Classicalization of nonclassical quantum states in loss and noise: Some no-go theorems

The general problem of performance advantage obtainable by the use of nonclassical transmitted states over classical ones is considered. Attention is focused on the situation where system loss is significant and additive Gaussian noise may be present at the receiver. Under the assumption that the total received state is classical, rigorous output density operator representations and their trace distance bounds are developed for classical and nonclassical transmitted states. For applications with high loss in all modes, a practical no-go theorem is enunciated that rules out the possibility of significant advantage of nonclassical over classical states. The recent work on quantum illumination is discussed as an example of our no-go approach.