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When we say that information cant travel faster than light, we mean that phase velocity can go beyond $c$ but the group velocity can't. Hence, we say that a plane wave carries no information. What I don't understand is what we mean by information here, is it supposed to be energy? Because plane waves do possess energy.

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Yes, information here is meant to be energy, because it's the thing you can switch on and off at one end then measure at the other end.

No, phase velocity does not carry energy, it locally modulates the energy carried by group velocity.

A common example is a packet of water waves trigered by a boat in a (deep enough) arbor :you see waves appearing at the rear of the packet, traverse it at double velocity, and die at the other end (but you could pretend they continue with null energy). Note that capillary waves would do the opposite, since their phase is slower than group velocity. So "information" there seems to be in advance.

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What I don't understand is what we mean by information here, is it supposed to be energy?

We mean signalling, that is sending and receiving some wave pattern that the two parties agreed will mean certain symbol or statement. Energy is a different concept altogether.

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