Currencies tend to weaken during QE as the bond purchases by central banks boost the amount of money in circulation. Lower interest rates compound the effect as they encourage consumers to spend and businesses to invest, boosting the economy.
A weak euro is broadly positive for the struggling euro zone, and should help it tackle deflation and stimulate the region's exports, which become cheaper in the global market as a result.
Conversely, a strengthening dollar worries U.S. exporters, as it makes their products more expensive in foreign markets.
The weakness in the euro has been compounded by concerns that Greece – which is battling an ongoing economic crisis -- could ultimately leave the single currency and others could follow, undermining the future of single currently. Expectations of a rate hike by the Federal Reserve on the back of a strengthening U.S. economy is also giving the dollar a boost.
The ECB's 1 trillion euro bond buying program has, predictably, caused the yields on euro zone sovereign debt hit record lows (and, conversely, prices to rise) and has led investors to look for higher returns elsewhere.
Read MoreECB begins bond-buying: What should you do?
Strategists at Deutsche Bank warned that capital outflows from the euro zone could be greater than anticipated by the ECB, putting more pressure on the euro.
"The euro-area's huge current account surplus reflects a very large pool of excess savings that…combined with ECB quantitative easing and negative rates (will) lead to large-scale capital flight from Europe causing a collapse in the euro and exceptionally depressed global bond yields," Deutsche Bank strategists George Saravelos and Robin Winkler said in a note Tuesday.
"The greater the European outflows, the more the euro can weaken and the lower global bond yields can stay," they added. "We now foresee a move down to 1.00 by the end of the year, 90 cents by 2016 and a new cycle low of 85 cents by 2017."
Ominously for ECB President Mario Draghi, who spoke at a conference organized by the Center for Financial Studies in Frankfurt on Wednesday, Saravelos and Winkler warned that, "Europe will continue being a major source of global imbalances for the rest of this decade."