Locally maximally mixed states

Lin Chen; Mengyao Hu

doi:10.1007/s11128-020-02804-4

Locally maximally mixed states

Lin Chen
, Mengyao Hu^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Preparing the locally maximally mixed (LMM) states is a physically operational work. We investigate the set P_d 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 P_d. 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.

Original language	English
Article number	305
Journal	Quantum Information Processing
Volume	19
Issue number	9
DOIs	https://doi.org/10.1007/s11128-020-02804-4
State	Published - 1 Aug 2020

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title = "Locally maximally mixed states",

abstract = "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.",

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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.

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Locally maximally mixed states

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