  We experimentally verify the Jarzynski and W\"ojcik quantum heat exchange
fluctuation relation by implementing the interferometric technique in
liquid-state Nuclear Magnetic Resonance setup and study the exchange heat
statistics between two weakly coupled spin-1/2 quantum systems. In presence of
uncorrelated initial state with individual spins prepared in local Gibbs
thermal states at different temperatures, the exchange fluctuation symmetry is
verified for arbitrary transient time. In contrast, when the initial
preparation includes correlation, the fluctuation symmetry breaks down and
further leads to an apparent spontaneous flow of heat from cold to hot. Our
experimental approach is general and can be systematically extended to study
heat statistics for more complex out-of-equilibrium many-body quantum systems.
