  Here we briefly discuss how negative numbers, or "negative probabilities",
can naturally arise in probabilistic expressions and be given an operational
interpretation. Like the use of negative numbers in arithmetical expressions,
the use of negative probabilities can have substantial practical value. Indeed,
some of the ideas discussed here have led to stochastic simulation algorithms
that require much less memory than the best classical algorithms known to date
[arXiv:1906.00263].
