Place the blackberries in a saucepan.
Add the lime juice and water.
Bring to a boil over a medium heat.
Boil for 3-5 minutes.
Once softened, mash the blackberries using a fork.
Pour through a fine mesh sieve and using a spoon, press the blackberries through so that only the skins and seeds remain in the sieve.
Pour into a jar.
The juice should be quite thick, almost the consistency of syrup.
Add the powdered Erythritol and mix until combined.
Let it cool and refrigerate until ready.
The juice will keep refrigerated for up to 5 days.
To serve, optionally decorate your cocktail glasses by dipping the rims in water and then in a mixture of acai powder (or any berry powder).
Fill each glass with ice and pour in the vodka.
Add the sweetened blackberry juice.
Decorate with more fresh blackberries or mint leaves and serve.