressions of GQD for two classes of multi-qubit states. The phenomena of sudden transition and freeze of GQD are also discussed.
We study analytically the dynamic behaviors of quantum correlation measured by quantum discord between two uncoupled qubits, which are immersed in a common Ohmic environment. We show that the quantum discord of the two noninteracting qubits can be greatly amplified or protected for certain initially prepared $X$-type states in the time evolution. Especially, it is found that there does exist the stable amplification of the quantum discord for the case of two identical qubits, and the quantum discord can be protected for the case of two different qubits with a large detuning. It is also indicat…
We check the decoherence dynamics of Measurement-induced Nonlocality(in short, MIN) and compare it with geometric discord for two qubit systems. There are quantum states, on which the action of dephasing channel cannot destroy MIN in finite or infinite time. We check the additive dynamics of MIN on a qubit state under two independent noise. Geometric discord also follows such additive dynamics like quantum discord. We have further compared non-Markovian evolution of MIN and geometric discord under dephasing and amplitude damping noise for pure state and it shows distinct differences between th…
The conditions are established for nullity of quantum discord for mixed states of a general two-qubit system whose dynamical behaviour is given by an X-state form density matrix. It is found that quantum discord can vanish at a finite time even in the presence of correlations between qubits. The degeneracy of the populations of the combined states of the qubits and the multi-qubit quantum coherences are shown to be responsible for vanishing of the discord. We illustrate our considerations by examining the coherent-state Tavis-Cummings model in which two qubits interact dispersively with the ca…
So far, super quantum discord has been calculated explicitly only for Bell-diagonal states and expressions for more general quantum states are not known. In this paper, we derive explicit expressions for super quantum discord for a larger class of two-qubit states, namely, a 4-parameter family of two-qubit states. We observe that, weak measurements obtain more quantumness of correlations than strong measurements. As an application, the dynamic behavior of the super quantum discord under decoherence channel is investigated. We find that, the super quantum discord decreases monotonically as a fu…
Quantum discord plays a pragmatic role in analyzing nonclassical feature of quantum correlations beyond entanglement. It is used in several information processing protocols which lacks sufficient amount of entanglement to be used as a resource. We have provided with an analytical method of detecting quantum discord of an arbitrary two qubit state. We have formulated a set of necessary and sufficient conditions for any two qubit state to be a both-way non-zero quantum discord state. As quantum discord is asymmetric in nature, we have framed the set of if and only if conditions for a two qubit s…
We use quantum discord to characterize the correlations present in the quantum computational model DQC1, introduced by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)]. The model involves a collection of qubits in the completely mixed state coupled to a single control qubit that has nonzero purity. The initial state, operations, and measurements in the model all point to a natural bipartite split between the control qubit and the mixed ones. Although there is no entanglement between these two parts, we show that the quantum discord across this split is nonzero for typical instances of the…
Xu [Jianwei Xu, J. Phys. A: Math. Theor. 45 405304 (2012)] generalized geometric quantum discord [B.Dakic, V. Vedral, and C . Brukner, Phys. Rev. Lett. 105 190502 (2010)] to multipartite states and proposed the geometric global quantum discord. In this paper, we first derive the analytical formulas of the geometric global quantum discord and geometric quantum discord for two-qubit X states, respectively. Second, we give five concrete examples to demonstrate the use of our formulas. Finally, we prove that the geometric quantum discord is a tight lower bound of the geometric global quantum disco…
We study the level surfaces of quantum discord for a class of two-qubit states with parallel nonzero Bloch vectors. The dynamic behavior of quantum discord under decoherence is investigated. It is shown that a class of X states has sudden transition between classical and quantum correlations under decoherence. Our results include the ones in M. D. Lang and C. M. Caves [Phys. Rev. Lett. 105, 150501 (2010)] as a special case and show new pictures and structures of quantum discord.
