Fig. 1: Experimental implementation scheme for detecting quantum work fluctuations using a trapped-ion qubit.

a Sequence of operations for obtaining a single measured value of work. The flame represents thermalisation to a Gibbs state in the computational basis. \(\left\vert 0\right\rangle\) represents qubit initialisation. A two-point measurement is realised around a work step, given by a qubit rotation \(\hat{R}(\theta )\). The inset shows a non-demolition energy measurement, which is emulated via conditional re-initialisation (see text). b The relevant energy levels of a ⁴⁰Ca⁺ ion. The qubit is encoded in the Zeeman sub-levels of the 4²S_1/2 ground state. c Discrete protocol visualised on the Bloch sphere, with the arrows showing the instantaneous eigenstates of the Hamiltonian Eq. (2). In the step-wise protocol, these are separated by the fixed angle Δθ. The low (high) energy contributions to the thermal Gibbs state Eq. (3) are shown in blue (red).