A simple probate-avoidance living trust has no effect on state or federal estate taxes.
Keep in mind that for deaths in 2016, only estates worth more than $5.45 million will owe federal estate tax. This means that very few people have to worry about this tax. This exemption amount will increase with inflation.
In the past, AB trusts were used to help couples save on estate taxes. However, the large personal exemption and "portability" for spouses make AB trusts largely unnecessary. To learn more, read Nolo's article Tax-Saving AB Trusts.