Quantum Discord (QD) is a measure of the total quantum non-local correlations of a quantum system. The formalism of quantum discord has been applied to various two-qubit mixed states and it has been reported that there is a non-zero quantum discord even when the states are unentangled. To this end, we have calculated the Quantum Discord for higher than two qubit mixed state, that is, the generalized n-qubit Werner state with a bipartite split. We found that the QD saturates to a straight line with unit slope in the thermodynamic limit. Qualitative studies of entanglement between the two subsys…
Quantum discord quantifies quantum correlations beyond entanglement and assumes nonzero values, which are notoriously hard to compute, for almost all quantum states. Here we provide computable tight bounds for the quantum discord for qubit-qudit states. In the case of two qubits our lower and upper bounds coincide for a 7-parameter family of filtered $X$-states, whose quantum discords can therefore be evaluated analytically. An application to the accessible information of the binary qubit channel is also presented. For the qubit-qudit state output by the circuit of deterministic computation wi…
The dynamics of the quantum discord for two identical qubits in both two independent single-mode cavities and a common single-mode cavity are discussed. For the initial Bell state with correlated spins, while the entanglement sudden death can occur, the quantum discord vanishes only at discrete moments in the independent cavities and never vanishes in the common cavity. Interestingly, quantum discord and entanglement show opposite behaviors in the common cavity, unlike in the independent cavities. For the initial Bell state with anti-correlated spins, quantum discord and entanglement behave in…
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-qu…
The common use in literature of orthogonal measurements in obtaining quantum discord for two-qubit states is discussed and compared with more general measurements. We prove the optimality of orthogonal measurements for rank 2 states. While for rank 3 and 4 mixed states they are not optimal, we present strong numerical evidence showing that they give the correct quantum discord up to minimal corrections. Based on the connection, through purification with an ancilla, between discord and entanglement of formation (EoF), we give a tight upper bound for the EoF of a $2\otimes N$ mixed state of rank…
We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We first introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state wi…
Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find analytical expression of quantum discord is an intractable task. Exact results are known only for very special states, namely, two-qubit X-shaped states. We present in this paper a geometric viewpoint, from which two-qubit quantum discord can be described clearly. The known results about X state discord are restated in the directly perceivable geometric language. As a consequence, the dynamics of classical correlations and quantum discord for an X state in the presence of decoherenc…
Calculation of the quantum discord requires to find the minimum of the quantum conditional entropy $S(ρ^{AB}|\{Π^B_{k}\})$ over all measurements on the subsystem $B$. In this paper, we provide a simple relation for the conditional entropy as the difference of two Shannon entropies. The relation is suitable for calculation of the quantum discord in the sense that it can by used to obtain the quantum discord for some classes of two-qubit states, without the need for minimization. We also present an analytical procedure of optimization and obtain conditions under which the quantum conditional ent…
Quantum discord is significant in analyzing quantum nonclassicality beyond the paradigm of entanglement. Presently we have explored the effectiveness of global unitary operations in manifesting quantum discord from a general two qubit zero discord state. Apart from the emergence of some obvious concepts such as absolute classical-quantum, absolute quantum-classical states, more interestingly, it is observed that set of states characterized by absoluteness contains only maximally mixed state. Consequently this marks the peak of effectiveness of global unitary operations in purview of manifestin…
A type of two qubits Josephson charge system is constructed in this paper, and properties of the quantum discord (QD) as well as the differences between thermal QD and thermal entanglement were investigated. A detailed calculation shows that the magnetic flux $Φ_{Xk}$ is more efficient than the voltage $V_{Xi}$ in tuning QD. By choosing proper system parameters, one can realize the maximum QD in our two qubits Josephson charge system.
We investigate decoherence-free evolution (DFE) of quantum discord (QD) for two initially-correlated qubits in two finite-temperature reservoirs using an exactly solvable model. We study QD dynamics of the two qubits coupled to two independent Ohmic reservoirs when the two qubits are initially prepared in X-type quantum states. It is found that reservoir temperature significantly affects the DFE dynamics. We show that it is possible to control the DFE and to prolong the DFE time by choosing suitable parameters of the two-qubit system and reservoirs.
