Geometry of skew information-based quantum coherence

We study the skew information-based coherence of quantum states and derive explicit formulas for Werner states and isotropic states in a set of autotensors of mutually unbiased bases (MUBs). We also give surfaces of skew information-based coherence for Bell-diagonal states and a special class of X states in both computational basis and in MUBs. Moreover, we depict the surfaces of the skew information-based coherence for Bell-diagonal states under various types of local nondissipative quantum channels. The results show similar as well as different features compared with relative entropy of coherence and l₁ norm of coherence.     

Geometric measure of quantum discord over two-sided projective measurements

The original definition of quantum discord of bipartite states was defined over one-sided projective measurements, it describes quantum correlations more extensively than entanglement. Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105 (2010) 190502] introduced a geometric measure of quantum discord, Luo and Fu [Phys. Rev. A 82 (2010) 034302] simplified the variation expression of this geometric measure. In this Letter we introduce a geometric measure of quantum discord over two-sided projective measurements. A simplified expression and a lower bound of this two-sided geometric measure are derived and explicit expressions are obtained for some special cases.     

Quantum discord and the geometry of Bell-diagonal states

The set of Bell-diagonal states for two qubits can be depicted as a tetrahedron in three dimensions. We consider the level surfaces of entanglement and quantum discord for Bell-diagonal states. This provides a complete picture of the structure of entanglement and discord for this simple case and, in particular, of their nonanalytic behavior under decoherence. The pictorial approach also indicates how to show that discord is neither convex nor concave.     

Quantum Discord of 2<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>-Dimensional Bell-Diagonal States

In this study, using the concept of relative entropy as a distance measure of correlations we investigate the important issue of evaluating quantum correlations such as entanglement, dissonance and classical correlations for 2 ⁿ -dimensional Bell-diagonal states. We provide an analytical technique, which describes how we find the closest classical states(CCS) and the closest separable states(CSS) for these states. Then analytical results are obtained for quantum discord of 2 ⁿ -dimensional Bell-diagonal states. As illustration, some special cases are examined. Finally, we investigate the additivity relation between the different correlations for the separable generalized Bloch sphere states.     

Dynamics of geometric discord and measurement-induced nonlocality at finite temperature

By using geometric measure of discord (GMOD) [B. Dakić, V. Vedral, Č. Brukner, Phys. Rev. Lett. 105, 109502 (2010)] and measurement-induced nonlocality (MIN) [S. Luo, S. Fu, Phys. Rev. Lett. 106, 120401 (2011)], we investigate quantum correlation of a pair of two-level systems, each of which is interacting with a reservoir at finite temperature T. We show that, for a broad class of states of the system, GMOD and MIN can endure sudden death, and there is no asymptotic decay for MIN while asymptotic decay exists for GMOD. We also give the dynamics of GMOD and MIN with respect to the temperature and illustrate their different characteristics.     

Dynamics of Super Quantum Correlations and Quantum Correlations for a System of Three Qubits

The dynamics of quantum discord for two qubits independently interacting with dephasing reservoirs have been studied recently.The authors [Phys.Rev.A 88(2013) 034304] found that for some Bell-diagonal states(BDS)which interact with their environments the calculation of quantum discord could experience a sudden transition in its dynamics,this phenomenon is known as the sudden change.Here in the present paper,we analyze the dynamics of normal quantum discord and super quantum discord for tripartite Bell-diagonal states independently interacting with dephasing reservoirs.Then,we find that basis change does not necessary mean sudden change of quantum correlations.     

Exact Entanglement Dynamics in Three Interacting Qubits

Motivated by recent experimental studies on coherent dynamics transfer in three interacting atoms or electron spins [Phys. Rev. Lett 114(2015) 113002, Phys. Rev. Lett 120(2018) 243604], here we study entanglement entropy transfer in three interacting qubits. We analytically calculate time evolutions of wave function, density matrix and entanglement of the system. We find that initially entangled two qubits may alternatively transfer their entanglement entropy to other two qubit pairs. Thus dynamical evolution of three interacting qubits may produce a genuine three-partite entangled state through entanglement entropy transfers. In particular, different pairwise interactions of the three qubits endow symmetric and asymmetric evolutions of the entanglement transfer,characterized by the quantum mutual information and concurrence. Finally, we discuss an experimental proposal of three Rydberg atoms for testing the entanglement dynamics transfer of this kind.     

