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numerical-range:generalizations:joint-numerical-range [2018/11/04 09:56]
lpawela
numerical-range:generalizations:joint-numerical-range [2019/10/01 13:02] (current)
rkukulski
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 == Three qutrit matrices == == Three qutrit matrices ==
-This classification is taken from [( :​szymanski2017classification )]. Such JNRs must obey the following rules+This classification is taken from [( :​szymanski2017classification )] (see for details). Such JNRs must obey the following rules
  
-  - In this case we may restrict ourselves to only pure states ​(see [( :​szymanski2017classification )] for details).+  - In this case we may restrict ourselves to only pure states.
   - Any flat part in the boundary is the image of the Bloch sphere - two-dimensional subspace of a the sapce of $3 \times 3$ Hermitian matrices without corner points for   - Any flat part in the boundary is the image of the Bloch sphere - two-dimensional subspace of a the sapce of $3 \times 3$ Hermitian matrices without corner points for
 all configurations of Figure 2. We are unaware of earli all configurations of Figure 2. We are unaware of earli
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   * JNR is the convex hull of an ellipsoid and a point outside the ellipsoid, $e=0$, $s=\infty$, {{ :​numerical-range:​generalizations:​img_5944.png?​nolink&​200 |}}   * JNR is the convex hull of an ellipsoid and a point outside the ellipsoid, $e=0$, $s=\infty$, {{ :​numerical-range:​generalizations:​img_5944.png?​nolink&​200 |}}
   * JNR is the convex hull of an ellipse and a point outside the affine hull of the ellipse, $e=1$, $s=\infty$, {{ :​numerical-range:​generalizations:​img_5944bis.png?​nolink&​200 |}}   * JNR is the convex hull of an ellipse and a point outside the affine hull of the ellipse, $e=1$, $s=\infty$, {{ :​numerical-range:​generalizations:​img_5944bis.png?​nolink&​200 |}}
 +
 +====Application====
 +An example application of numerical range can be found in [( :​szymanski2019geometric )], [( :​czartowskiseparability )].
numerical-range/generalizations/joint-numerical-range.1541325384.txt.gz · Last modified: 2018/11/04 09:56 by lpawela