We study the relative strength of classical and quantum correlations, as measured by discord, for two-qubit states. Quantum correlations appear only in the presence of classical correlations, while the reverse is not always true. We identify the family of states that maximize the discord for a given value of the classical correlations and show that the largest attainable discord for mixed states is greater than for pure states. The difference between discord and entanglement is emphasized by the remarkable fact that these states do not maximize entanglement and are, in some cases, even separab…
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 fo…
Quantum teleportation of an unknown quantum state is one of the few communication tasks which has no classical counterpart. Usually the aim of teleportation is to send an unknown quantum state to a receiver. But is it possible in some way that the receiver's state has more quantum discord than the sender's state? We look at a scenario where Alice and Bob share a pure quantum state and Alice has an unknown quantum state. She performs joint measurement on her qubits and channel to prepare Bob's qubits in a mixed state which has higher quantum discord than hers. We also observe an interesting fea…
We evaluate analytically the quantum discord for a large family of multiqubit states. It is interesting to note that the quantum discord of three-qubits and five-qubits is the same, as is the quantum discord of two-qubits and six-qubits. We discover that the quantum discord of this family states can be concluded into three categories. The level surfaces of the quantum discord in the three categories is shown through images. Furthermore, we investigated the dynamic behavior of quantum discord under decoherence. For the odd partite systems, we prove the frozen phenomenon of quantum discord doesn…
We address the experimental determination of entropic quantum discord for systems made of a pair of polarization qubits. We compare results from full and partial tomography and found that the two determinations are statistically compatible, with partial tomography leading to a smaller value of discord for depolarized states. Despite the fact that our states are well described, in terms of fidelity, by families of depolarized or phase-damped states, their entropic discord may be largely different from that predicted for these classes of states, such that no reliable estimation procedure beyond …
We present an efficient method to solve the quantum discord of two-qubit X states exactly. A geometric picture is used to clarify whether and when the general POVM measurement is superior to von Neumann measurement. We show that either the von Neumann measurement or the three-element POVM measurement is optimal, and more interestingly, in the latter case the components of the postmeasurement ensemble are invariant for a class of states.
We find that when a qubit initialized in a pure state experiences pure dephasing due to interaction with an environment, separable qubit-environment states generated during the evolution also have zero quantum discord with respect to the environment. What follows is that the set of separable states which can be reached during the evolution has zero volume and hence, such effects as sudden death of qubit-environment entanglement are very unlikely. In case of the discord with respect to the qubit, a vast majority of separable states qubit-environment is discordant, but in specific situations zer…
We study the dynamics of geometric measure of quantum discord (GMQD) under the influences of two local phase damping noises. Consider the two qubits initially in arbitrary X-states, we find the necessary and sufficient conditions for which GMQD is unaffected for a finite period. It is further shown that such results also hold for the non-Markovian dephasing process.