Quantum Correlations in a Family of Two-Qubit Separable States

Quantum correlations in a family of two-qubit separable classical-quantum correlated states are intensively studied with four different approaches, namely, quantum discord [Phys. Rev. Lett. 88 (2002) 017901], measurement- induced disturbance (MID) [Phys. Rev. A 77 (2008) 022301], ameliorated MID [J. Phys. A: Math. Theor. 44 (2011) 352002] and quantum dissonance [Phys. Rev. Lett. 104 (2010) 080501]. Quantum correlations captured with different approaches are compared and discussed so that their three distinct features are exposed.     

Sufficient and Necessary Conditions of Entanglement Transformations Between Mixed States

Based on a new measure of entanglement for finite-dimensional bi-particle pure states, we give sufficient and necessary conditions that a bi-particle mixed state ρ can be transformed into another mixed state σ by local operations and classical communication (LOCC). This result can be regarded as a generalization of Nielsen’s theorem (Nielsen, Phys. Rev. Lett. 83:436, 1999). However, we find that it is more difficult to determine the entanglement transformations between mixed states than to do between pure ones.     

Quantum Correlations in a Family of Two-Qubit Separable States

Quantum correlations in a family of two-qubit separable classical-quantum correlated states are intensively studied with four diferent approaches,namely,quantum discord[Phys.Rev.Lett.88(2002)017901],measurementinduced disturbance(MID)[Phys.Rev.A 77(2008)022301],ameliorated MID[J.Phys.A:Math.Theor.44(2011)352002]and quantum dissonance[Phys.Rev.Lett.104(2010)080501].Quantum correlations captured with diferent approaches are compared and discussed so that their three distinct features are exposed.     

Measurement-induced nonlocality

We interpret the maximum global effect caused by locally invariant measurements as measurement-induced nonlocality, which is in some sense dual to the geometric measure of quantum discord [Dakic, Vedral, and Brukner, Phys. Rev. Lett. 105, 190502 (2010)]. We quantify measurement-induced nonlocality from a geometric perspective in terms of measurements, and obtain analytical formulas for any dimensional pure states and 2 × n dimensional mixed states. We further derive a tight upper bound to measurement-induced nonlocality in general case. The physical significance of measurement-induced nonlocality is discussed in the context of correlations, entanglement, quantumness, and cryptographic communication.     

One-Way Information Deficit and Geometry for a Class of Two-Qubit States

The work deficit, as introduced by Jonathan Oppenheim et al. [Phys. Rev. Lett. 89 (2002) 180402] is a good measure of the quantum correlations in a state and provides a new standpoint for understanding quantum non-locality. In this paper, we analytically evaluate the one-way information deficit (OWID) for the Bell-diagonal states and a class of two-qubit states and further give the geometry picture for OWID. The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID of some classes of X states is more robust against the decoherence than the entanglement.     

Quantum correlations in spin models

Bell nonlocality, entanglement and nonclassical correlations are different aspects of quantum correlations for a given state. There are many methods to measure nonclassical correlations. In this paper, nonclassical correlations in two-qubit spin models are measured by the use of measurement-induced disturbance (MID) [S. Luo, Phys. Rev. A 77 (2008) 022301] and geometric measure of quantum discord (GQD) [B. Daki?, V. Vedral, C. Brukner, Phys. Rev. Lett. 105 (2010) 190502]. Their dependences on external magnetic field, spin–spin coupling, and the Dzyaloshinskii–Moriya (DM) interaction are presented in detail. We also compare Bell nonlocality, entanglement measured by concurrence, MID and GQD and illustrate their different characteristics.     

