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.
In other words, the 2 transformations ( 2) can be realized approximately with an arbitrary precision for all states in the class
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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.