2018/12/21 by Frank L. Schmidt, Frank Schmidt, Peter van Loock
Computer Science · Mathematics · Physics and Astronomy · #Arithmetic #Binary number #Discrete mathematics #Mathematics #Neural Networks and Reservoir Computing #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum mechanics #Qubit #quant-ph
paper · pdf · doi:10.1103/physreva.99.062308
published as Phys. Rev. A 99, 062308 (2019) · 21 pages, 14 figures
arxiv created 2018/12/21 · openalex created_date 2019/01/01 · openalex publication_date 2019/06/10 · arxiv updated 2019/06/19 · openalex updated_date 2026/08/05
We show how the efficiency of a logical Bell measurement (BM) can be calculated for arbitrary Calderbank-Shor-Steane (CSS) codes with the experimentally important constraint of using only transversal static linear-optical BMs on the physical single-photon qubit level. For this purpose, we utilize the codes' description in terms of stabilizers in order to calculate general efficiencies for the loss-free case, but also for specific cases including photon loss. These efficiencies can be, for instance, used for obtaining transmission rates of all-optical quantum repeaters. In the loss-free case, we demonstrate that the important class of CSS codes with identical physical-qubit support for the two logical Pauli (Z and X) operators can only achieve a logical BM efficiency of (1)/(2) if one always employs the same ancilla-free static linear optical BMs on the physical level. We apply our methods to various CSS codes including two-dimensional planar color and planar surface codes. We then find that in many cases, the fixed use of the standard linear-optical BM for all physical BMs is suboptimal and performing linear-optical transformations before doing the standard linear-optical BM (still without any ancillary photons and without any feedforward) can increase the efficiency enormously. In fact, using this generalization in the no-loss (or sometimes also in the low-loss) case allows us, on the one hand, to improve the logical BM efficiency of quantum parity codes compared to previously known results and, on the other hand, it also enables us to enhance the efficiency of two-dimensional planar color codes, whose efficiency is otherwise subject to the above (1)/(2) bound, to arbitrarily close to unity.