Bounding the dimension of quantum systems via sequential projective measurements

Bounding the dimension of quantum systems with sequential measurements. The optimizations are obtained with MOSEK and can be changed whenever necessary. This repository has been used in the folowwing reference.

Requirements

• Python 3.6+
• CVXPY 1.0
• Seaborn

pip install -r requirements.txt

Example: Save the basis of moment matrices.

python save_basis.py \
    --dim 2 \
    --num_obs 2 \
    --len_seq 2 \
    --num_out 2 \
    --stop 10000 \
    --save_metadata True \
    --save_data True

Example: Compute the visibility of random moment matrices for a chosen dimension with given basis of moment matrices.

python save_visibility.py \
    --num_obs 3 \
    --len_seq 2 \
    --num_out 2 \
    --dimX 3 \
    --data_samp 10 \
    --dim_base 2 \
    --level 1 \
    --basis_filename data_basis/2-dim-3-num_obs-2-len_seq-2-num_out.npy

Example: Generate a random witness for between two specific dimensions in a chosen scenario

python random_witness_generator.py \
    --num_obs 3 \
    --len_seq 2 \
    --num_out 2 \
    --dimX 3 \
    --num_samples 100 \
    --dim_base 2 \
    --remove_last_out True \
    --basis_filename data/data_basis/2-dim-3-num_obs-2-len_seq-2-num_out-1-level.npy

Citing

@article{2021,
  title={Certifying dimension of quantum systems by sequential projective measurements},
  volume={5},
  ISSN={2521-327X},
  url={http://dx.doi.org/10.22331/q-2021-06-10-472},
  DOI={10.22331/q-2021-06-10-472},
  journal={Quantum},
  publisher={Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften},
  author={Sohbi, Adel and Markham, Damian and Kim, Jaewan and Quintino, Marco Túlio},
  year={2021},
  month={Jun},
  pages={472}
}

License

Apache License 2.0