Detailed fluctuation theorem from the one-time measurement scheme

We study the quantum fluctuation theorem in the one-time measurement (OTM) scheme, where the work distribution of the backward process has been lacking and which is considered to be more informative than the two-time measurement (TTM) scheme. We find that the OTM scheme is the quantum nondemolition TTM scheme, in which the final state is a pointer state of the second measurement whose Hamiltonian is conditioned on the first measurement outcome. Then, by clarifying the backward work distribution in the OTM scheme, we derive the detailed fluctuation theorem in the OTM scheme for the characteristic functions of the forward and backward work distributions, which captures the detailed information about the irreversibility and can be applied to quantum thermometry. We also verified our conceptual findings with the IBM quantum computer. Our result clarifies that the laws of thermodynamics at the nanoscale are dependent on the choice of the measurement and may provide experimentalists with a concrete strategy to explore laws of thermodynamics at the nanoscale by protecting quantum coherence and correlations.