Step down open collector circuit
I took a look at the Japanese datasheet and could see enough to make sense of it. (My Japanese is limited to asking a few dumb questions like, "What is this called?")

The datasheet specifies the device as operating on anything from \$5\:\text{V}\$ to \$24\:\text{V}\$. This means that the red wire requires a voltage between those two. If you look over the datasheet, you can see where that is specified for that wire, too.

This, however, doesn't mean that the open collector outputs also must be run from the same voltage. While it is true that the sample schematic they provide suggests the idea, you actually do NOT usually have to comply with that idea for open-collector outputs. In fact, that's one of the advantages of having them be open-collector. You can use different rail voltages for the pull-up!!

The open-collector outputs are made either active or inactive, using the internal circuitry that is powered entirely by the \$5\:\text{V}\$ to \$24\:\text{V}\$ supply rail you provide on the red/black wire pair. So you do need to supply a voltage rail in that range or else the circuitry inside the unit can't actually work properly. However, so far as the green and white wires are concerned, that internal circuitry simply enables or disables the open-collector outputs. When active (or closed), these outputs on either the green or white wire are "shorted" to the black wire. When inactive (or open), these outputs are "floating" and aren't directly connected to anything. (This allows you to add a pull-up resistor to any reasonable voltage [which you can fairly take to mean anything \$\le 24\:\text{V}\$] which will take over when the green or white wire is inactive.)

The only limitation for the rail voltage used by the pull-up resistor is when the pull-up rail voltage exceeds the maximum \$V_\text{CE}\$ of their transistors used to create the open-collector output lead. The datasheet doesn't specify a limiting value here, but most small-signal BJTs can handle \$24\:\text{V}\$ (\$30\:\text{V}\$ to \$60\:\text{V}\$ isn't at all uncommon.) And since they specify a schematic showing a direct pull up to the red wire voltage, I'd have to assume the open-collector outputs can readily handle up to at least \$24\:\text{V}\$. And that is far more than you need. So there should be no worry about using \$3.3\:\text{V}\$ for your pull-ups.

In short, you need just two voltage rails: \$5\:\text{V}\$ (for the red wire, referenced to ground with the black wire) and \$3.3\:\text{V}\$ (for your Arduino as well as the resistor pull-up rail used with the green and white wires.)

Ignoring speed of rotation issues, the only possible remaining question is whether or not the active output voltage of the green and white wires (A/B open-collector outputs, when actively "shorting" their wires to ground) provide a low enough voltage output that will meet with your Arduino input level requirements. I would tend to guess, otherwise ignorant due to the datasheet limitations, that this output voltage will readily be \$\le 300\:\text{mV}\$ if you use reasonably valued pull-up resistors. This is well within the usual guidelines for digital inputs powered off of \$3.3\:\text{V}\$ rails. So I don't expect a problem here, either. (But you should verify this, once you select your pull-up values.)