Quantum Fluctuation Theorem of the Quantum Work Conditioned on the Initial Energy Measurement

The two-time measurement scheme is a standard approach to the quantum fluctuation theorem. However, the second energy measurement will destroy the quantum coherence and correlations; therefore, the informational contribution to the maximal work relation will be erased by the second measurement. To solve this problem, the one-time measurement (OTM) scheme, where the stochastic work is determined by the expectation value of the energy conditioned on the initial measurement, was proposed to derive a Jarzynski equality that leads to a tighter bound on the maximal work relation. However, the detailed fluctuation theorem clarifying the backward process has not been investigated. In this presentation, we present the derivation of the detailed fluctuation theorem in the OTM, and verify the derived fluctuation theorem via quantum computer.