  We show that excitons and free carriers in K and K' valleys of transition
metal dichalcogenide monolayers can be entangled with respect to their valley
degree of freedom by absorbing linearly polarized single photons. This effect
does not require any interaction between K and K' excitons in contrast to
conventional mechanisms of entanglement that are mediated by coupling between
quantum systems (e.g.~entanglement of photons in nonlinear optical
interactions). The valley entanglement of excitons and free carriers can be
verified by measuring the polarization of their photoluminescence or
fluctuations of the photocurrent under an applied in-plane DC bias.
