Nonclassicality via the Superpositions of Photon Addition and Subtraction and Quantum Decoherence for Thermal Noise

Two new photon‐modulated states are introduced by operating a more general coherent superposition (υa+ra†)m on two classical states (coherent and thermal) and their nonclassicality caused by the operation (υa+ra†)m is investigated via examining the squeezing, sub‐Poissonian statistics, nonclassical depth, and negativity of Wigner distribution. Their density‐operator and Wigner‐distribution evolutions in the thermal channel are also explored. It is found that the high‐order operation (υa+ra†)m has better performance in creating nonclassicality for certain ratios r and more robustness against decoherence of the two photon‐modulated states for thermal noise. For convenience, a new three‐variable special polynomial and its generating function are introduced via the normal ordering of operators. The nonclassicality of two new photon‐modulated states that is generated by operating a more general coherent superposition (υa+ra†)m on two classical states and their decoherence evolution in the thermal channel is theoretically investigated. It is found that the high‐order operator (υa+ra†)m has better performance in creating nonclassicality for certain ratios r and more robustness against decoherence of the two photon‐modulated states for thermal noise.