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We obtain in closed form the probability distribution for individualmeasurements of the stress-energy tensor of two-dimensional conformal fieldtheory in the vacuum state, smeared in time against a Gaussian test function.The result is a shifted Gamma distribution with the shift given by thepreviously known optimal quantum inequality bound. For small values of thecentral charge it is overwhelmingly likely that individual measurements of thesampled energy density in the vacuum give negative results. For the case of asingle massless scalar field, the probability of finding a negative value is84%. We also report on computations for four-dimensional massless scalar fieldsshowing that the probability distribution of the smeared square field is also ashifted Gamma distribution, but that the distribution of the energy density isnot.

Probability distributions of smeared quantum stress tensors