We present a general quantum fluctuation theorem for the entropy production of an open quantum system whose evolution is described by a Lindblad master equation. Such theorem holds for both local and global master equations, thus settling the dispute on the thermodynamic consistency of the local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of an Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is valid for arbitrary number of baths and for time-dependent Hamiltonians. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to non-thermal baths, as long as microreversibility is preserved. We finally present some numerical examples to showcase the exact results previously obtained.
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