Research On Nonclassical Correlation And Its Related Problems In Two-qubit Systems

Coherence and nonclassical correlation represent two crucial natural properties which are widely applied to quantum information processing and computation.Coherence is essentially the consequence of the quantum states superposition,and it can be utilized to represent the capability of the interference of the interaction fields.Besides,entanglement and Bell nonlocality are two fundamental concepts which can be utilized to characterize the nonclassical correlation in quantum information.Moreover,entanglement is a necessary and insufficient condition for Bell nonlocality.In this paper,we have investigated the relations between the coherence,the entanglement and the Bell nonlocality.The results are as follows.1.Complementarity between coherence and intrinsic concurrenceCoherence and quantum entanglement are generally regarded as two very crucial quantum resources,so a come very naturally question is whether there is a certain kind connection between them.Herein,the relation between first-order coherence and concurrence have been investigated for the two-qubit pure states.It turns out that the decrease(increase)of the systemic first-order coherence will definitely result in the increase(decrease)of the systemic concurrence,and it is known as the complementarity of first-order coherence and concurrence.However,for two-qubit mixed states,the complementarity of first-order coherence and concurrence is no longer satisfied.A two-qubit mixed state can be actually decomposed into many kinds of pure state ensembles.For the sake of extending the complementarity from pure states to mixed states,we try to seek a pure state ensemble possessing particular properties,where the first-order coherence and the concurrence of these pure states can satisfy the complementarity.To achieve this goal,we introduce two theories that all two-qubit mixed states are divide into four pure states that satisfy the tilde orthogonality.For the convenience of the following discussion,we present a definition of the intrinsic concurrence for two-qubit states.Although the intrinsic concurrence is not a measure of entanglement,it embodies the concurrence of four pure states that are partners of a special pure state ensemble for an arbitrary two-qubit state.Then,we demonstrate that intrinsic concurrence is always complementary to first-order coherence.In fact,this complementarity is an extension of the complementarity of first-order coherence and concurrence,and it issatisfied by all two-qubit pure states.It turns out to be that the first-order coherence and the concurrence of the four pure states transform each other for two-qubit mixed states,which causes the change of the concurrence.Finally,we apply the complementarity of intrinsic concurrence and first-order coherence in some composite systems composed by a single-qubit state coupling with four typical noise channels respectively,and find the interconversion relation between first-order coherence and concurrence.Therefore,this universal complementarity provides significant theoretical foundation on the mutual transformation between these two important quantum resources.2.Constraint relation between concurrence and Bell nonlocalityBell-nonlocal states form strict subset of entangled states.A natural question arises concerning how much territory Bell nonlocality occupies entanglement for a general two-qubit entangled state.Here,the relation between concurrence and Bell nonlocality is investigated in open systems.The results show that concurrence and Bell nonlocality of Werner state in phase damping(PD)channel satisfy one external parameter equation(Eq.4.10),and it is vivid that the relation of concurrence and Bell nonlocality under PD channel is not a kind of linear relation,but a regional relation;concurrence and Bell nonlocality of Werner state in phase damping(AD)channel satisfy equation relations(Eqs.4.14,4.15)with only one external parameter,it is also vivid that the relation of concurrence and Bell nonlocality in AD channel is not a kind of linear relation,but a regional relation.When we only consider the Bell state in PD channel or AD channel,we find two laws: concurrence and Bell nonlocality are equal;concurrence and Bell nonlocality satisfy an equality relation(Eq.4.18)without external parameters.Finally,we give the inequality relation(Eq.4.19)between the two resources(concurrence and Bell nonlocality).In order to prove this inequality,we use the numerical method,that is,enough random quantum states to study the domain graph of concurrence and Bell nonlocality.It shows that the graph of region(Fig.4.3)corresponds to the inequality relation(expressed in Eq.4.19),thus we defined the quantum states satisfying that concurrence equals to Bell nonlocality on the left(right)side of as the inequality the minimally(maximally)nonlocal entangled states,because they can minimize(maximize)the value of Bell nonlocality for a given value of concurrence.