iqm.error_reduction_tools.utils.general_utils.total_variational_distance

iqm.error_reduction_tools.utils.general_utils.total_variational_distance(dist_a, dist_b)

Total Variation Distance between two probability distributions.

The Total Variation Distance between the probability distributions P and Q is defined as

\[\text{TVD}(P, Q) = \frac{1}{2} \sum_x |P(x) - Q(x)|.\]

TVD is always in \([0, 1]\).

This function accepts both:

• Proper probability distributions (dict[str, float] with values summing to 1)

• Samplings of distributions (dict[str, int] with arbitrary sums)

The distributions are automatically normalized before computing the distance, so the input values do not actually need to sum to 1.

Parameters:

• dist_a (dict[str, int | float]) – First probability distribution.

• dist_b (dict[str, int | float]) – Second probability distribution.

Returns:

Total Variation Distance between the two distributions.

Return type:

float