Or do you mean modern bourgeois private property?

But does wage labor create any property for the laborer? Not a bit. It creates capital, _i.e._, that kind of property which exploits wage-labor, and which cannot increase except upon condition of begetting a new supply of wage-labor for fresh exploitation. Property, in its present form, is based on the antagonism of capital and wage labor. Let us examine both sides of this antagonism.

Manifesto of the Communist Party — Part 18

To be a capitalist, is to have not only a purely personal, but a social status in production. Capital is a collective product, and only by the united action of many members, nay, in the last resort, only by the united action of all members of society, can it be set in motion.

Manifesto of the Communist Party — Part 18

Capital is therefore not a personal, it is a social power.

Manifesto of the Communist Party — Part 18

When, therefore, capital is converted into common property, into the property of all members of society, personal property is not thereby transformed into social property. It is only the social character of the property that is changed. It loses its class character.

The average price of wage-labor is the minimum wage, _i.e._, that quantum of the means of subsistence, which is absolutely requisite to keep the laborer in bare existence as a laborer. What, therefore, the wage-laborer appropriates by means of his labor, merely suffices to prolong and reproduce a bare existence. We by no means intend to abolish this personal appropriation of the products of labor, an appropriation that is made for the maintenance and reproduction of human life, and that leaves no surplus wherewith to command the labor of others. All that we want to do away with, is the miserable character of this appropriation, under which the laborer lives merely to increase capital, and is allowed to live only in so far as the interest of the ruling class requires it.

In bourgeois society living labor is but a means to increase accumulated labor. In Communist society accumulated labor is but a means to widen, to enrich, to promote the existence of the laborer.

In bourgeois society, therefore, the past dominates the present; in Communist society, the present dominates the past. In bourgeois society capital is independent and has individuality, while the living person is dependent and has no individuality.