Restricted numerical shadow

Introduction

Combining the ideas of the restricted numerical range with the numerical shadow one is led in a natural way to the definition of a restricted numerical shadow, \[ P^R_A(z) \coloneqq \int_{R} {\rm d} \mu(\psi) \ \delta\Bigl( z-\langle \psi|A|\psi\rangle\Bigr), \] where $R$ is a selected subset of ${\Omega}_d$, the set of dimension $d$ pure quantum states.

Examples

For a full list of examples of restricted numerical shadows, go here: examples

Interesting shadows

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Table of contents

• Real numerical shadow
• Product numerical shadow
• Entangled numerical shadow
• GHZ numerical shadow
• W numerical shadow
• $SU(2)$ coherent states