Uniform approximation of ideal photon subtraction and addition by fair beam splitter operations holds exactly under the stated energy moment conditions, and the conditions are tight.
Physically, the problem 3 arises due to a high energy of the input
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On quantum operations of photon subtraction and photon addition
Uniform approximation of ideal photon subtraction and addition by fair beam splitter operations holds exactly under the stated energy moment conditions, and the conditions are tight.