Why are the 10 year German bunds and 10 year US treasury yield highly correlated? And when the ECB started QE this year, the 10 year bunds rate naturally plummetted, but so did the 10 year US treasury rate. What fundamental reason could cause the US rate to drop in synchrony?
Because they are the so called "Fly to Quality". When markets turmoil investors look where to safely invest their money to avoid volatility and risk. This lead to a depreciation (because of the more demand in bonds, the less bond rate) in rates. After the QE, as you said, the left risk about the already solid Germany was cut out because of the unlimited coverage by the ECB on European Bonds. Germany and US are considered the two solid major economics of the World and every rational investor who wants to do not run too risk (because it is impossible to avoid it entirely, see "idiosyncratic risk" for further information) prefers to invest there. A similar but slightly different chapter is for gold, considered a "Fly-to-Quality" good as well. Concluding, part of the correlation is due to economic relationships that there are between US and EU and it also accentuates the effects of important macroeconomic news of one or the other party. 

TIP

Do you know why, sometimes, it is possible to see negative rates (as Danish or Switzerland or some Scandinavians)? Because sometimes, even if the rate is negative (you have to pay the issuer) the cost of carry is higher and then investors just leave their money there, paying less than to disinvest and invest again in another kind of security. This happened for some days to German rates too!