Related papers: One way quantum repeaters with quantum Reed-Solomo…
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…
We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…
A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name of quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the…
A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n,k,d]] = [[2^r, 2^r - C(r,t) - 2 sum_{i=0}^{t-1} C(r,i), 2^t + 2^{t-1} ]].
An important family of quantum codes is the quantum maximum-distance-separable (MDS) codes. In this paper, we construct some new classes of quantum MDS codes by generalized Reed-Solomon (GRS) codes and Hermitian construction. In addition,…
Folded Reed-Solomon codes, introduced by Guruswami and Rudra in 2007, have been shown to achieve the information-theoretically best possible trade-off between the rate of a code and the error-correction radius. In 2024, Bergamaschi,…
This paper considers quantum network coding, which is a recent technique that enables quantum information to be sent on complex networks at higher rates than by using straightforward routing strategies. Kobayashi et al. have recently showed…
Quantum communication enables the implementation of tasks that are unachievable with classical resources. However, losses on the communication channel preclude the direct long-distance transmission of quantum information in many relevant…
Quantum optical states are fragile and can become corrupted when passed through a lossy communication channel. Unlike for classical signals, optical amplifiers cannot be used to recover quantum signals. Quantum repeaters have been proposed…
The quantum repeater protocol is a promising approach to implement long-distance quantum communication and large-scale quantum networks. A key idea of the quantum repeater protocol is to use long-lived quantum memories to achieve efficient…
This paper proposes a new class of multi-dimensional nonsystematic Reed-Solomon codes that are constructed based on the multi-dimensional Fourier transform over a finite field. The proposed codes are the extension of the nonsystematic…
Define the codewords of the Tensor Reed-Muller code $\mathsf{TRM}(r_1,m_1;r_2,m_2;\dots;r_t,m_t)$ to be the evaluation vectors of all multivariate polynomials in the variables $\left\{x_{ij}\right\}_{i=1,\dots,t}^{j=1,\dots m_i}$ with…
Quantum repeaters (QRs) provide a way of enabling long distance quantum communication by establishing entangled qubits between remote locations. We investigate a new approach to QRs in which quantum information can be faithfully transmitted…
Let $\mathbb{F}_q$ be a finite field with $q=p^{e}$ elements, where $p$ is a prime number and $e \geq 1$ is an integer. In this paper, by means of generalized Reed-Solomon (GRS) codes, we construct two new classes of quantum…
Scalable quantum networks require quantum repeaters to overcome major challenges such as photon loss and decoherence in long-distance quantum communication. In this paper, we present a cavity-magnon quantum repeater architecture that…
Within the framework of quantum memory channels we introduce the notion of repeatability of quantum channels. In particular, a quantum channel is called repeatable if there exist a memory device implementing the same channel on each…
The field of quantum communications promises the faithful distribution of quantum information, quantum entanglement, and absolutely secret keys. However, the highest rates of these tasks are fundamentally limited by the transmission…
Long-distance quantum communication necessitates the use of quantum repeaters, which typically include highly coherent quantum memories. We provide a theoretical analysis of the secret key rates for a quantum repeater system incorporating…
Reed-Solomon codes are a classic family of error-correcting codes consisting of evaluations of low-degree polynomials over a finite field on some sequence of distinct field elements. They are widely known for their optimal unique-decoding…
The classical family of Reed-Solomon codes consist of evaluations of polynomials over the finite field $\mathbb{F}_q$ of degree less than $k$, at $n$ distinct field elements. These are arguably the most widely used and studied codes, as…