That's my interpretation as well.

Traditionally deep space bandwidth is low so that sending huge amount of data takes a long time in addition to time of travel.

Yup, no realtime communications of any sort, even texting, with people living in the Mars cities. I think living in the moon will be much more attractive to people, given that you can still have video/voice calls with a slight lag (2600ms roundtrip) and text conversations with no perceptible latency increase (vs ones to people still on Earth).

If they ever figure how to do quantum entanglement type of communication, it would bypass the need for transmit data directly.

There is a lot of investment / ongoing research into this because it would also help us locally (bypassing the need of undersea cables for an example).

Faster-than-light communication of any sort breaks causality and is not permitted by physics.

Quantum entanglement does not allow you to communicate. It just means two particles have a linked but random state.

Personally I don't think an up to 20-40 minute lag for communications will be that big of a deal, it'll take a bit of getting used to, plus mechanisms to synchronize internet data with Earth, but we're pretty used to asynchronous communications, and prior to the advent of electricity, not having realtime communication over large distances was normal and tolerable.

>plus mechanisms to synchronize internet data with Earth

Even in a future where there's a city on Mars, that seems unlikely.

I disagree, long term I think we'd have at least a significant portion of internet data synchronized between the two. Of course early on it'd probably just be in the form of certain popular entertainment sources and informational resources being periodically uploaded from Earth, more akin to a Plex or Invidious server and Wikipedia backup for Mars.

But as the size of a colony grows, it just makes more and more sense to sync up as much data as possible. Eg a YouTube Mars which downlinks ahead of time trending videos + videos from people subscribed to by Martians + videos the algorithm thinks Martians will like and uplinks the same stuff for Earth.

Some very small subset is perhaps plausible, but I think you're overestimating how much Google or Netflix would care about addressing a small and inconvenient market.

A major self-sustaining colony on Mars will probably take 50-100 years, at which point Google as well as its current jurisdiction of registration (Delaware) will likely both be history.

Self-sustaining? I think that's far enough out that is basically pointless to speculate a deadline. It would require too many breakthroughs.

Maybe you can get an AI agent for both of you who knows how to perfectly simulate you in a dialogue or predict to great accuracy what you would say on both sides.