Numerical Shadow

The web resource on numerical range and numerical shadow

User Tools

Site Tools


numerical-range:generalizations:joint-numerical-range

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
Next revision Both sides next revision
numerical-range:generalizations:joint-numerical-range [2018/11/04 09:56]
lpawela
numerical-range:generalizations:joint-numerical-range [2019/10/01 13:02]
rkukulski
Line 22: Line 22:
  
 == 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
Line 45: Line 45:
   * 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.txt · Last modified: 2020/06/30 07:28 by plewandowska