Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes
Filip Rozpędek, Kyungjoo Noh, Qian Xu, Saikat Guha, Liang Jiang
备注：
17 + 26 pages, 17 figures. v2: additional discussions of generation of higher-level-encoded states and of the secret-key rate performance metric; detailed simulation error analysis; restructuring of the sections with the new "Methods" section; published version. See also the related work by Fukui et al., arXiv:2011.14876
We propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous-variable GKP code encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.
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.
Quantum repeaters are essential ingredients for quantum networks that link distant quantum modules such as quantum computers and sensors. Motivated by distributed quantum computing and communication, quantum repeaters that relay discrete-variable quantum information have been extensively studied; while continuous-variable (CV) quantum information underpins a variety of quantum sensing and communication application, a quantum-repeater architecture for genuine CV quantum information remains largely unexplored. This paper reports a CV quantum-repeater architecture based on CV quantum teleportatio…
One of the most sought-after goals in experimental quantum communication is the implementation of a quantum repeater. The performance of quantum repeaters can be assessed by comparing the attained rate with the quantum and private capacity of direct transmission, assisted by unlimited classical two-way communication. However, these quantities are hard to compute, motivating the search for upper bounds. Takeoka, Guha and Wilde found the squashed entanglement of a quantum channel to be an upper bound on both these capacities. In general it is still hard to find the exact value of the squashed en…
Upper bounds on the secret-key-agreement capacity of a quantum channel serve as a way to assess the performance of practical quantum-key-distribution protocols conducted over that channel. In particular, if a protocol employs a quantum repeater, achieving secret-key rates exceeding these upper bounds is a witness to having a working quantum repeater. In this paper, we extend a recent advance [Liuzzo-Scorpo et al., arXiv:1705.03017] in the theory of the teleportation simulation of single-mode phase-insensitive Gaussian channels such that it now applies to the relative entropy of entanglement me…
We investigate a quantum repeater scheme for quantum key distribution based on the work by Muralidharan et al., Phys. Rev. Lett. 112, 250501 (2014). Our scheme extends that work by making use of error syndrome measurement outcomes available at the repeater stations. We show how to calculate the secret key rates for the case of optimizing the syndrome information, while the known key rate is based on a scenario of coarse-graining the syndrome information. We show that these key rates can surpass the Pirandola-Laurenza-Ottaviani-Banchi bound on secret key rates of direct transmission over lossy …
In quantum repeater protocols, measurements are performed in multiple relay points. Classical communications are used to convey the measurement results. It is important to improve the way of conveying the measurement results so that EPR pairs are not affected by noises during classical communications. One solution is execution in the blind mode. In the blind mode, correction operations of multiple ES operations and multiple EPP operations are performed in a lump after EPR pairs are shared between the sender and the receiver. That is, the following quantum operations are performed without perfo…
Quantum repeaters are indispensable for high-rate, long-distance quantum communications. The vision of a future quantum internet strongly hinges on realizing quantum repeaters in practice. Numerous repeaters have been proposed for discrete-variable (DV) single-photon-based quantum communications. Continuous variable (CV) encodings over the quadrature degrees of freedom of the electromagnetic field mode offer an attractive alternative. For example, CV transmission systems are easier to integrate with existing optical telecom systems compared to their DV counterparts. Yet, repeaters for CV have …
We consider the explicit construction of resource states for measurement-based quantum information processing. We concentrate on special-purpose resource states that are capable to perform a certain operation or task, where we consider unitary Clifford circuits as well as non-trace preserving completely positive maps, more specifically probabilistic operations including Clifford operations and Pauli measurements. We concentrate on $1 \to m$ and $m \to 1$ operations, i.e. operations that map one input qubit to $m$ output qubits or vice versa. Examples of such operations include encoding and dec…
Higher transmission loss diminishes the performance of optical communication|be it the rate at which classical or quantum data can be sent reliably, or the secure key generation rate of quantum key distribution (QKD). Loss compounds with distance|exponentially in an optical fiber, and inverse-square with distance for a free-space channel. In order to boost classical communication rates over long distances, it is customary to introduce regenerative relays at intermediate points along the channel. It is therefore natural to speculate whether untended regenerative stations, such as phase-insensit…
