Research On Continuous Variable Entanglement And Underwater Quantum Key Distribution Under Nonlinear Operation

Quantum mechanics has been studied for more than half a century.On this basis,quantum information technology,as a new emerging discipline,is of great significance to information security and other fields.The emergence of quantum information technology provides new ideas and new methods for the development of information technology.Quantum key distribution(QKD)is based on quantum mechanics and has the characteristics of unconditional security.In the field of QKD research,there are usually two different protocols.One is the QKD of discrete variables(DV),and the other is the QKD of continuous variables(CV).Compared with the former,the latter has obvious advantages,such as high key rate through heterodyne or homodyne detection(rather than single photon detection),simple preparation and operation,and more compatible with communication technology.However,compared with the transmission distance of DVQKD,the transmission distance of CVQKD is still shorter.In order to further overcome this shortcoming,non-Gaussian operation is an effective method to improve the performance of CVQKD in free space and optical fiber.At the same time,underwater secure communication is urgent,and we try to apply it to underwater optical communication.In addition,quantum nonlinear processes(optical parametric amplification or squeezing)are often used to prepare quantum resources to achieve various quantum tasks.We propose the coherent state representation of the squeezing operator and its application,and strive to provide help for continuous variable quantum teleportation,quantum key distribution,quantum measurement,etc.The specific research content of this paper is summarized as follows:Firstly,Quantum key distribution with continuous-variable(CVQKD)provides an alternative way for the security improvement of underwater optical communication,but facing into the awkward situation of short distance.For this reason,here we exploited photon addition operation at the emitter into enhancing the performance of underwater CVQKD.Based on numerical simulation,it is shown that applying photon-addition non-Gaussian operation between entangled resource and the sender can further enhance both the secure key rate and the transmission distance,compared to applying photon subtraction operation between entangled resource and the receiver.In addition,the influence of seawater quality factors in underwater CVQKD system was also considered,so as to provide technical support for underwater safety communication.Secondly,in a previous paper Zhan et al.(2022),we proposed the coherent state representation for linear operator,which shows a beautiful theoretical value.Inspired by the work,we further extended it to the nonlinear case,including single and twomode squeezing process.Based on squeezing operators’ transformation relation,we introduced their coherent state representations and derived their normal ordering forms by using the technique of integration within product of operator.As applications,we examined some operators’ normal ordering forms and showed the entanglement property of prepared quantum states via the Schmidt decomposition.In particular,we further considered two cascaded two-mode squeezing operators,in which a generalized SU(1,1)interferometer is involved.In addition,the application of two-mode squeezing operator followed by photon-subtraction to generate nonGaussian entangled states in quantum teleportation is discussed.Our results will be useful in preparation of quantum states and quantum metrology.