  The notions of predictability and visibility are essential in the
mathematical formulation of wave particle duality. The work of Jakob and Bergou
[Phys. Rev. A 76, 052107] generalises these notions for higher-dimensional
quantum systems, which were initially defined for qubits, and subsequently
proves a complementarity relation between predictability and visibility. By
defining the single-party information content of a quantum system as the
addition of predictability and visibility, and assuming that entanglement in a
bipartite system in the form of concurrence mutually excludes the single-party
information, the authors have proposed a complementarity relation between the
concurrence and the single-party information content. We show that the
information content of a quantum system defined by Jakob and Bergou is nothing
but the Hilbert-Schmidt distance between the state of the quantum system of our
consideration and the maximally mixed state. Motivated by the fact that the
trace distance is a good measure of distance as compared to the Hilbert-Schmidt
distance from the information theoretic point of view, we, in this work, define
the information content of a quantum system as the trace distance between the
quantum state and the maximally mixed state. We then employ the quantum
Pinsker's inequality and the reverse Pinsker's inequality to derive a new
complementarity and a reverse complementarity relation between the single-party
information content and the entanglement present in a bipartite quantum system
in a pure state. As a consequence of our findings, we show that for a bipartite
system in a pure state, its entanglement and the predictabilities and
visibilities associated with the subsystems cannot be arbitrarily small as well
as arbitrarily large.