The coherent-state qubit is a promising candidate for optical quantum information processing due to its nearly-deterministic nature of the Bell-state measurement (BSM). However, its non-orthogonality incurs difficulties such as failure of the BSM. One may use a large amplitude ($α$) for the coherent state to minimize the failure probability, but the qubit then becomes more vulnerable to dephasing by photon loss. We propose a hardware-efficient concatenated BSM (CBSM) scheme with modified parity encoding using coherent states with reasonably small amplitudes ($|α| \lessapprox 2$), which simulta…
Quantum communications promises reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks, we need to determine the optimal point-to-point rates that are achievable by two remote parties at the ends of a quantum channel, without restrictions on their local operations and classical communication, which can be unlimited and two-way. These two-way assisted capacities represent the ultimate rates that are reachable without quantum repeaters. By constructing an upperbound based on the relative entropy of entang…
The Gottesman-Kitaev-Preskill (GKP) code offers the possibility to encode higher-dimensional qudits into individual bosonic modes with, for instance, photonic excitations. Since photons enable the reliable transmission of quantum information over long distances and since GKP states subject to photon loss can be recovered to some extent, the GKP code has found recent applications in theoretical investigations of quantum communication protocols. While previous studies have primarily focused on GKP qubits, the possible practical benefits of higher-dimensional GKP qudits are hitherto widely unexpl…
We investigate cat codes that can correct multiple excitation losses and identify two types of logical errors: bit-flip errors due to excessive excitation loss and dephasing errors due to quantum back-action from the environment. We show that selected choices of logical subspace and coherent amplitude can efficiently reduce dephasing errors. The trade-off between the two major errors enables optimized performance of cat codes in terms of minimized decoherence. With high coupling efficiency, we show that one-way quantum repeaters with cat codes feature drastically boosted secure communication r…
Using a technique based on quantum teleportation, we simplify the most general adaptive protocols for key distribution, entanglement distillation and quantum communication over a wide class of quantum channels in arbitrary dimension. Thanks to this method, we bound the ultimate rates for secret key generation and quantum communication through single-mode Gaussian channels and several discrete-variable channels. In particular, we derive exact formulas for the two-way assisted capacities of the bosonic quantum-limited amplifier and the dephasing channel in arbitrary dimension, as well as the sec…
The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of both the ultimate capacities of quantum channels and the efficiency of imperfect quantum repeaters. In this work, using a recently developed node-splitting technique which introduces internal losses and noise into repeater devices, we present achievable end-to-end rates for noisy-repeater quantum networks. These are obtained by extending the coherent and re…
Quantum error correction is essential for robust quantum information processing with noisy devices. As bosonic quantum systems play a crucial role in quantum sensing, communication, and computation, it is important to design error correction codes suitable for these systems against various different types of noises. While most efforts aim at protecting qubits encoded into the infinite dimensional Hilbert space of a bosonic mode, [Phys. Rev. Lett. 125, 080503 (2020)] proposed an error correction code to maintain the infinite-dimensional-Hilbert-space nature of bosonic systems by encoding a sing…
We consider quantum and private communications assisted by repeaters, from the basic scenario of a single repeater chain to the general case of an arbitrarily-complex quantum network, where systems may be routed through single or multiple paths. In this context, we investigate the ultimate rates at which two end-parties may transmit quantum information, distribute entanglement, or generate secret keys. These end-to-end capacities are defined by optimizing over the most general adaptive protocols that are allowed by quantum mechanics. Combining techniques from quantum information and classical …
In quantum mechanics, a fundamental law prevents quantum communications to simultaneously achieve high rates and long distances. This limitation is well known for point-to-point protocols, where two parties are directly connected by a quantum channel, but not yet fully understood in protocols with quantum repeaters. Here we solve this problem bounding the ultimate rates for transmitting quantum information, entanglement and secret keys via quantum repeaters. We derive single-letter upper bounds for the end-to-end capacities achievable by the most general (adaptive) protocols of quantum and pri…
University of Sydney（悉尼大学）；Chalmers University of Technology（查尔姆斯理工大学）；Freie Universität Berlin（柏林自由大学）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料能源中心）；École Normale Supérieure, PSL University（巴黎高等师范学院，PSL大学）
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