This paper studies the higher-order nonclassical and entanglement properties in the photon-added trio coherent state (PATCS). We use the criterion of higher-order single-mode antibunching to evaluate the role of the photon addition operation. Furthermore, the general criteria for detection of higher-order three-mode sum squeezing and entanglement features in the PATCS are also investigated. The results show that the photon addition operation to a trio coherent state can enhance the degree of both the higher-order single-mode antibunching and the higher-order three-mode sum squeezing and enlarge the value of the higher-order three-mode entanglement factor in the photon-added trio coherent state. In addition, the manifestation of the single-mode antibunching and the entanglement properties are more obvious with increasing the higher values of orders.
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