  Evolutions under non-Hermitian Hamiltonians with unbroken PT-symmetry can be
considered unitary under appropriate choices of inner products, facilitated by
the so-called metric operator. While it is understood that the choice of the
metric operator has no bearing on the description of the system, in this work
we show that this choice does dictate the properties of the subsystem.
Subsystem dynamics therefore does depend on the choice of the metric. We argue
that this result is a reformulation of the previously known result that the set
of observables, chosen to characterize the state, determines its decomposition
into subsystems. In this work we take a non-Hermitian PT-symmetric quantum walk
with an internal and external degree of freedom to show this. The Hamiltonian
of the quantum walk is chosen to not allow a metric operator with a tensor
product structure over these subspaces. Under these constraints, we investigate
the properties of the internal state of the system under different choices of
the metric operator and show that properties like bipartite entanglement and
non-Markovianity depend on the choice of the metric operator.
