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 |
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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