Optimizing quantum codes with an application to the loss channel with partial erasure information

Abstract

Quantum error correcting codes (QECCs) are the means of choice whenever quantum systems suffer errors, e.g., due to imperfect devices, environments, or faulty channels. By now, a plethora of families of codes is known, but there is no universal approach to finding new or optimal codes for a certain task and subject to specific experimental constraints. In particular, once found, a QECC is typically used in very diverse contexts, while its resilience against errors is captured in a single figure of merit, the distance of the code. This does not necessarily give rise to the most efficient protection possible given a certain known error or a particular application for which the code is employed. In this paper, we investigate the loss channel, which plays a key role in quantum communication, and in particular in quantum key distribution over long distances. We develop a numerical set of tools that allows to optimize an encoding specifically for recovering lost particles both deterministically and probabilistically, where some knowledge about what was lost is available, and demonstrate its capabilities. This allows us to arrive at new codes ideal for the distribution of entangled states in this particular setting, and also to investigate if encoding in qudits or allowing for non-deterministic correction proves advantageous compared to known QECCs. While we here focus on the case of losses, our methodology is applicable whenever the errors in a system can be characterized by a known linear map.

28 pages, 14 figures, changed title; version accepted in Quantum

References in corpus (22)

• Quantum Repeaters with Photon Pair Sources and Multi-Mode Memories
• Long term performance of the SwissQuantum quantum key distribution network in a field environment
• A Survey on Quantum Channel Capacities
• Multiplexed Memory-Insensitive Quantum Repeaters
• Experimental entanglement of a six-photon symmetric Dicke state
• Long-distance entanglement purification for quantum communication
• 3/4-efficient Bell measurement with passive linear optics and unentangled ancillae
• Deterministic Dicke state preparation with continuous measurement and control
• A Quantum Network Node with Crossed Optical Fibre Cavities
• Heralded Storage of a Photonic Quantum Bit in a Single Atom
• Nondestructive detection of photonic qubits
• Optimal approach to quantum communication using dynamic programming
• Qudit surface codes and gauge theory with finite cyclic groups
• Nonadditive quantum error-correcting code
• A simple family of nonadditive quantum codes
• Asymptotic adaptive bipartite entanglement distillation protocol
• Loss Tolerant Linear Optical Quantum Memory By Measurement Based Quantum Computing
• Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles
• Detecting an Itinerant Optical Photon Twice without Destroying It
• Freely Scalable Quantum Technologies using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links
• More Efficient Purifying scheme via Controlled- Controlled NOT Gate
• Dicke States Generation via Selective Interactions in Dicke-Stark Model