Quantum Imaginarity-Mixedness Trade-off: Characterizing Maximally Imaginary Mixed States
arxiv(2024)
摘要
We investigate the trade-off relations between imaginarity and mixedness in
arbitrary d-dimensional quantum systems. For given mixedness, a quantum state
with maximum imaginarity is defined to be a "maximally imaginary mixed state"
(MIMS). By using the l_1 norm of imaginarity and the normalized linear
entropy, we conclusively identify the MIMSs for both qubit and qutrit systems.
For high-dimensional quantum systems, we present a comprehensive class of
MIMSs, which also gives rise to complementarity relations between the 1-norm
of imaginarity and the 1-norm of mixedness, as well as between the relative
entropy of imaginarity and the von Neumann entropy. Furthermore, we examine the
evolution of the trade-off relation for single-qubit states under four specific
Markovian channels: bit flip channel, phase damping channel, depolarizing
channel and amplitude damping channel.
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