The most direct way to describe the relationship between property rights and freedom is to define property in terms of its effects on freedom.
Ownership of physical property has two effects on freedom:
The important thing about physical property is that the freedom in item 1 can only exist if the non-freedom in the item 2 is enforced.
If I own a house, my freedom to use my house how I want to use it depends on other people not being allowed to be in my house. Unless I say they can be in my house.
The definition of physical property rights creates an allocation of freedoms.
This allocation of freedom is critical to the efficient use of private property. It is very difficult to live in a house if anyone else can also come into the house. A house that anyone can come into at any time is not a house worth living in.
Private property rights are also essential to the maintenance of physical property. For example, if everyone can come into my house, not only do they get in the way, but many of the intruders might damage the house. And if they do damage it, they may have very little interest in repairing the damage. And even less interest in trying to improve and develop my house to make it into a better house.
Even though the assignment of property rights allows the efficient use of physical property, it is not necessarily a good thing for private property rights to be assigned to every physical object and location in the world.
For example, if all the land in a country was privately held, there would be no public roads, and therefore no guarantee that anyone could travel from their own private land to anyone else's private land.
In theory it might be possible for private land ownership to somehow support the development of a private road system, but in practice we regard the right of public movement as too important to be left to such mechanisms, for example private road owners might conspire to limit the free movement of certain people that they don't like. We also regard the friction involved in systems of charging people for use of private roads as being likely to add too much to the overall cost of maintaining, developing and using a road system. (Yes there are toll roads, but in almost all cases these toll roads are still public roads, possibly partly funded by a private road builder, but still subject to a publicly defined right of transit – to anyone able to pay the toll. Also, in almost all cases, there is a non-toll alternative route for people who don't want to pay the toll.)
Intellectual property can also be defined in terms of freedom and non-freedom. We can consider patents, copyright and trademarks as intellectual property relating to the freedoms to use an invention, a "work" or a name, respectively.
The logic seems similar to that for physical property:
However, there is one major difference. In the case of patents and copyright, the freedom of the owner to use the property does not depend in any way whatsoever on the "non-freedom" of everyone else. If I invent something, and other people use "my" invention, this does not stop me from also using it. If I create a "work", and other people use it by making copies of it, this does not stop me from using the original copy. (The case for trademarks is somewhat similar to that of physical property, because a name is only useful if it reliably refers to one thing and not to something else.)
What this means is that intellectual property is not an allocation of freedom, it is a reduction in freedom.
Furthermore, there is no notion of maintenance of intellectual property (at least not if we restrict ourselves to consideration of digital "works" in the copyright case). And as far as improvements go, allowing other people to improve an invention or "work" does nothing to prevent the "owner" also improving it.
Copyright decreases freedom in another manner, because the enforcement of copyright requires methods of preventing unauthorized copying, which in the long run can only be achieved by some central authority which controls and monitors all the computers in the world, and all public networks, and all information which travels within those networks.
The enforcement of copyright also requires extreme punishments, due to the difficulty of intercepting acts of copying taking place between individuals. (That is, hardly anyone gets caught, so when they are caught, they must be punished as severely as possible, so that the deterrent remains credible.) Such extreme punishments reduce the freedom of all those who wish to share information, or even to assist others to share information, due to the "chilling effect" raised by even the smallest possibility that the information sharers might be accused of sharing something that they do not have permission to share, and might thus be subject to those punishments.
If we consider the effect that intellectual property has on freedom, and compare it to physical property, the institutions of intellectual property appear to be both pointless and destructive, and we would wonder why anyone would invent such things.
The justification for forms of intellectual property such as copyright and patents is not that the unfreedoms defined by these forms of property are directly beneficial to anyone. Rather, it is assumed, firstly, that intellectual property is something that can be created, and, secondly, that giving the creators of intellectual property the rights to impose non-freedoms on other potential users of that property is the only effective way to attribute the value of those creations to the people who created them.
If indeed these two assumptions hold true, then there may be sufficient justification for the existence of intellectual property, even though intellectual property results in a potentially harmful reduction in human freedom, and, in particular, a reduction in "intellectual" freedom.
But do we know that these assumptions are so true? Is intellectually property truly "created" in the sense that the value contained within such property is entirely due to the efforts of the deemed creator, and would not otherwise exist? And is there truly no other way of attributing value to those who invent and those who publish content?
The worst case is that of "junk" patents, where the first person to think of an idea – an "invention" – gets to "own" that idea, even though almost certainly someone else would have thought of the same idea very soon after (or, in some cases, the idea would have been thought of very quickly once circumstances arose where the relevant "invention" became practically useful). For this type of "invention", intellectual property is not "created" in the strong sense of something being created that would otherwise not exist. The value of this type of intellectual property is entirely negative, and the system is "incentivising" the destruction of freedom, for no purpose other than the benefit of those who take part at the expense of everyone else.
If there were a thousand people lost at sea, and they came across a large uninhabited but fertile island, then it would make sense for them to settle there. It would also make sense to allocate land on the island into a thousand parcels, so that each settler could have their own private property, to live in, to maintain, to develop, to grow food on. It would also make sense to not allocate all the island as private property; especially it would be a good idea to set some aside as public property for roads, and for other public purposes.
Now imagine that the thousand settlers were magically gifted a thousand ideas. Would it make sense to allocate ownership of each idea to one settler, with each owner of an idea given the right to prevent anyone else from using "their" idea?
It wouldn't make any sense at all – such an allocation of property "rights" would be a senseless act of destruction, which would pointlessly prevent the settlers getting the maximum possible benefit from the use of those ideas.
There is no definite conclusion that one can draw. Intellectual property has its pros and cons.
The one conclusion I want to draw is that the freedom-related benefits of physical property do not have a corresponding analog in intellectual property.
Part of the argument that intellectual property rights are a "good thing" is based on the analogous assertion that property rights are a good thing in general. But, as I have shown, part of what makes physical property rights a good thing is that they define an efficient allocation of freedom, whereas with intellectual property there is only a reduction in freedom, and the corresponding benefit does not exist.
In the very long run, it seems likely that the freedom to create will become more important than financial incentives to create, and we will regard freedom as the primary value, to be strongly defended, and any system of incentives for creating intellectual property, if it is to exist at all, will only be allowed to exist if it doesn't threaten intellectual freedom.