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numerical-range:generalizations:joint-numerical-range

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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 Both sides previous revision Previous revision 2019/10/01 13:02 rkukulski 2019/10/01 13:01 plewandowska 2019/10/01 12:55 plewandowska 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 Next revision Previous revision 2019/10/01 13:02 rkukulski 2019/10/01 13:01 plewandowska 2019/10/01 12:55 plewandowska 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 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 )].