We introduce a measure of quantum correlations in the $N$-qubit quantum system which is invariant with respect to the $SU(2^N)$ group of transformations of this system. This measure is a modification of the quantum discord introduced earlier and is referred to as the unitary or $SU(2^N)$-invariant discord. Since the evolution of a quantum system is equivalent to the proper unitary transformation, the introduced measure is an integral of motion and is completely defined by eigenvalues of the density matrix. As far as the calculation of the unitary invariant discord is rather complicated computa…
We study a behavior of two-qubit states subject to tomographic measurement. We propose a novel approach to definition of asymmetry in quantum bipartite state based on its tomographic Shannon entropies. We consider two types of measurement bases: the first is one that diagonalizes density matrices of subsystems and is used in a definition of tomographic discord, and the second is one that maximizes Shannon mutual information and relates to symmetrical form quantum discord. We show how these approaches relate to each other and then implement them to the different classes of two-qubit states. Con…
We investigate the pairwise thermal quantum discord in a three-qubit XXZ model with Dzyaloshinskii-Moriya (DM) interaction. We find that the DM interaction can increase quantum discord to a fixed value in the anti- ferromagnetic system, but decreases quantum discord to a minimum first, then increases it to a fixed value in the ferromagnetic system. Abrupt change of quantum discord is observed, which indicates the abrupt change of groundstate. Dynamics of pairwise thermal quantum discord is also considered. We show that thermal discord vanishes in asymptotic limit regardless of its initial valu…
Except for a few special states, computing quantum discord remains a complicated optimization process. In this paper we present analytical solutions for computing quantum discord of the most general class of X-states and the criteria for each analytical solution to be valid. We discuss parameter regions that correspond to different analytical solutions and explain the underlying reasons for such structure to exist. We apply our formalism to study both arbitrary X-states and X-states with certain symmetries. We find that our analytical formalism is in excellent agreement with numerical calculat…
Fernando Galve \emph{et al.} $[Phys. Rev. Lett. \textbf{110}, 010501 (2013)]$ introduced discording power for a two-qubit unitary gate to evaluate its capability to produce quantum discord, and found that a $π/8$ gate has maximal discording power. This work analyzes the entangling power of a two-qubit unitary gate, which reflects its ability to generate quantum entanglement in another way. Based on the renowned Cartan decomposition of two-qubit unitary gates, we show that the magic power of the $π/8$ gate produces maximal entanglement for a general value of purities for two-qubit states.
The counterintuitive effect of non-unique ordering of two-qubit states with quantum entanglement measures was discovered over ten years ago. More precisely, it was shown by Monte Carlo simulations that there exist states for which the entanglement of formation and the negativity do not impose the same ordering of states, i.e. $E_{F}(ρ_{AB}) \leq (\geq) E_{F}(ρ_{AB}^{\prime})$ is not equivalent to $N(ρ_{AB}) \leq (\geq) N(ρ_{AB}^{\prime})$. Recently, it was discovered that quantum discord and the geometric quantum discord do not necessarily imply the same ordering of two-qubit $X$-states, which…
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 d…
Quantum discord is a measure of quantum correlation beyond entanglement. Computing quantum discord for simple quantum states is a basic problem. An analytical formula of quantum discord for two-qubit X states is first claimed in [Ali, Rau, and Alber, Phys. Rev. A 81, 042105 (2010)], but later found to be not always correct. I observe numerically that the formula is valid with worst-case absolute error 0.0021. For symmetric two-qubit X states, I give a counterexample to the analytical formula derived in [F. F. Fanchini et al., Phys. Rev. A 81, 052107 (2010)], but observe that the formula is val…
We analyze the roles of initial correlations between the two-qubit system and a dissipative cavity on quantum discord dynamics of two qubits. Considering two initial system-cavity states, we show that the initial system-cavity correlations not only can initially increase the two-qubit quantum discord but also would lead to a larger long-time quantum discord asymptotic value. Moreover, quantum discord due to initial correlations is more robust than the case of the initial factorized state. Finally, we show the initial correlations' importance for dynamics behaviors of mutual information and cla…
It is known that quantum discord might experience a sudden transition in its dynamics when calculated for certain Bell-diagonal states (BDS) that are in interaction with their surroundings. We examine this phenomenon known as the sudden change of quantum discord, considering the case of two qubits independently interacting with dephasing reservoirs. We first numerically demonstrate that, for a class of initial states which can be chosen arbitrarily close to BDS, the transition is in fact not sudden, although it might numerically appear so if not studied carefully. Then, we provide an extension…
Quantum discord provides a measure for quantifying quantum correlations beyond entanglement and is very hard to compute even for two-qubit states because of the minimization over all possible measurements. Recently a simple algorithm to evaluate the quantum discord for two-qubit X-states is proposed by Ali, Rau and Alber [Phys. Rev. A 81, 042105 (2010)] with minimization taken over only a few cases. Here we shall at first identify a class of X-states, whose quantum discord can be evaluated analytically without any minimization, for which their algorithm is valid, and also identify a family of …
We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions, the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behaviour of two-qubit discord versus two-qubit entanglement. Our calculations provide the firs…
Quantum systems in mixed states can be unentangled and yet still correlated in a way that is not possible for classical systems. These correlations can be quantified by the quantum discord and might provide a resource for certain mixed-state quantum information processing tasks. Here we report on the generation of discordant states of two trapped atomic ions via Markovian decoherence processes. While entanglement is strictly non-increasing under such operations, discord can be generated in various forms. Firstly we show that, starting from two classically correlated qubits, it is possible to g…
In this article, we investigate the error bound of quantum discord, obtained by the analytic formula of Ali et al.[Phys. Rev. A 81(2010), 042105] in case of general X states and by the analytic formula of Fanchini et al.[Phys. Rev. A 81(2010), 052107] in case of symmetric X states. We show that results of Ali et. al. to general X states and Fanchini et al. to symmetric X states may have worst-case error of 0.004565 and 0.0009 respectively.
