Narrow bounds for the quantum capacity of thermal attenuators

• Published in: Nature communications Vol. 9; no. 1; pp. 4339 - 9
• Main Authors: Rosati, Matteo, Mari, Andrea, Giovannetti, Vittorio
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 18.10.2018; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/400/482; 639/766/483/2802; 639/766/483/481; 639/766/483/640; Attenuation; Attenuators; Channels; Humanities and Social Sciences; multidisciplinary; Noise; Qubits (quantum computing); Science; Science (multidisciplinary); Thermal noise; Upper bounds
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-018-06848-0

Thermal attenuator channels model the decoherence of quantum systems interacting with a thermal bath, e.g., a two-level system subject to thermal noise and an electromagnetic signal traveling through a fiber or in free-space. Hence determining the quantum capacity of these channels is an outstanding open problem for quantum computation and communication. Here we derive several upper bounds on the quantum capacity of qubit and bosonic thermal attenuators. We introduce an extended version of such channels which is degradable and hence has a single-letter quantum capacity, bounding that of the original thermal attenuators. Another bound for bosonic attenuators is given by the bottleneck inequality applied to a particular channel decomposition. With respect to previously known bounds we report better results in a broad range of attenuation and noise: we can now approximate the quantum capacity up to a negligible uncertainty for most practical applications, e.g., for low thermal noise. Bounding the capacity of thermal attenuators would give a powerful instrument to describe decoherence occurring in optical fibres and free space links. Here, the authors improve on the existing upper bounds in the region of small thermal noise, which is of interest for quantum communication.