  Entanglement plays an important role in our ability to understand, simulate,
and harness quantum many-body phenomena. In this work, we investigate the
entanglement spectrum for open one-dimensional systems, and propose a natural
quantifier for how much a 1D quantum state is entangled while being subject to
decoherence. We demonstrate our method using a simple case of single-particle
evolution and find that the open system entanglement spectrum is composed of
generalized concurrence values, as well as quantifiers of the state's purity.
Our proposed entanglement spectrum can be directly obtained using a correct
scaling of a matrix product state decomposition of the system's density matrix.
Our method thus offers new observables that are easily acquired in the study of
interacting 1D systems, and sheds light on the approximations employed in
matrix product state simulations of open system dynamics.
