Your question is misleading. Depending on the bandwidth allocated in the radio spectrum to such communication, we can very well have gigabit links to pluto and back. Major problem in deep space communication is latency, not bandwidth.
The limiting factor for digital bandwidth is signal to noise ratio (so, power alone wont cut) and bandwidth (this is the [in]famous shannon-hartley-nyquist theorem afterall), bandwidth here is the size, "width" of the radio spectrum allocated to transmissions. When you say "my FM transmitter uses the 100mhz frequency" you are not saying it all, because no transmission occurs in a single frequency, but on a continuous spectrum of frequencies called 'a channel', the size of such channel in MHz is the aforementioned bandwidth. Digital bandwidth is then a consequence of this channel size and the signal to noise level. Usually, the ammount of information you can inprint on a signal is half as much as the size of the channel in hertz (so 0.5 bits/hertz of bandwidth). For example, FM radio uses a ~200khz channel (this would mean that the 100mhz station mentioned earlier occupies from 99.900mhz to 100.100mhz contiguous spectrum). This size holds the guard bands between channels, two audio channels and a pilot tone that allows decoding the stereo arrangement. This same 200khz band would mean a ~100kbit/sec digital bandwidth using a first-order modulation scheme like PSK, by virtue of the nyquist limit. This cannot, however prevent second-order or higher-order modulation schemes (like QAM etc). Using higher order modulation schemes the same 200khz band can carr more information per second (called symbols per second) than the normal first-order modulation. But, as the symbol density of the modulated signal increases, the signal loses the capability to survive noise. This is where the signal to noise ratio comes into play. (The shannon part).
Another factor to be considered is the Friis equation, that allows calculating the signal power at the receiving end of a transmission/receiving system. Following this equation, a system with a low gain antenna and a very powerfull transmitter, will usually have a poorer performance than a system with low power but a very high gain antenna. Both characteristics (transmitter power and antenna gain) are expressed as decibels. The path loss (free space loss) is calculated as the sum of the gas loses (the energy that gases in the path convert to thermal energy) and the geometric loss (the decoherence of the beam, inverse square law). In space you should care only with the geometric loss. At such distances, the geometric loss is huge, so, a low directivity antenna pair will have bad performances, even if operating with very high power. The way to go is to have very very directional antennas. The Friis equation (also called radar equation) sums all gains and all loses on a system, like Rpower = AntennaGain1 + AntennaGain2 + Power1 - Pathloss. In decibels (a logarithmic scale) the difference between a 1w signal and a 1000w (1kw) signal is circa 36db(w). A parabolic antenna can usually have 36db gain over the isotropic transmitter. This means that a system transmitting at 1000w of power but using an isotropic antenna (theoretical) will reach the receiver with the same power as a transmitter with mere 1w of power but a 36db parabolic antenna, and cheaper too. Higher power transmitters tend to emit a lot more noise than lower power ones, so, in the end of the day, lower power is usually better than too much power (Your priority goes from finding the bigger gain antenna possible, to the lower noise equipment to the largest power, in that order).
Summarizing both poins above, the bandwidth is limited by the capability of the system to send a large bandwidth signal across space while maintaining a good signal to noise ration, and using very directional antennas. But, you asked about bandwidth, and there we have no big problems. Like I said earlier, major problem for space communications is latency, the time that a wave takes to go from pluto to earth will have a major impact on protocols like TCP/IP. We will need better protocols. If error rate is too high (your latency will prevent simple acknowledge protocols to work satisfactorily) we do have some forward error correction protocols which may prove good enough. TCP/IP does not use forward error correction protocols due to the best effort nature of our networks and the low latency usually involved. But, nothing prevents someone from using a error correction protocol at the physical layer of the network.
Forward error correction protocols go a step further from error detecting protocols, in that they allows not only to detect errors, but to use aditional information in the packet itself to correct a certain maximum ammount of errors induced by the propagation media. This why you decrease the need for acknowledge packets (wich are limited by the very high latency of the network). Its right at the aknowledge system where latency might become a bandwidth limitation, becase to transmit the next packet the network might need to wait for the aknowledgement of the previous packet sent. TCP/IP uses a sliding window protocol to prevent this, but, the size of the windows involved in such a case are too small to be used in huge latency situations like those in the question. So, you might use bigger, FEC-protected packets and go away with acks altogether.
Bandwidth is not a problem. Latency is the real problem and we dont have a way to break the speed of light limitations but we can mitigate that problem with forward-error-correction protocols.
(This question is right into my professional area (networks).)