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.
The distinguishability between two quantum states̺ andσ reads 1 2 ‖̺−σ‖1 and quantifies the optimal minimum-error discrimination [1, 2]
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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.