Efficiencies of logical Bell measurements on CSS codes with static linear optics

Abstract

We show how the efficiency of a logical Bell measurement (BM) can be calculated for arbitrary 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 $\frac{1}{2}$ 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 $\frac{1}{2}$ bound, to arbitrarily close to unity.

arXiv comment21 pages, 14 figures

References in corpus (24)

• Fundamental Limits of Repeaterless Quantum Communications
• General Benchmarks for Quantum Repeaters
• Stabilizer Codes and Quantum Error Correction
• Topological Quantum Distillation
• All photonic quantum repeaters
• On Bell measurements for teleportation
• Efficient long distance quantum communication
• Fundamental rate-loss tradeoff for optical quantum key distribution
• Maximum efficiency of a linear-optical Bell-state analyzer
• Quantum Repeater with Encoding
• Ultrafast and Fault-Tolerant Quantum Communication across Long Distances
• 3/4-efficient Bell measurement with passive linear optics and unentangled ancillae
• Loss Tolerant Optical Qubits
• Universal transversal gates with color codes - a simplified approach
• Rate-distance tradeoff and resource costs for all-optical quantum repeaters
• Ultrafast Long-Distance Quantum Communication with Static Linear Optics
• Error Correction and Degeneracy in Surface Codes Suffering Loss
• Long-range big quantum-data transmission
• Fundamental building block for all-optical scalable quantum networks
• Protecting an optical qubit against photon loss
• Ultrafast Fault-Tolerant Long-Distance Quantum Communication with Static Linear Optics
• Large-scale quantum networks based on graphs
• Nearly Deterministic Bell Measurement for Multiphoton Qubits and Its Application to Quantum Information Processing
• Investigating the optimality of ancilla-assisted linear optical Bell measurements

Cited by in corpus (5)

• Advances in Quantum Cryptography
• High photon-loss threshold quantum computing using GHZ-state measurements
• Error-correcting entanglement swapping using a practical logical photon encoding
• Parameter regimes for surpassing the PLOB bound with error-corrected qudit repeaters
• Memory-corrected quantum repeaters with adaptive syndrome identification