  Noise is in general inevitable and detrimental to practical and useful
quantum communication and computation. Under the resource theory framework,
resource distillation serves as a generic tool to overcome the effect of noise.
Yet, conventional resource distillation protocols generally require operations
on multi-copies of resource states, and strong limitations exist that restrict
their practical utilities. Recently, by relaxing the setting of resource
distillation to only approximating the measurement statistics instead of the
quantum state, a resource-frugal protocol, virtual resource distillation, is
proposed, which allows more effective distillation of noisy resources. Here, we
report its experimental implementation on a photonic quantum system for the
distillation of quantum coherence (up to dimension 4) and bipartite
entanglement. We show the virtual distillation of the maximal superposed state
of dimension four from the state of dimension two, an impossible task in
conventional coherence distillation. Furthermore, we demonstrate the virtual
distillation of entanglement with operations acting only on a single copy of
the noisy EPR pair and showcase the quantum teleportation task using the
virtually distilled EPR pair with a significantly improved fidelity of the
teleported state. These results illustrate the feasibility of the virtual
resource distillation method and pave the way for accurate manipulation of
quantum resources with noisy quantum hardware.
