According to our current understanding of physics, information cannot be transmitted faster than the speed of light (c) in a vacuum. The speed of light is considered to be the cosmic speed limit, as established by Einstein's theory of relativity.
In the scenario you described, where electromagnetic (EM) waves at a particular frequency pass through negative-permittivity plasma, resulting in a phase velocity greater than c, it is important to note that the phase velocity is not the same as the velocity of information transmission. The phase velocity refers to the velocity of the peak or phase of the wave, while the group velocity is the velocity at which the actual information travels.
In certain mediums with special properties, such as negative-permittivity plasma or metamaterials, the phase velocity of electromagnetic waves can exceed the speed of light in a vacuum. However, this does not imply that information can be transmitted faster than c. The group velocity, which determines the speed of information transmission, is what matters in this context.
In these situations, the group velocity can still be less than or equal to the speed of light in a vacuum, ensuring that information propagates at or below the speed of light. This is due to the complex interaction of the wave's components and the material properties, which result in peculiar phenomena like superluminal phase velocities without violating the principles of causality or allowing for faster-than-light information transfer.
In summary, even if the phase velocity of electromagnetic waves can exceed the speed of light in certain mediums, it does not imply that information can be transmitted faster than c. The group velocity, responsible for information transmission, remains consistent with the principles of relativity, ensuring that information is limited by the speed of light.