tl;dr- The maximum data rate you're looking for would be called the maximum entropy flux. Realistically speaking, we don't know nearly enough about physics yet to meaningfully predict such a thing.
But since it's fun to talk about a data transfer cord that's basically a $1\mathrm{mm}$-tube containing a stream of black holes being fired near the speed of light, the below answer shows an estimate of $1.3{\cdot}{10}^{75}\frac{\mathrm{bit}}{\mathrm{s}}$, which is about $6.5{\cdot}{10}^{64}$ faster than the current upper specification for USB, $20\frac{\mathrm{Gbit}}{\mathrm{s}}=2{\cdot}{10}^{10}\frac{\mathrm{bit}}{\mathrm{s}}$.
Intro
You're basically looking for an upper bound on entropy flux:
* entropy: the number of potential states which could, in theory, codify information;
* flux: rate at which something moves through a given area.
So,$$\left[\text{entropy flux}\right]~=~\frac{\left[\text{information}\right]}{\left[\text{area}\right]{\times}\left[\text{time}\right]}\,.$$ Note: If you search for this some more, watch out for "maximum entropy thermodynamics"; "maximum" means something else in that context.
In principle, we can't put an upper bound on stuff like entropy flux because we can't claim to know how physics really works. But, we can speculate at the limits allowed by our current models.
Speculative physical limitations
Wikipedia has a partial list of computational limits that might be estimated given our current models.
In this case, we can consider the limit on maximum data density, e.g. 388
as discussed in this answer. Then, naively, let's assume that we basically have a pipeline shipping data at maximum density arbitrarily close to the speed of light.
The maximum data density was limited by the <PERSON> bound:
In physics, the <PERSON> bound is an upper limit on the entropy $S$, or information $I$, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the quantum level.
–"<PERSON> bound", Wikipedia [references omitted]
Wikipedia lists it has allowing up to$$ I ~ \leq ~ {\frac {2\pi cRm}{\hbar \ln 2}} ~ \approx ~ 2.5769082\times {10}^{43}mR \,,$$where $R$ is the radius of the system containing the information and $m$ is the mass.
Then for a black hole, apparently this reduces to$$ I ~ \leq ~ \frac{A_{\text{horizon}}}{4\ln{\left(2\right)}\,{{\ell}_{\text{Planck}}^2}} \,,$$where
* ${\ell}_{\text{Planck}}$ is the <PERSON> length;
* $A_{\text{horizon}}$ is the area of the black hole's event horizon.
This is inconvenient, because we wanted to calculate $\left[\text{entropy flux}\right]$ in terms of how fast information could be passed through something like a wire or pipe, i.e. in terms of $\frac{\left[\text{information}\right]}{\left[\text{area}\right]{\times}\left[\text{time}\right]}.$ But, the units here are messed up because this line of reasoning leads to the holographic principle which basically asserts that we can't look at maximum information of space in terms of per-unit-of-volume, but rather per-unit-of-area.
So, instead of having a continuous stream of information, let's go with a stream of discrete black holes inside of a data pipe of radius $r_{\text{pipe}}$. The black holes' event horizons have the same radius as the pipe, and they travel at $v_{\text{pipe}} \, {\approx} \, c$ back-to-back. 388