Testing Quantum Nonlocality Of Entangled States Under Decoherence

Quantum non-locality is one of the important bases for the realization of modern quantum information theory and technology.With the rapid development of quantum information theory and technology in recent years,quantum non-local correlation has been applied in much quantum information technologies.For example,quantum secures multi-party computation,quantum key distribution and quantum secure direct communication.They are all based on the quantum non-local correlation characteristics of quantum entanglement.However,any real physical system will inevitably interact with the environment,so that the coherence of the entangled state will inevitably degenerate when it is transmitted on the quantum channel,which leads to the weakening of the non-local correlation characteristics of the entangled state.Therefore,it is a worthy topic to study the non-local correlation properties of quantum states affected by the noise of the transmission channel.At present,there are mainly Bell theorem based on inequality and Hardy theorem without equality in the test of quantum non-local correlation.Hardy theorem is considered as "the simplest form of Bell’s theorem" because it can test the quantum non-local correlation properties of quantum entangled states in an equal-free way.However,it has not been reported testing and studying the quantum non-local correlation characteristics of the quantum state under the condition of decoherence after the quantum channel transmission of the prepared quantum state with the decoherence effect,based on the high-probability quantum non-local correlation test scheme of Hardy-paradox.On the other hand,to overcome the decoherence effect of transmission channel,the research of correlation decoherence suppression scheme is also carried out one after another.Among them,quantum weak measurement and weak measurement reversal operation(WMR)is one of the common methods that can effectively suppress the decoherence effect.Therefore,it is also worth studying the quantum non-local correlation properties of entangled states under weak measurement and weak measurement reversal operation.However,based on the Hardy-type paradox,testing and researching the quantum non-local correlation of the quantum state under the decoherence suppression operation has not been reported.In this article,we take two bits of polarization entanglement as the research object,using a high probability of quantum non-local correlation test scheme based on Hardy-type paradox,mainly study the quantum non-local correlation of the quantum state through amplitude damping channel(ADC),phase damping channel(PDC)and depolarization damping channel(DC).In addition,the non-local correlation properties of quantum states after weak measurement,amplitude damping channel transmission and weak measurement reversal are tested and studied.The results show that when the transmission channel is DC transmission channel,the influence on the quantum non-local correlation test characteristics of the quantum state is great,but when the transmission channel is PDC transmission channel,the influence on testing non-local correlation of the quantum state is small.Then,the condition of successful quantum non-local correlation test for polarization entanglement is given when weak measurement combined with weak measurement reversal is used to overcome ADC decoherence.The results show that when the intensity of weakening measurement increases,the influence of ADC decoherence effect on successful quantum non-local correlation test of polarization entanglement can be effectively reduced.Finally,the quantum non-local correlation properties of quantum states under decoherence conditions are studied based on CHSH inequality.