TY - JOUR
T1 - Locally maximally mixed states
AU - Chen, Lin
AU - Hu, Mengyao
N1 - Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/8/1
Y1 - 2020/8/1
N2 - Preparing the locally maximally mixed (LMM) states is a physically operational work. We investigate the set Pd containing two-qudit LMM states. We show that the point with a canonical decomposition (CD) has either the unique or infinitely many CDs. Next we show that the point in P2 has infinitely many CDs. Further we construct the necessary and sufficient condition by which the non-extreme point of rank two has the unique CD. We also show that the maximally correlated state of rank d is not an extreme point of Pd. As an application, we show that if the range of rank-three ρ∈ P3 is spanned by product vectors, then ρ is not an extreme point of P3. Moreover, ρ is realizable by unitary channels as a method of constructing a family of two-qutrit LMM states. We also prove that Conjecture 1 in [C. King et al., J. Phys. A: Math. Theor40, 7939 (2007)] holds for ρ.
AB - Preparing the locally maximally mixed (LMM) states is a physically operational work. We investigate the set Pd containing two-qudit LMM states. We show that the point with a canonical decomposition (CD) has either the unique or infinitely many CDs. Next we show that the point in P2 has infinitely many CDs. Further we construct the necessary and sufficient condition by which the non-extreme point of rank two has the unique CD. We also show that the maximally correlated state of rank d is not an extreme point of Pd. As an application, we show that if the range of rank-three ρ∈ P3 is spanned by product vectors, then ρ is not an extreme point of P3. Moreover, ρ is realizable by unitary channels as a method of constructing a family of two-qutrit LMM states. We also prove that Conjecture 1 in [C. King et al., J. Phys. A: Math. Theor40, 7939 (2007)] holds for ρ.
UR - https://www.scopus.com/pages/publications/85089736983
U2 - 10.1007/s11128-020-02804-4
DO - 10.1007/s11128-020-02804-4
M3 - 文章
AN - SCOPUS:85089736983
SN - 1570-0755
VL - 19
JO - Quantum Information Processing
JF - Quantum Information Processing
IS - 9
M1 - 305
ER -