Testing The Quantum Non-local Correlation Based On The Orbital Angular Momentum Mixed State

Quantum non-local correlation is one of the most important and essential features of quantum mechanics theory.It plays an important role in verifying the correctness of quantum mechanics theory.So far,people have done a lot of research on quantum non-local correlation test,both in theory and experiment.Including inequality and no inequality test methods,all proved the correctness of the quantum theory theory.However,in the research on the quantum nonlocal correlation test for the orbital angular momentum entangled state,most of the quantum pure states are used as the main research object,and there is no quantum nonlocalization using the orbital angular momentum entangled mixed state.Associated inspection research.In the actual experimental preparation process of the orbital angular momentum entangled state,limited by various experimental conditions,the prepared state is often a quantum mixed state.Therefore,it is of great significance to study whether the orbital angular momentum mixed entangled state can be tested for quantum non-local correlation.The main content of this paper is based on Hardy's theorem.It proposes a test logic not only for orbital angular momentum entangled pure states,but also for orbital angular momentum entangled mixed states,and uses this logic to detect orbital angular momentum entangled pure states and orbits.The angular momentum entangled mixed state has been studied for quantum non-local correlation test.Firstly,it briefly reviewed the development process of quantum theory and then led to the quantum non-local correlation theory,the related development and preparation methods of orbital angular momentum,and the corresponding research background,basic concepts,etc.,which lay a certain foundation for the subsequent theoretical research.Secondly,the test logic proposed based on Hardy's theorem is elaborated,and the commonly used orbital angular momentum entangled pure state is tested using this logic in the low-order case of quantum non-local correlation,and the first-order and second-order cases are obtained.The maximum probability that the quantum non-local correlation can be successfully tested is and respectively.Then,a special orbital angular momentum entangled state is tested for quantum non-local correlation.The research results show that in the case of first-order and second-order,the maximum probability of successful detection is 0.0902and 0.1745.Comparing this result with the literature result obtains a consistent result,so that the correctness and applicability of the logic have been theoretically verified.Then the general orbital angular momentum entangled pure state is extended to the K-order situation.The research results show that with the increase of the number of ladders K,the maximum probability that the quantum non-local correlation can be successfully tested is close to50%.In particular,when the quantum non-local correlation test is performed on the special orbital angular momentum entangled state in the high-order case,the research results show that when the orbital angular momentum quantum number m=1,the quantum non-local correlation test can be successfully tested.The maximum probability value of the association is about 30%,and the minimum value of the corresponding number of steps is16.Then,the test logic proposed in this paper based on Hardy's theorem studies the quantum non-local correlation test of the orbital angular momentum entangled mixed state.Taking the general Werner state as an example,the research and analysis are carried out,and the conditions for successfully testing the quantum non-local correlation in the first and second order are given.The results show that when the number of steps K is 1,the parameter is t(29)0.8472and when the number of steps K=2,the parameter is t(29)0.7412,the quantum non-local correlation can be successfully tested.Then we studied the restriction conditions of the general Werner-like mixed state that can successfully test the quantum non-local correlation in the high-order case.The result shows that when the number of steps K is constant,the entanglement degree of the mixed state increases.,The minimum value of the parameter t has a tendency to decrease first and then increase.When the entanglement degree of the mixed state is constant,as the value of K increases,the minimum value of the parameter t shows a decreasing trend,that is,the range of the mixing degree of the general Werner-like state that can successfully test the quantum non-local correlation gradually increases.Large;when the number of steps K increases to a certain extent,the minimum value of the parameter t will tend to 0.5.Finally,we took a special Werner-like mixed state(e(28)0.66^m-n)as an example to study the quantum non-local correlation test.The research results show that whether K=1 or K=2,with the purity of the mixed state(that is,the larger the parameter t),the greater the probability of successfully testing the quantum non-local correlation.As the value of the orbital angular momentum quantum number m is different,the value for successfully testing the quantum non-local correlation is also different.In particular,when K=1,m=2,when the parameter t satisfies greater than 0.848,and when K=2,m=1,and the parameter t satisfies greater than 0.764,the special Werner-like state corresponding to this time can successfully test the quantum Non-local association.Then the quantum non-local correlation test is carried out in the case of high steps:when the value of the number of steps K increases to a certain extent,the minimum value of the parameter t will eventually stabilize at 0.6223,and the minimum value of the number of steps K is 17.That is,the range of the mixed state corresponding to the special Werner-like state that satisfies the quantum non-local correlation condition is the largest,and the range is0.6223?t?1.