How about "the means of production are collectively owned, said collective ownership usually expressed by state ownership".
In a fully realized socialist state there wouldn't be a political government to own anything.
http://www.slp.org/res_state_htm/socialism_m_p.html
Socialist government is not state government. It would not rule over people and places, but would empower the people to rule over things. Socialism means a government in which the people collectively own and democratically operate the industries and social services through an economic democracy. And when we say “collectively own,” we are not talking about homes, or cars, or other personal belongings. We are talking about the things needed to produce and distribute homes, cars and all the other things we need and want.
Under socialism the workers who operate the industries and services would collectively own and democratically manage them. In each factory and other workplace, the rank and file would elect their own immediate supervisors and management committees. They would also elect representatives to local and national assemblies of the industry or service in which they work, and to an all-industrial congress to coordinate production and distribution of all goods and services throughout the country. In short, socialism would replace the political government run by politicians with an industrial government run by workers and their elected representatives.
Instead of a senator from California or a representative from New York, there would be worker-delegates from the automotive industry, from the transportation systems, from the mines, from the clothing factories, from services such as restaurants, hospitals, schools and so on. These representatives would have the single task of deciding what should be produced and how best to produce it.
Today we have political democracy only. Workers do not have economic democracy. The owners of the factories have almost absolute power over their employees. They can fire whomever they please, whenever they please. They can close the plant down and move to another state or another country. They can even order their workers to manufacture something worthless or harmful. In short, they have all the power of dictators—economic dictators.
Socialism means economic democracy. Instead of voting once every two or four years for politicians, workers would be making decisions every day where they work and in the field in which they are most qualified. Here is where their vote counts because it vitally affects their own personal lives.
When we use the word “worker,” we mean everyone who sells his or her labor power, or ability to work, at so much per hour, or so much per week, to a capitalist employer. Coal miners are workers, but so are musicians, scientists, nurses, teachers, architects, inventors and mathematicians.