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arXiv:2404.18586

How to surpass no-go limits in Gaussian quantum error correction and entangled Gaussian state distillation?

En-Jui Chang, Ching–Yi Lai

Published Apr 29, 2024• 0 citations
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Abstract

Gaussian quantum information processing with continuous-variable (CV) quantum information carriers holds significant promise for applications in quantum communication and quantum internet. However, applying Gaussian state distillation and quantum error correction (QEC) faces limitations imposed by no-go results concerning local Gaussian unitary operations and classical communications. This paper introduces a Gaussian QEC protocol that relies solely on local Gaussian resources. A pivotal component of our approach is CV gate teleportation using entangled Gaussian states, which facilitates the implementation of the partial transpose operation on a quantum channel. Consequently, we can efficiently construct a two-mode noise-polarized channel from two noisy Gaussian channels. Furthermore, this QEC protocol naturally extends to a nonlocal Gaussian state distillation protocol.

DOI
10.48550/arxiv.2404.18586

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Gaussian quantum information processing with continuous-variable (CV) quantum information carriers holds significant promise for applications in quantum communication and quantum internet. However, applying Gaussian state distillation and quantum error correction (QEC) faces limitations imposed by no-go results concerning local Gaussian unitary operations and classical communications. This paper introduces a Gaussian QEC protocol that relies solely on local Gaussian resources. A pivotal component of our approach is CV gate teleportation using entangled Gaussian states, which facilitates the implementation of the partial transpose operation on a quantum channel. Consequently, we can efficiently construct a two-mode noise-polarized channel from two noisy Gaussian channels. Furthermore, this QEC protocol naturally extends to a nonlocal Gaussian state distillation protocol.
Continuous Variable (CV) non-Gaussian resources are fundamental in the realization of quantum error correction for CV-based quantum communications and CV-based computing. In this work, we investigate the use of CV non-Gaussian states as quantum teleportation resource states in the context of the transmission of coherent and squeezed states through noisy channels. We consider an array of different non-Gaussian resource states, and compute the fidelity of state teleportation achieved for each resource. Our results show that the use of non-Gaussian states presents a significant advantage compared to the traditional resource adopted for CV teleportation; the Gaussian two-mode squeezed vacuum state. In fiber-based quantum communications, the range of quantum teleportation is increased by approximately 40% via the use of certain non-Gaussian states. In satellite-to-ground quantum communications, for aperture configurations consistent with the Micius satellite, the viable range of quantum teleportation is increased from 700 km to over 1200 km. These results represent a significant increase in the performance of pragmatic and realizable quantum communications in both terrestrial and space-based networks.
Quantum computation and communication are important branches of quantum information science. However, noise in realistic quantum devices fundamentally limits the utility of these quantum technologies. A conventional approach towards large-scale and fault-tolerant quantum information processing is to use multi-qubit quantum error correction (QEC), that is, to encode a logical quantum bit (or a logical qubit) redundantly over many physical qubits such that the redundancy can be used to detect errors. The required resource overhead associated with the use of conventional multi-qubit QEC schemes, however, is too high for these schemes to be realized at scale with currently available quantum devices. Recently, bosonic (or continuous-variable) quantum error correction has risen as a promising hardware-efficient alternative to multi-qubit QEC schemes. In this thesis, I provide an overview of bosonic QEC and present my contributions to the field. Specifically, I present the benchmark and optimization results of various single-mode bosonic codes against practically relevant excitation loss errors. I also demonstrate that fault-tolerant bosonic QEC is possible by concatenating a single-mode bosonic code with a multi-qubit error-correcting code. Moreover, I discuss the fundamental aspects of bosonic QEC using the framework of quantum communication theory. In particular, I present improved bounds on important communication-theoretic quantities such as the quantum capacity of bosonic Gaussian channels. Furthermore, I provide explicit bosonic error correction schemes that nearly achieve the fundamental performance limit set by the quantum capacity. I conclude the thesis with discussions on the importance of non-Gaussian resources for continuous-variable quantum information processing.
We will show that no distillation protocol for Gaussian quantum states exists that relies on (i) arbitrary local unitary operations that preserve the Gaussian character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local Gaussian unitary operations on two symmetric identically prepared copies. This analysis shows that unlike the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time, there is no such procedure in the case of continuous variables for Gaussian initial states and the above Gaussian operations. The ramifications for the distribution of Gaussian states over large distances will be outlined. We will also comment on the generality of the approach and sketch the most general form of a Gaussian local operation with classical communication in a bi-partite setting.
We propose a quantum repeater for continuous variable (CV) quantum optical states. Our repeater relies on an error correction protocol for loss on CV states based on CV teleportation and entanglement distillation via noiseless linear amplification. The error correction protocol is concatenated to preserve the same effective transmission coefficient for the quantum channel over increasing distance. The probability of successful operation of the repeater scales polynomially with distance. However, the protocol is limited by a trade-off between fidelity and probability of success.
Robust continuous-variable (CV) quantum information processing requires correcting realistic errors in bosonic systems, but all existing schemes rely on auxiliary Gottesman-Kitaev-Preskill (GKP) states which the preparation and operation are demanding in many platforms. In this work, we propose a novel CV quantum error correction (QEC) scheme that utilizes a broadly accessible resource: discrete-variable (DV) ancilla. Our scheme extracts information about CV displacement to the DV ancilla, measuring that allows counteracting the unwanted displacement error. We show that a simple single-qubit ancilla can already suppress CV infidelity by more than 20%. By concatenating with DV QEC codes, our scheme is robust against the physical errors in hybrid CV-DV systems, and yields a new class of oscillator-in-oscillator code that does not involve GKP states. Our work facilitates the implementation of CV QEC on realistic platforms.