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Quantum electrodynamics predicts the vacuum to behave as a non-linear medium,including effects such as birefringence. However, for experimentally availablefield strengths, this vacuum polarizability is extremely small and thus veryhard to measure. In analogy to the Heisenberg limit in quantum metrology, westudy the minimum requirements for such a detection in a given strong field(the pump field). Using a laser pulse as the probe field, we find that itsenergy must exceed a certain threshold depending on the interaction time.However, a detection at that threshold, i.e., the Heisenberg limit, requireshighly non-linear measurement schemes - while for ordinary linear-opticsschemes, the required energy (Poisson or shot noise limit) is much larger.Finally, we discuss several currently considered experimental scenarios fromthis point of view.

On the Heisenberg limit for detecting vacuum birefringence