General monogamy property of global quantum discord and the application

We provide a family of general monogamy inequalities for global quantum discord (GQD), which can be considered as an extension of the usual discord monogamy inequality. It can be shown that those inequalities are satisfied under the similar condition for the holding of usual monogamy relation. We find that there is an intrinsic connection among them. Furthermore, we present a different type of monogamy inequality and prove that it holds under the condition that the bipartite GQDs do not increase when tracing out some subsystems. We also study the residual GQD based on the second type of monogamy inequality. As applications of those quantities, we investigate the GQDs and residual GQD in characterizing the quantum phase transition in the transverse field Ising model.     

Some New Properties of Quantum Correlations

Quantum coherence measures the correlation between different measurement results in a single-system, while entanglement and quantum discord measure the correlation among different subsystems in a multipartite system. In this paper, we focus on the relative entropy form of them, and obtain three new properties of them as follows: 1) General forms of maximally coherent states for the relative entropy coherence, 2) Linear monogamy of the relative entropy entanglement, and 3) Subadditivity of quantum discord. Here, the linear monogamy is defined as there is a small constant as the upper bound on the sum of the relative entropy entanglement in subsystems.     

Influences of Detuning on Geometrical Quantum Discord in Coupled Cavities System

Geometrical quantum discord (GQD) is adopted to quantify the degree of correlation between two subsystems. We consider the situation that two two-level atoms are separately trapped in coupled single-mode cavities, and each atom non-resonantly interacts with cavity via a one-photon hopping. GQD dynamic between atoms and that between cavities are studied. The influences of detuning on GQD dynamics are discussed. The results obtained by the numerical method show that GQD between atoms is strengthened with the increase of the detuning. Contrarily, GQD between cavities is weakened with the increase of the detuning.     

Strong monogamy of bipartite and genuine multipartite entanglement: the Gaussian case

We demonstrate the existence of general constraints on distributed quantum correlations, which impose a trade-off on bipartite and multipartite entanglement at once. For all N-mode Gaussian states under permutation invariance, we establish exactly a monogamy inequality, stronger than the traditional one, that by recursion defines a proper measure of genuine N-partite entanglement. Strong monogamy holds as well for subsystems of arbitrary size, and the emerging multipartite entanglement measure is found to be scale invariant. We unveil its operational connection with the optimal fidelity of continuous variable teleportation networks.     

Quantifying coherence with dynamical discord

Quantum coherence and discord are two kinds of manifestations of nonclassicality. By calculating the coherence and discord in the specific bipartite quantum systems, we show quantitative connections between the coherence and the discord in the bipartite quantum systems created from local systems with the help of incoherent operations. We show that the coherence bounds the dynamical discord, and under particular conditions of the initial quantum states, the coherence of single systems is equal to the dynamical discord. We extend these results to the multipartite quantum systems.     

Global quantum discord and quantum phase transition in XY model

We study the relationship between the behavior of global quantum correlations and quantum phase transitions in XY model. We find that the two kinds of phase transitions in the studied model can be characterized by the features of global quantum discord (GQD) and the corresponding quantum correlations. We demonstrate that the maximum of the sum of all the nearest neighbor bipartite GQDs is effective and accurate for signaling the Ising quantum phase transition, in contrast, the sudden change of GQD is very suitable for characterizing another phase transition in the XY model. This may shed lights on the study of properties of quantum correlations in different quantum phases.     

Influences of Detuning on Geometrical Quantum Discord Dynamics in Double Jaynes-Cummings System

We consider the case that the two-level atom off-resonantly interacts with cavity field via a one-photon hopping in double Jaynes-Cummings system. Geometrical quantum discord (GQD) is adopted to quantify the degree of correlation between two subsystems. GQD dynamics between two atoms, between cavity fields, as well as between atom and cavity fields are studied. The influences of detuning on GQD are discussed. The results obtained using the numerical method show that GQD between two atoms, between cavity fields, and between atom and cavity fields all display periodic oscillations. Furthermore, their periodic oscillations frequencies increase with the increase of detuning. On the other hand, GQD between two cavity fields and that between atom and cavity are weakened with increase of detuning.

     

Renormalization of quantum discord and Bell nonlocality in the XXZ model with Dzyaloshinskii–Moriya interaction

In this paper, we have investigated the dynamical behaviors of the two important quantum correlation witnesses, i.e. geometric quantum discord (GQD) and Bell–CHSH inequality in the XXZ model with DM interaction by employing the quantum renormalization group (QRG) method. The results have shown that the anisotropy suppresses the quantum correlations while the DM interaction can enhance them. Meanwhile, using the QRG method we have studied the quantum phase transition of GQD and obtained two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. It is worth mentioning that the block–block correlation is not strong enough to violate the Bell–CHSH inequality in the whole iteration steps. Moreover, the nonanalytic phenomenon and scaling behavior of Bell inequality are discussed in detail. As a byproduct, the conjecture that the exact lower and upper bounds of Bell inequality versus GQD can always be established for this spin system although the given density matrix is a general X state.     

Protecting geometric quantum discord via partially collapsing measurements of two qubits in multiple bosonic reservoirs

We study the dynamics of geometric quantum discord (GQD) between two qubits, each qubit interacting at the same time with K independent multiple bosonic reservoirs at zero temperature. In both weak and strong qubit-reservoirs coupling regimes, we find that the increase of the number K of reservoirs can induce the damped oscillation of GQD, and enhance the memory effects of the overall environment. And the Hilbert-Schmidt norm GQD (two-norm GQD) is always smaller than the trace norm geometric quantum discord (one-norm GQD). Therefore, the one-norm GQD is a better way to measure the quantum correlation. Finally, we propose an effective strategy to improve GQD by using partially collapsing measurements, and we find that the protection effect is better with the increase of the weak measurement strength.     

