Monopoly on violence

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https://en.wikipedia.org/wiki/Monopoly_on_violence

As such, states can resort to coercive means such as incarceration, expropriation, humiliation, and death threats to obtain the population's compliance with its rule and thus maintain order.

Such a monopoly, according to Max weber, must occur via a process of legitimation.

from Politics as a Vocation Max Weber

Regardless, the state exists wherever a single authority can legitimately authorize violence.

fiscal (taxation) and legal capacity (the state's supremacy as sole arbiter of conflict resolution and contract enforcement)

https://www.britannica.com/topic/state-monopoly-on-violence

Under feudalism no lords, including the king, could claim a monopoly over the use of violence, since their vassals promised to serve them but remained free to exercise power in their fiefdoms

states can use violence "legitimately"