Traditionally the main concern for a bond investor is inflation. It reduces the real returns of a bond, hence prompting higher long term interest rates, and causes the authorities to increase short term interest rates as a policy response. The increases in rates cause the current value of bonds to fall. Inflation is bad for bonds, full stop.
Quantitative easing is now threatening to turn that relationship on its head. The printing of money and purchasing of governments bonds by central banks has the primary aim of increasing inflation, thus, in normal circumstances, lowering bond returns. However the increase in money supply not only reduces its value from a real perspective but also means that the cost of borrowing falls, hence driving short term rates lower, which is a positive event for bonds. Additionally, the purchasing of government bonds by the authorities also drives long term bond yields down and therefore prices higher – again a positive event for bond holders.
Normally, if an economy has higher inflation one would expect it to have higher bond yields. Under QE, if an economic block such as the US is printing money while another economic block like the Eurozone is not turning on the printing presses, one would have traditionally expected that European government bonds would yield less than US bonds due to their position within the lower inflation zone. However, in an extreme example where the US Fed lowered every US Treasury yield to 1% and then bought them back with freshly minted dollars, it could be observed that the US would have both the highest inflation economy and the lowest long and short term government yields.
This may all appear to be counterintuitive, but if you want to stimulate an economy from a monetary perspective you need negative real rates. Usually, when you do this, the Bond Vigilantes turn up and push long rates up, thus negating the government policy. QE rides roughshod over this possibility, and you therefore end up with a potentially topsy turvey outcome.