We investigate the statistical properties and inseparability of the field states generated by any order nonlocal coherent photon addition (CPA) to the two-mode squeezed vacuum (TMSV). It is shown that the normalization factor of the CPA-TMSV is a Legendre polynomial, a compact expression. The statistical properties are discussed according to the analytical expressions of cross-correlation function, antibunching effect, and the negativity of its Wigner function. The inseparability is presented by using Shchukin–Vogel criteria and the Einstein–Podolsky–Rosen correlation. It is found that the symmetrical CPA-TMSV may possess stronger correlation than the single-mode photon-addition case. The lower bound of entanglement of the CPA-TMSV is considered, which indicates the logarithmic negativity is invalid for verifying the entanglement when the squeezing parameter is less than a threshold value, a period function of . In addition, quantum teleportation is examined, which shows that asymmetric photon-added TMSV may be more useful for teleportation than the symmetric case.
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