Quantum capacity and codes for the bosonic loss-dephasing channel

Peter Leviant1, Qian Xu2, Liang Jiang2, and Serge Rosenblum1

1Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
2Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA

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Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the significant reduction of photon loss in recent bosonic qubit experiments suggests that dephasing errors should also be considered. However, a detailed understanding of the combined photon loss and dephasing channel is lacking. Here, we show that, unlike its constituent parts, the combined loss-dephasing channel is non-degradable, pointing towards a richer structure of this channel. We provide bounds for the capacity of the loss-dephasing channel and use numerical optimization to find optimal single-mode codes for a wide range of error rates.

In this paper, we shed light on the properties of bosonic (photonic) qubits undergoing photon loss errors and dephasing errors. This scenario is especially relevant in current quantum systems, where loss and dephasing often occur simultaneously and require active error correction. We show that the structure of the combined error channel is much more complex than its constituent parts. Nonetheless, we can provide bounds on how well information can be stored in the presence of loss and dephasing errors. We then use numerical optimization methods to find optimal error correction codes. One key finding is that encoded bosonic qubits have an optimal mean photon number for a large range of loss and dephasing error rates. This is in stark contrast with pure-loss or pure-dephasing errors, in which more photons always lead to better code performance.

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Cited by

[1] Aurélie Denys and Anthony Leverrier, "The $2T$-qutrit, a two-mode bosonic qutrit", arXiv:2210.16188.

[2] Victor V. Albert, "Bosonic coding: introduction and use cases", arXiv:2211.05714.

[3] Qian Xu, Guo Zheng, Yu-Xin Wang, Peter Zoller, Aashish A. Clerk, and Liang Jiang, "Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits", arXiv:2210.13406.

[4] Ludovico Lami and Mark M. Wilde, "Exact solution for the quantum and private capacities of bosonic dephasing channels", arXiv:2205.05736.

[5] Shahram Dehdashti, Janis Notzel, and Peter van Loock, "Quantum capacity of a deformed bosonic dephasing channel", arXiv:2211.09012.

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