The Behavior Of Gaussian Quantum Correlations Under Gaussian Quantum Channels

Quantum correlation is a key ingredient in quantum information science.Quantum correlation is also the key role in quantum communication,quantum computation,quantum measurement and quantum cryptography.For the last decades,quantum correlation has been widely investigated.Gaussian states,as the most important family of continuous variable quantum states,also has been widely investigated in recent years,most of the quantum states in quantum optical experiments are Gaussian states.So,it is very useful to study the quantum correlation of Gaussian states,which is Gaussian quantum correlation.In this paper,we focus on the behavior of four kinds of Gaussian quantum correlations,which are Gaussian quantum steering,Gaussian quantum entanglement,Gaussian discord and Gaussian coherence.Lots of researchers focus on Gaussian quantum correlations in recent years.The researchers have intensively investigated the Gaussian quantum steering,Gaussian quantum entanglement and Gaussian quantum discord of two-mode Gaussian states and the Gaussian quantum coherence of single-mode Gaussian states.They have obtained the analytical expression of the Gaussian quantum correlations.The measurement theory of the Gaussian quantum correlations have been intensively studied,but few researchers have investigated the behavior of Gaussian quantum correlations under Gaussian quantum channels and beam splitter.Gaussian quantum channels are real quantum channels and beam splitter is widely used in the theoretical investigation and experimental research of quantum information theory.Therefore,it is very useful to study the behavior of Gaussian quantum correlations under Gaussian quantum channels and beam splitter.Our research focus on the behavior of Gaussian quantum correlations under Gaussian quantum channels and beam splitter.We obtain the following three main research results.(1)We have studied the behavior of Gaussian quantum steering,Gaussian quantum entanglement and Gaussian quantum discord when the Gaussian states undergo the Gaussian quantum channels.We find that these three kinds of Gaussian quantum correlations will decrease with the influence of Gaussian quantum channels.We further observed the sudden death phenomena of Gaussian quantum steering and Gaussian quantum entanglement in theory.By control the Gaussian quantum channel,we obtained some Gaussian states have only one-way Gaussian quantum steering.Also we investigate the entangled Gaussian states without Gaussian quantum steering and correlated Gaussian states own no Gaussian quantum entanglement.(2)We have investigated the generation of Gaussian quantum steering and Gaussian quantum entanglement by using linear optical beam splitter.We have observed that single-mode Gaussian quantum coherence acts as the resource in generating Gaussian quantum entanglement and Gaussian quantum steering for two squeezed states as the input states.With the help of consecutive beam splitters,single-mode Gaussian quantum coherence and Gaussian quantum entanglement(or Gaussian quantum steering)can be converted to each other.(3)We have studied how to convert one-way Gaussian quantum steering to the other one-way Gaussian quantum steering and found the one-way Gaussian quantum steering can convert to anther one-way Gaussian quantum steering,and vice versa.