  In open quantum systems, a clear distinction between work and heat is often
challenging, and extending the quantum Jarzynski equality to systems evolving
under general quantum channels beyond unitality remains an open problem in
quantum thermodynamics. In this Letter, we introduce well-defined notions of
guessed quantum heat and guessed quantum work, by exploiting the one-time
measurement scheme, which only requires an initial energy measurement on the
system alone. We derive a modified quantum Jarzynski equality and the principle
of maximum work with respect to the guessed quantum work, which requires the
knowledge of the system only. We further show the significance of guessed
quantum heat and work by linking them to the problem of quantum hypothesis
testing.
