The web resource on numerical range and numerical shadow

### Site Tools

numerical-range:generalizations:joint-numerical-range

# Differences

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

 numerical-range:generalizations:joint-numerical-range [2018/11/04 09:48]lpawela numerical-range:generalizations:joint-numerical-range [2018/11/04 09:56] (current)lpawela Both sides previous revision Previous revision 2018/11/04 09:56 lpawela 2018/11/04 09:48 lpawela 2018/10/08 08:42 plewandowska [Definition] 2018/10/08 08:22 plewandowska [Definition] 2018/06/15 16:20 lpawela 2018/06/15 16:17 lpawela 2018/06/06 12:09 lpawela 2018/06/06 12:02 lpawela 2018/05/24 13:33 lpawela 2018/05/24 13:30 lpawela 2018/05/24 10:24 lpawela 2018/05/24 10:23 lpawela 2018/05/24 10:21 lpawela created 2018/11/04 09:56 lpawela 2018/11/04 09:48 lpawela 2018/10/08 08:42 plewandowska [Definition] 2018/10/08 08:22 plewandowska [Definition] 2018/06/15 16:20 lpawela 2018/06/15 16:17 lpawela 2018/06/06 12:09 lpawela 2018/06/06 12:02 lpawela 2018/05/24 13:33 lpawela 2018/05/24 13:30 lpawela 2018/05/24 10:24 lpawela 2018/05/24 10:23 lpawela 2018/05/24 10:21 lpawela created Line 25: Line 25: - 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 (see [( :​szymanski2017classification )] for details). - - 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 + - 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 - Two two-dimensional subspaces must share a common point, hence all flat parts are mutually connected. - Two two-dimensional subspaces must share a common point, hence all flat parts are mutually connected. - Convex geometry of a three-dimensional Euclidean space supports up to four mutually intersecting ellipses. - Convex geometry of a three-dimensional Euclidean space supports up to four mutually intersecting ellipses. Line 40: Line 41: * three ellipses $e=3$, $s=0$, {{ :​numerical-range:​generalizations:​img_5886.png?​nolink&​200 |}} * three ellipses $e=3$, $s=0$, {{ :​numerical-range:​generalizations:​img_5886.png?​nolink&​200 |}} * four ellipses $e=4$, $s=0$, {{ :​numerical-range:​generalizations:​img_5957.png?​nolink&​200 |}} * four ellipses $e=4$, $s=0$, {{ :​numerical-range:​generalizations:​img_5957.png?​nolink&​200 |}} + + Additionally in the qutrit case, if there exist of the JNR, the following configurations are possible: + * 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 |}}
numerical-range/generalizations/joint-numerical-range.txt · Last modified: 2018/11/04 09:56 by lpawela