A great way to do this is with a threshold to transition the 2 floors. You can find them done in wood, marble, and even granite. I had to transition a floor, that had a severe slope to it, to an existing tile floor. I measured the height difference and gave it to my granite guy who made a custom threshold for me. A 1/6th of an inch is very easy to transition.

You could use some type of felt paper or Ardex Feather Finish. With only 1/16" inch you can skim the floor out from doorways about 5' and you'll never notice the rise.

I'm trying to avoid having a threshold as I want the floor to flow from the entry way into the kitchen. But, if the threshold is intentional and made out of a nice material it could look good.

What is the depth of your threshold as it spans the two rooms?

After I posted last night, I got to thinking and thought maybe I could put down some 2.5 mm cork in the kitchen as an underlayment, and the 1 mm foam out in the entry way.

I've also thought about using a floor leveling compound but was unsure how far that would need to be tapered out. Five feet sounds reasonable.

If I understand correctly, you are putting in floating floor. I would just use #15 building paper, and taper it as JFCWood said. This is a 10 minute job. That will probably be about 3 layers at the 1/16" step, then 2 layers, then one layer. You could do that over as little as one foot, but I might taper it over the 3 foot width of the roll of felt paper. I personally don't have good "trowel skills," so I don't think I would use feather finish, but that would also be a quick job (hey, it dries in about 8 minutes, so it has to be quick).

I wouldn't try to match different thicknesses of different materials -- I don't think that they will squish the same. Better to match up the subfloor, then use the same underlayment everywhere.

Are you installing the floor or hiring a professional?

If hiring someone, explain to them what needs to be done, or at least your desired expectations. the installer should be able to add whatever material is needed to make 1/16".

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Thresholds look real nice in a doorway. I've done many of them, some in marble and some in granite. They are tapered on both sides and are an easy transition to walk over. Because you are only dealing with a 1/16TH of an inch, the threshold will be very low--maybe only 1/4 to 3/8 inch high. Just thick enough so it can be cut without cracking. Check with a good flooring company or a tile supplier, or a granite company. A good granite company can make nearly ANYTHING out of granite.

A stone threshold gives a higher end look than wood, in my opinion, and is much more durable.

Thanks everyone.

15# it is. Quick, easy, and inexpensive. And should not at all at the least affect the performance of the end result.