Quantum information in the presence of loss

To illustrate the loss problem I take the example of quantum metrology where for interferometric measurement of an optical phase θ, the fundamental limit or the standard quantum limit (SQL) Δθ ≥ 1/√n where n is the number of photons detected. In theory using entangled photons it is possible to beat the SQL and achieve the Heisenberg limit Δθ ≥ 1/n. However this involves detecting the photons in n-fold sets which implies losses will go as Lnwhile in the classical case photons are detected individually and n=1. As a result recent metrology experiments `beating the quantum limit' actually only do so in the artificial case where losses are factored out.