Continuity of Quantum Channel Capacities

John Watrous

Changchun Zhong, Changhun Oh, Liang Jiang

Quantum capacity, as the key figure of merit for a given quantum channel, upper bounds the channel's ability in transmitting quantum information. Identifying different types of channels, evaluating the corresponding quantum capacity, and finding the capacity-approaching coding scheme are the major tasks in quantum communication theory. Quantum channel in discrete variables has been discussed enormously based on various error models, while error model in the continuous variable channel has been less studied due to the infinite dimensional problem. In this paper, we investigate a general continuous variable quantum erasure channel. By defining an effective subspace of the continuous variable system, we find a continuous variable random coding model. We then derive the quantum capacity of the continuous variable erasure channel in the framework of decoupling theory. The discussion in this paper fills the gap of a quantum erasure channel in continuous variable setting and sheds light on the understanding of other types of continuous variable quantum channels.

Masanori Ohya, Dėnes Petz, Noboru Watanabe

Taylor, Adam, Michael Hanks, Hyukjoon Kwon +1 more

Quantum capacity gives the fundamental limit of information transmission through a channel. However, evaluating the quantum capacities of a continuous-variable bosonic quantum channel, as well as finding an optimal code to achieve the optimal information transmission rate, is in general challenging. In this work, we derive the quantum capacity and entanglement-assisted quantum capacity of the bosonic continuous-variable erasure channel when subject to energy constraints. We then construct random codes based on scrambling information within the typical subspace of the encoding state and prove that these codes are asymptotically optimal up to a constant gap. Finally, using our random coding scheme we design a bosonic variation of the Hayden-Preskill protocol and find that information recovery depends on the ratio between the input and output modes. This is in contrast with the conventional discrete-variable scenario which requires only a fixed number of additional output qudits.

Elloá B. Guedes, Francisco de Assis, Rex A. C. Medeiros

Paulina Trybek, Jerzy Dajka

A quantum model describing ion channels from an information-theoretic perspective is considered. The information χ-capacity of an ion channel, treated as an information channel whose properties are modified by continuous quantum measurements, is investigated. The behavior of the χ-capacity is analyzed as a function of the measurement parameters, in particular the type of measured observable, the measurement duration, and the measurement strength. It is shown that the information χ-capacity exhibits qualitatively different behaviors depending on the measurement conditions, including regimes of rapid decay as well as regimes where it remains finite for long observation times. These results indicate that, within the considered model, continuous observation may significantly influence the information-theoretic properties of the effective ion-channel dynamics.