Well, we can't do it now so the only answer we have is 'more than we have now'.

Alright, this isn't strictly true, insofar as we can cryogenically freeze embryos and the like, and we can then thaw them and bring them to term so depending on your definition of 'someone', arguably the minimum technology someone needs is the ability to create and maintain liquid nitrogen. For full fledged human beings however, the problem is a little more complex.

When you get down to it, the problem is that around 70% of the human body is water. That may not sound like so much of a big deal - we freeze water all the time, right? Well true, but it's the stuff around the water that presents the problem here.

Ever wonder about the Titanic? Why it was possible for it to hit an iceberg in the first place? I mean, water is a liquid and most liquids are less dense than the solid made of the same material right? But icebergs float. So do those little cubes we put in our Scotch. That's because water expands when frozen, unlike most other molecules and compounds. Suffice it to say that freezing a complex human body actually causes massive damage to the cells because the frozen water actually damages the rest of the chemical compounds in the cell. (This is a simplification, but functionally correct.)

So; either we find a way to freeze water in a way that doesn't cause it to expand while the compounds around it increase their density, or we replace the water with another compound that doesn't react in that manner.

The first is simple - we simply don't have that technology and our understanding of chemistry leads us to believe that without some new breakthrough discovery in science, it will never be done. Therefore, it's not a simple engineering problem we can throw money and other resources at. It would rely on a scientific discovery to be made that we simply can't predict.

As for the second idea, most of the liquids we can think of that would behave in the right manner as they freeze are actually toxic to us, so while it's possible we wouldn't suffer cell damage, we'd still most likely die.

Bottom line is that in order to successfully cryogenically freeze a person with a high probability of bringing them back, we would either need to be able to replace all the water in all the cells of a human body with something that is both non-toxic AND subject to density increase during freezing; or, we need to find a way for water to react differently to freezing and increase (rather than decrease) in density.

Both are currently outside our known science, which is evident by one simple observation;

We're not doing it yet.

Well, we can't do it now so the only answer we have is 'more than we have now'.

Alright, this isn't strictly true, insofar as we can cryogenically freeze embryos and the like, and we can then thaw them and bring them to term so depending on your definition of 'someone', arguably the minimum technology someone needs is the ability to create and maintain liquid nitrogen. For full fledged human beings however, the problem is a little more complex.

When you get down to it, the problem is that around 70% of the human body is water. That may not sound like so much of a big deal - we freeze water all the time, right? Well true, but it's the stuff around the water that presents the problem here.

Ever wonder about the Titanic? Why it was possible for it to hit an iceberg in the first place? I mean, water is a liquid and most liquids are less dense than the solid made of the same material right? But icebergs float. So do those little cubes we put in our Scotch drinks other than Scotch. That's because water expands when frozen, unlike most other molecules and compounds. Suffice it to say that freezing a complex human body actually causes massive damage to the cells because the frozen water actually damages the rest of the chemical compounds in the cell. (This is a simplification, but functionally correct.)

So; either we find a way to freeze water in a way that doesn't cause it to expand while the compounds around it increase their density, or we replace the water with another compound that doesn't react in that manner.

The first is simple - we simply don't have that technology and our understanding of chemistry leads us to believe that without some new breakthrough discovery in science, it will never be done. Therefore, it's not a simple engineering problem we can throw money and other resources at. It would rely on a scientific discovery to be made that we simply can't predict.

As for the second idea, most of the liquids we can think of that would behave in the right manner as they freeze are actually toxic to us, so while it's possible we wouldn't suffer cell damage, we'd still most likely die.

Bottom line is that in order to successfully cryogenically freeze a person with a high probability of bringing them back, we would either need to be able to replace all the water in all the cells of a human body with something that is both non-toxic AND subject to density increase during freezing; or, we need to find a way for water to react differently to freezing and increase (rather than decrease) in density.

Both are currently outside our known science, which is evident by one simple observation;

We're not doing it yet.