Quantum coherence and correlation dynamics of two-qubit system in spin bath environment

The quantum entanglement,discord,and coherence dynamics of two spins in the model of a spin coupled to a spin bath through an intermediate spin are studied.The effects of the important physical parameters including the coupling strength of two spins,the interaction strength between the intermediate spin and the spin bath,the number of bath spins and the temperature of the system on quantum coherence and correlation dynamics are discussed in different cases.The frozen quantum discord can be observed whereas coherence does not when the initial state is the Bell-diagonal state.At finite temperature,we find that coherence is more robust than quantum discord,which is better than entanglement,in terms of resisting the influence of environment.Therefore,quantum coherence is more tenacious than quantum correlation as an important resource.     

Tighter Weighted Polygamy Inequalities of Multipartite Entanglement in Arbitrary-Dimensional Quantum Systems

We investigate polygamy relations of multipartite entanglement in arbitrary-dimensional quantum systems. By improving an inequality and using the βth (0 ≤ β ≤ 1) power of entanglement of assistance, we provide a new class of weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems. We show that these new polygamy relations are tighter than the ones given in Kim (Phys. Rev. A 97, 042332 2018).

     

Separable States to Distribute Entanglement

It was shown [Cubitt et al. in Phys. Rev. Lett. 91: 037902, 2003] that two distant particles can be entangled by sending a third particle never entangled with the other two. In this paper, we present classes of multi-qubit separable states to distribute entanglement by the same way, and investigate the classes. Furthermore, we calculate the maximal amount of entanglement which two parties of separable states in the classes can have after applying the way.     

Masking Quantum Information Encoded in Pure and Mixed States

Masking of quantum information means that information is hidden from a subsystem and spread over a composite system. Modi et al. proved in [Phys. Rev. Lett. 120, 230501 (2018)] that this is true for some restricted sets of nonorthogonal quantum states and it is not possible for arbitrary quantum states. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively. Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator, we find that there exists a set of four states that can not be masked, which implies that to mask unknown pure states is impossible. We construct a masker S^? and obtain its maximal maskable set, leading to an affirmative answer to a conjecture proposed in Modi’s paper mentioned above. We also prove that an orthogonal (resp. linearly independent) subset of pure states can be masked by an isometry (resp. injection). Generalizing the case of pure states, we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry S^◇ while it is impossible to mask all of mixed states by any operator. We also find the maximal maskable sets of mixed states of the isometries S^? and S^◇, respectively.

     

Generation of entanglement via atomic coherence in a two-mode three-level cascade atomic system

The generation of continuous variable entanglement via atomic coherence in a two-mode three-level cascade atomic system is discussed according to the entanglement criterion proposed by Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)]. Atomic coherence between the top and bottom levels is induced with two photons of a strong external pump field. It shows that entanglement for the two-mode field in the cavity can be generated under certain conditions. Moreover, by means of the input-output theory, we show that the two-mode entanglement could also be approached at the output.     

Dynamics of Quantum Coherence in Bell-Diagonal States under Markovian Channels

We study the curves of coherence for the Bell-diagonal states including l_1-norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase flip channel, we find frozen coherence under l_1 norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. Also, we study the coherence evolution of Bell-diagonal states under Markovian channels in the first subsystem n times and find that coherence under depolarizing channel decreases initially then increases for small n and tends to zero for large n. The dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels is discussed.     

Entanglement, Quantum Discord, and Non-locality in Bell-Diagonal States

Experimental approach to characterize the non-locality, entanglement, and quantum correlation of a multiparity quantum system is one of the important subjects in quantum information theory. Here, by investigating the violations of Bell inequality (BI), we analyze the relations among the non-locality, concurrence C, and quantum discord Q typically for a family of Bell-diagonal states. It is shown that, for the optimal measurement basis the BI is always violated, if the quantum discord is larger than 0.5031 and the concurrence is larger than 0.5605. Certainly, the BI is maximally violated for the maximal entanglement and quantum discord, i.e., C=Q=1. Our generic results are demonstrated with a thermal XY model of the two-qubit system with controllable interbit couplings.