Quantum State Preparation Based On Non-Gaussian Operations And Its Quantum Propertie

The preparation of quantum states is one of the core tasks in quantum computing and quantum information technology.Recently,non-Gaussian quantum states have attracted considerable interest from researchers due to their immense potential in the field of quantum optics,and have gradually become a hot topic in this area.With the development of quantum information science,researchers have found that nonGaussian states prepared through methods such as photon addition,photon subtraction,coherent superposition,conditional measurement,and non-Gaussian operations,exhibit unique advantages and wide application potential in various aspects such as quantum coding,quantum teleportation,quantum imaging,and quantum precision measurement.Based on these significant advantages,this paper mainly utilizes multiphoton catalysis and conditional measurement to propose several new schemes for the preparation of non-Gaussian quantum states,and delves into the nonclassical properties exhibited by these non-Gaussian quantum states.The main research of this paper includes the following five aspects:1.We introduce two new multi-variable special polynomials and their generating functions utilizing an approach based on operator ordering of operators.This framework enables us to unveil new operator identities and integral formulas that involve these novel polynomials.we efficiently tackle normalization concerns,photocount and Wigner distributions for a variety of physically realizable quantum states.These findings facilitate further explorations into the unique properties and potential applications of these states with increased ease and precision.2.We propose two new photon-modulated spin coherent states(SCSs)by applying spin ladder operators J± to conventional SCSs within the Holstein-Primakoff framework,revealing their nonclassical attributes through various measures such as photon number distribution,second-order correlation,photocount distribution,and Wigner distribution negativity.Analytical results show that the photocount distribution conforms to a Bernoulli profile,while the Wigner functions correlate with wo-variable Hermite polynomials.When compared to ordinary SCSs,these photon-modulated SCSs display more pronounced nonclassicality in specific domains characterized by the photon modulation number and the spin quantum number.This suggests that by finetuning the parameters,nonclassicality within the system can be significantly enhanced.3.In our theoretical exploration,we introduce a novel type of non-Gaussian state-the mixture of multiphoton added thermal states achieved through multiphoton measurements at one of the beam splitter’s output ports,a technique we refer to as multiphoton catalysis.We discuss the probabilities of successful detection,which also serve as normalization factors.Our investigation into their nonclassical attributes covers the nonclassical depth,photon number distribution,and photocount distribution.Our findings reveal that by controlling the thermal state parameters,the number of photons catalyzed,and the transmissivity of the beam splitter,the state demonstrates enhanced nonclassical performance.The partial negativity of Wigner function further discusses this nonclassicality,confirming the significant enhancement achievable via multiphoton catalysis.4.We propose a distinct non-Gaussian quantum state achieved through multiphoton measurement based catalysis with a two-mode squeezed thermal state input.The generation of this state is contingent on various parameters including the thermal state,catalyzed photon number,and squeezing.We analyze their nonclassical nature by inspecting the photon number and photocount distributions,along with the partial negativity of Wigner function.The study corroborates that the careful application of multiphoton catalysis,guided by these parameters,is instrumental in cultivating nonclassicality.5.By applying a general coherent superposition(va+ra~?)~m to conventional coherent and thermal states,we introduce two new types of photon-modulated states and proceed to evaluate their nonclassical characteristics.Parameters under scrutiny include squeezing,sub-Poissonian distributions,nonclassical depth,and the negativity of the Wigner distribution.The results indicate that higher-order coherent superposition operations(va+ra~?)~m are more adept at fostering nonclassicality,depending on certain parameters.