Information transmission with continuous variable quantum erasure channels

Changchun Zhong, Changhun Oh, and Liang Jiang

Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA

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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.

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[2] Yanbo Lou, Yinghui Lv, Jiabin Wang, Shengshuai Liu, and Jietai Jing, "Orbital Angular Momentum Multiplexed Deterministic All-Optical Quantum Erasure-Correcting Code", Physical Review Letters 132 4, 040601 (2024).

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