Quantum decoherence happens when the system interacts with the environment. Quantum correlation behaviours in the two-qubit spin squeezing model are studied under the influence of intrinsic decoherence. Quantitative results were determined, which depend on parameters of the physical system by checking different quantifiers of quantum correlation such as entanglement, local quantum uncertainty, trace distance discord and uncertainty-induced quantum nonlocality. We show that the entanglement suffers from intrinsic decoherence and exhibits sudden death, whereas the other measures are more robust …
We employ the concepts of local quantum uncertainty and geometric quantum discord based on the trace norm to investigate the environmental effects on quantum correlations of two bipartite quantum systems. The first one concerns a two-qubit system coupled with two independent bosonic reservoirs. We show that the trace discord exhibits frozen phenomenon contrarily to local quantum uncertainty. The second scenario deals with a two-level system, initially prepared in a separable state, interacting with a quantized electromagnetic radiation. Our results show that there exists an exchange of quantum…
In a recent article S. Gharibian [\href{http://dx.doi.org/10.1103/PhysRevA.86.042106}{Phys. Rev. A {\bf 86}, 042106 (2012)}] has conjectured that no two qubit separable state of rank greater than two could be maximally non classical (defined to be those which have normalized geometric discord $1/4$) and asked for an analytic proof. In this work we prove analytically that among the subclass of $X$ states, there is a unique (up to local unitary equivalence) maximal separable state of rank two. Partial progress has been made towards the general problem and some necessary conditions have been deri…
Open quantum systems have attracted great attention, since inevitable coupling between quantum systems and their environment greatly affects the features of interest of these systems. Quantum discord, is a measure of the total nonclassical correlation in a quantum system that includes, but is not exclusive to, the distinct property of quantum entanglement. Quantum discord can exist in separated quantum states and plays an important role in many fundamental physics problems and practical quantum information tasks. There have been numerous investigations on quantum discord and its counterpart cl…
Recently, Girolami and Adesso have demonstrated that the calculation of quantum discord for two-qubit case can be viewed as to solve a pair of transcendental equation (Phys. Rev. A, {\bf 83}, 052108(2011)). In present work, we introduce the generalized Choi-Jamiolkowski isomorphism and apply it as a convenient tool for constructing transcendental equations. For the general two-qubit case, we show that the transcendental equations always have a finite set of universal solutions, this result can be viewed as a generalization of the one get by Ali, Rau, and Alber (Phys. Rev. A, {\bf 81}, 042105 (…
We present the complete solution of the problem of determination of trace-norm geometric discord for arbitrary two-qubit state. Final answer is achieved due to effective reduction of the problem to the study of critical points of certain mapping depending on projectors. Our results are illustrated on various, also new, families of two-qubit states and compared to already known special solutions.
