Logic W State And Logic Bell Entanglement Concentration

In recent decades,quantum mechanics has developed rapidly.In addition to its own physics,it has been applied in many disciplines such as chemistry,materials science,and information science,and has achieved great development.Quantum communication is one of the more interesting areas.Quantum communication uses the special properties of quantum mechanics to transfer information,and is an interdisciplinary subject of quantum mechanics and information science.Quantum communication includes quantum teleportation,quantum key distribution,quantum secure direct communication,and quantum dense coding.In the process of quantum communication,quantum entangled states are very important resources.In the process of entanglement distribution,due to the equipment or the external environment,quantum loss,qubit errors,or quantum decoherence may occur during transmission,thereby causing the entire system to run incorrectly.In order to solve the problem of quantum loss and qubit errors,scholars have proposed a method of logical coding.Even if a small number of qubits are lost or erroneous during transmission,reliable information can be provided from the remaining qubits.However,logic entangled states may also be decoherent due to the presence of environmental noise.Researchers have found that the use of entanglement concentration can also reduce degraded non-maximally entangled logical entangled states to maximally logical entangled states.The concatenated Greenberger-Horne-Zeilinger(C-GHZ)state is a new type of logic entangled state.It is a logic GHZ state with the GHZ state as a logic bit.The C-GHZ state can effectively solve the problem of information loss caused by photon loss,and is widely used in quantum fault-tolerant computing and distributed quantum networks.The main work of this paper is to study the problem of entanglement concentration using logic entangled states,and to propose entanglement concentration schemes for logic W states with GHZ states as logic bits and for logic Bell states with C-GHZ states as logic bits.For the logic W state,we propose a single photon-assisted entanglement concentration protocol.The W-state of 3 logic bits is used as an example to describe the entanglement concentration protocol.We divide the entanglement concentration protocol into two parts.Each part is assisted by a single photon,and the polarization parity check(PPC)gate is used to analyze the entanglement of the logic W state.PPC gate can realize parity check under the condition of quantum non-demolition(QND)measurement.Then,we generalize the scheme to the logical W state of arbitrary logical bits.For the logic Bell state,we propose an entanglement concentration protocol based on entangled state.We also use PPC gates to implement entanglement analysis.Then take the simplest logic Bell state as an example to show our entanglement concentration protocol,which is gradually extended to any form of entanglement concentration of logic Bell states.Through QND,even if the entanglement concentration of the logic W state and the logic Bell state fails,the obtained non-maximally entangled state can be retained to perform entanglement concentration again,thereby reducing the consumption of entanglement resources and increasing the success probability of entanglement concentration.Based on the above advantages,the concentration of logic entangled states is of great significance in long-distance quantum communication.