Supplemental Material for “ Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals ”
نویسندگان
چکیده
The unitary operator for the free-evolution part is defined as Û0(−∞, t) ≡ T exp{−(i/~) ∫ t −∞ dt Ĥdet(t)} with T being the time-ordering, and, for the interaction part, we have defined ÛI(−∞, t) ≡ T exp{−(i/~) ∫ t −∞ dt ′Ĥ int (t ′)}. For the measurement to be linear, Ĥdet only involves linear or quadratic functions of canonical coordinates, among which their commutators are classical numbers, i.e., not operators; the interaction Ĥint is in the bilinear form:
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