The Chinese do not need any agreements to tap undersea cables and are more than capable of doing just that.

Sure, but they don't have the "home field advantage" that the NSA does, whereby much of the core internet infrastructure is housed in the US. I forget the exact number, but something like 70% of the world's internet traffic transits the US. (they mention this constantly in NSA-related articles)

But how much of the core infrastructure is made by the Chinese?

An astute question, considering the strange wifi-chips-in-irons story.

Are they? That's a very complicated thing to pull off and China isn't known for having the most advanced Navy (e.g. they can't secure their own oil tankers in the Persian Gulf) and they only have a small number of submarines.

But they could easily have agreements with every chip fab to build back doors into every piece of networking equipment.

This is exactly why Australia is very leery of letting the Chinese telecom hardware manufacturer Huawei have any of the contracts for networking hardware on the nascent National Broadband Network -- they are suspected of having ties to the Chinese government / army: https://en.wikipedia.org/wiki/Huawei#Security_concerns

My sister in law works for Huawei in Kenya. Her job (so far) has largely involved ripping out Siemens made mobile-telephony infrastructure and replacing it with Huawei-made mobile-telephony infrastructure. Such are today's instruments of empire.

You can packet-trace networking equipment you own.

You can't packet-trace a cloned switch port you don't know about.

That's very unlikely nobody would have noticed them by now, if it were the case.

Do you mean - as unlikely as not spotting the weakening of encryption standards - for example by another branch of the same government (NIST/NSA)?

Those were spotted.

eventually.

So can the US.

How do you know that?