Welcome!

This is a SageMath package for computing moment polytopes associated with finite-dimensional representations of compact and connected Lie groups, based on the algorithm proposed by Vergne and Walter (2014) (see also Walter (2014) for further detail).

Introduction

The following code solves the one-body quantum marginal problem for three qubits:

import moment_polytopes
import logging

# enable logging
logging.basicConfig(level=logging.DEBUG)

# compute three-qubit moment polytope in H-representation
three_qubits = (2, 2, 2)
hrepr = moment_polytopes.qmp.hrepr(three_qubits)
print(f"{len(hrepr.ieqs)} facets")

# convert to V-representation
vrepr = hrepr.vrepr()
print(f"{len(vrepr.vertices)} vertices")

You can install the latest version of this package as follows:

sage -i lrslib
sage -pip install git+git://github.com/qi-rub/moment_polytopes --upgrade

Now download the three_qubits.py example and run it via sage three_qubits.py. See Installation for further detail and troubleshooting.

We have used this package to compute moment polytopes associated with various Quantum Marginal Problems.

Documentation

• Installation
  • Troubleshooting
  • Mathematica Integration
• Quantum Marginal Problems
  • \(C(4,4,4)\)
  • \(C(2,2,3,12)\)
  • Further Examples
• Reference
  • Ressayre Elements
  • Representations
  • Quantum Marginal Problem
  • Polyhedra
  • Combinatorics
  • Third-Party Data
  • Internals
• Changelog
  • Version 1.1
  • Version 1.0
• License

Citation

If you use this software, please consider citing our article:

@article{moment_polytopes,
  author  = {Vergne, M. and Walter, M.},
  title   = {Inequalities for moment cones of finite-dimensional representations},
  journal = {Journal of Symplectic Geometry},
  year    = {2017},
  volume  = {15},
  number  = {4},
  pages   = {1209--1250},
  eprint  = {1410.8144},
  doi     = {10.4310/JSG.2017.v15.n4.a8},
  note    = {Software available at \url{https://qi-rub.github.io/moment_polytopes/}.},
}