Can quantative easing be summarized as "The state prints cash to pay its debt to private sector"? I find that most sources describe quantitative easing in an overly complicated way that obscures what it basically means.

As far as I understand a central bank is a public entity  owned by a state, so I don't see much point in distinguishing a state entity from a central bank entity. 

Therefore, I tend to find that the traditional descriptions like  "the central banks buys government bonds from private banks in order to inject money in the economy" are ridiculously  convoluted and funny.

As far as I understand, if I have a government bond, it is a promise that the state will pay me back some money at some point. So when I'm hearing "the central bank buys government bonds", all I'm hearing is actually "the government is printing cash from nothing to pay me right now, and destroy its debt".

Is my interpretation correct? Why isn't my interpretation the standard official intuitive explanation of quantitative easing? Is it just for newspapers and bankers to sound "serious"?
Altough you are correct saying that the state "own" central banks, they should be independent from their government. This gives freedom to monetary policymakers from direct political or governmental influence in the conduct of policy.

Given that, I would say that your interpretation is a bit exaggerated and maybe biased somehow.

Quantitative easing (QE) is a monetary policy in which a central bank purchases government securities or other securities from the market in order to increase the money supply. This is made with newly created bank reserves, but doesn't mean that new currency (bills and coins) has been printed. In theory, with more liquidity, the domestic demand would increase and eventually promote economic growth. Then, the excess of liquidity is absorbed by the growth and inflation would remain low.

The problem is if the economic growth don't happen, there will be inflation.

Using a more informal language, it's correct to say that the government is creating money in the present, hoping that this fresh money will increase economic growth in the future.