与XY双自旋链耦合的双量子比特系统的关联性与相干性

研究了双量子比特系统中在具有Dzyaloshinsky-Moriya相互作用的独立XY自旋链环境下的相干性与关联性动力学.推导出相干性与关联性的演化规律.发现在自旋链的临界点附近,当tt_0时,系统相干性的演化与经典关联完全相同;而在tt_0时,则与量子关联完全相同;在t_0时刻,量子关联突变为经典关联.     

Monogamy Relations of Measurement-Induced Disturbance

The standard monogamy imposes severe limitations to sharing quantum correlations in multipartite quantum systems, which is a star topology and is established by Coffman, Kundu and Wootters. In this work, we discuss some monogamy relations beyond it, and focus on the measurement-induced disturbance (MID) which quantifies the multipartite quantum correlation. We prove exactly that MID obeys the property of discarding quantum systems never increases in an arbitrary quantum state. Moreover, we define a new kind of sharper monogamy relation which shows that the sum of all bipartite MID can not exceed the amount of total MID. This restriction is similarly called a mesh monogamy. We numerically study how MID is distributed in a 4-qubit mixed state, and which relation exists between the mesh monogamy of MID and the level of obeying the standard monogamy.     

Quantum correlations support probabilistic pure state cloning

The probabilistic scheme for making two copies of two nonorthogonal pure states requires two auxiliary systems, one for copying and one for attempting to project onto the suitable subspace. The process is performed by means of a unitary-reduction scheme which allows having a success probability of cloning different from zero. The scheme becomes optimal when the probability of success is maximized. In this case, a bipartite state remains as a free degree which does not affect the probability. We find bipartite states for which the unitarity does not introduce entanglement, but does introduce quantum discord between some involved subsystems.     

阻尼Jaynes-Cummings模型中两原子的量子关联动力学

几何量子失协 (geometrical quantum discord, GQD)是目前度量量子体系中量子关联的一种行之有效的方法, 本文利用几何量子失协考察了有阻尼存在的Jaynes-Cumming (J-C)模型中两原子的量子关联动力学. 给出了几何量子失协在原子和光场发生共振和非共振耦合两种情况下的动力学演化行为, 尤其揭示了阻尼耗散对几何量子失协的影响. 关键词： 阻尼Jaynes-Cummings(J-C) 模型 量子关联 几何量子失协 (GQD)     

Geometry of Quantum Coherence for Two Qubit X States

The geometry of the structure of entanglement and discord for Bell-diagonal states is depicted by Lang and Caves (Phys. Rev. Lett. 105, 150501, 2010). In this paper, we investigate the geometry with respect to several distance-based quantifiers of coherence for Bell-diagonal states. We find that as both l₁ norm and relative entropy of coherence vary continuously from zero to one, their related geometric surfaces move from the region of separable states to the region of entangled states, a fact illustrating intuitively that quantum states with nonzero coherence can be used for entanglement creation. We find the necessary and sufficient conditions that quantum discord of Bell-diagonal states equals to its relative entropy of coherence, and depict the surfaces related to the equality. We give surfaces of relative entropy of coherence for X states. We show the surfaces of dynamics of relative entropy of coherence for Bell-diagonal states under local nondissipative channels and find that all coherences under local nondissipative channels decrease.

     

Analytical expressions of global quantum discord for two classes of multi-qubit states

Global quantum discord (GQD), proposed by Rulli and Sarandy [C.C. Rulli, M.S. Sarandy, Phys. Rev. A 84 (2011) 042109], is a generalization of quantum discord to multipartite states. In this Letter, 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.     

Distribution of Mutual Information in Multipartite States

Using the relative entropy of total correlation, we derive an expression relating the mutual information of n-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications. Besides, by utilizing the extended strong subadditivity of von Neumann entropy, we obtain generalized monogamy relations for the total correlation in three-partite mixed states. These inequalities lead to a tight lower bound for this correlation in terms of the sum of the bipartite mutual informations. We use this bound to propose a measure for residual three-partite total correlation and discuss the non-applicability of this kind of quantifier to measure genuine multiparty correlations.     

Deformed Subadditivity Condition for Qudit States and Hybrid Positive Maps

We extend the subadditivity condition for q-deformed entropy of a bipartite quantum system to the case of an arbitrary quantum system including the single qudit state. We present the subadditivity condition for the density matrix of the single qutrit state in an explicit form. We obtain the inequality for the purity parameters of a bipartite quantum system and its subsystems. We propose a positive map construction using the fiducial density matrix.     

Geometric Quantum Discord of a Two-Qutrit System Under Decoherence at Finite Temperature

The dynamics and protection of geometric quantum discord (GQD) for a two-qutrit system under amplitude damping channel with finite temperature have been studied in detail. By using of a lower bound of GQD, numerical results show that the GQD dynamics suffering from amplitude damping channels is more robust against the decoherence at lower temperature. Moreover, by combining weak measurement with measurement reversal, we have also investigated the protecting of the GDQ for a two-qutrit system under decoherence. It is found that the measurement technique can effectively protect the GQD against decoherence at lower temperature, but fails to protect GQD at higher temperature of channel.     

Entanglement irreversibility from quantum discord and quantum deficit

We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation--quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under local operations and classical communication for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distillable secret key, and the quantum discord.     

A Generalized Geometric Measurement of Quantum Discord:Exact Treatment

A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition it also does not suffer from the recently raised critiques about quantum discord. The exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition. For bipartite mixed states the exact result can also be found for a special case. Furthermore the generalization into multipartite case is direct. It is shown that it can be evaluated exactly when the measured state is invariant under permutation or translation. In addition the detection of quantum phase transition is also discussed for Lipkin–Meshkov–Glick and Dicke model.