How to identify visitors using different devices?

Question

Browsers

The task is to solve the problem of identifying unique visitors to the site, but the task is not only to determine the browser's finger print - here, everything is clear and solvable.
Visitors visit the site in the morning from a home device, in traffic from a mobile device, and at work from a work computer. It is necessary with some degree of probability to define the visitor as unique.
Are there any approaches, services, products or ways to solve such problems. I would be grateful for a tip in which direction to dig :) Best
regards,
Alexander

Answer 1

Services such as pluso, etc. are actively involved in this now (as far as I know there is no external public api yet)
The idea is that on a bunch of sites we connect a code that identifies the user through a cookie on the third domain. At the moment when the user is authorized somewhere, we save it separately, then we glue different cookies into the profile of one user.
Works well when a bunch of sites are connected

Answer 2

It's simple: authentication.
Modern authentication methods allow you to do this in 2 mouse clicks ("Facebook" button, "Allow" button).