Studies Of Quantum Violation Of Bell-type Inequalities

Quantum correlation includes quantum nonlocality,quantum entanglement,quantum discord,quantum steering,etc,which is one of the basic characteristics of quantum mechanics.Quantum nonlocality and quantum entanglement,as important resources in quantum information technology,are widely used in many aspects,such as quantum key distribution,quantum computing,quantum teleportation and true random number generation.Bell-type inequalities are powerful criterion for witnessing nonlocality.In recent years,the violation of Bell-type inequalities in various scenarios and the entanglement after sequential measurements havecaused extensive concern.Related studies have certain theoretical value and practical significance for quantum information processing technology.The bipartite Bell-type inequalities I3322?I4422 and I5522,as the criteria for discriminating quantum nonlocality,have attracted much concern.Considering the non-ideal factors in experiments,we study the influence of single entangled state,mixed entangled state and noisy channels on the quantum violation of inequalities in detail.Results show that for a single entangled state,these inequalites can be violated only when the degree of entanglement is large enough;for mixed entangled state,these inequalities can be violated within a larger range of parameters;the phase diagram about the violation and non-violation of these inequalities is obtained under the noise represented by two-kraus operator.Bell nonlocality and quantum entanglement are often used to detect the quantum phase transition.The traditional Bell experiment needs to align the measurement basis in advance.The method of randomly chosen measurements is proposed in recent years.Based on the numerical renormalization group method,we use random measurements to calculate quantum violation of the CHSH inequality and I3322 inequality in one-dimensional Ising model with a transverse field.The result shows that they can distinguish the paramagnetic phase,ferromagnetic phase and phase transition point.The probability about violation of the inequality can also reflect the quantum phase transition point.Unsharp measurement is a type of weak measurement that can gain information with less disturbance.One qubit for a two-qubit entangled state is possessed by Alice,while the other qubit is possessed by multiple Bobs.Each Bob performs unsharp measurement,and sequentially sends the qubit to next Bob.We study negativity Ne,visibility V2,predictability p2,and mixedness SL of the quantum state in the sequential measurement model.Results show that as the number of measurements n increases,Ne?V2 and p2 gradually reduce and SL gradually become larger;When the measurement is closer to the strong measurement,i.e.the ? closer to 1,the maximal measurement time N is smaller.