Entanglement Purification And Concentration In Solid-state Quantum System

Quantum entanglement has been widely used in various branches of quantum information science,such as quantum cryptography,quantum teleportation,quantum dense coding,quantum secure direct communications(QSDC),quantum machine learning and so on.And it is becoming the key resource of quantum information processing(QIP),as the high-fidelity entangled state is required to construct the quantum channel between quantum nodes.Practically,quantum entanglement cannot be created with local operations and classical communications.It relies on the efficient distribution of entanglement during a quantum channel after the entanglement generation.However,it appears that the maximally entanglement will inevitably suffer from decoherence in the process of distribution,and transforms to mixed entangled states which will reduce the fidelity of entanglement.In order to eliminate the effect of decoherence,the concept of quantum repeaters was proposed to decrease the effect of channel noise and establish the link between two distant quantum nodes.In the model of quantum repeaters,a quantum node should have the ability to coherently absorb and emit photons as well as the relatively long coherence time.Furthermore,each node should have additional processing qubits for entanglement purification、concentration or to perform quantum error corrections to maximize the entanglement.The solid-state systems have revealed some prominent properties as a quantum node for QIP,for example,the quantum dot,nitrogen-vacancy(NV)centers,silicon-vacancy(Si-V)centers and so on.In particular,entanglement between light and solid-state systems is attractive owing to their anticipated respective roles as flying and stationary qubits in quantum information technologies.However,the entangled state in solid-state system also can be influenced by channel noise,decreasing the effiency of quantum information processing.Therefore,the purification and concentration of solid-state system are very important.We present a hybrid entanglement purification and concentration protocol for nuclear spin entangled states of nitrogen-vacancy centers resorting to the ancillary photons and electrons.In the entanglement purification protocol,the mixed entangled states of the NV centers can be purified with high fidelity using two pairs of entangled photons to interact with each electron in NV centers.By performing local measurement on the electrons,the original entangled state can be obtained between the two remote parities.In the entanglement concentration protocol,the partially entangled states of the nuclear spin in NV centers can be concentrated to the maximally entangled state by using an ancillary photon on one local user.The fidelity of the entangled state with different excited state decay rate and the relation between the yield and different decay rate are numerically simulated.