Related papers: Entanglement-Assisted and Subsystem Quantum Codes:…
In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian curve. We cover Steane-enlargement of both usual one-point Hermitian codes and of order bound improved Hermitian codes. In…
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
Quantum information technology has the potential to revolutionize computing, communications, and security. To fully realize its potential, quantum processors with millions of qubits are needed, which is still far from being accomplished.…
We demonstrate a novel scheme to generate frequency-entangled qudits with dimension number higher than 10 and to distribute them over optical fibers of 15 km in total length. This scheme combines the technique of spectral engineering of…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
A key goal of quantum communication is to determine the maximum number of bits shared between two quantum systems. An important example of this is in entanglement based quantum key distribution (QKD) schemes. A realistic treatment of this…
We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted…
Nested code pairs play a crucial role in the construction of ramp secret sharing schemes [Kurihara et al. 2012] and in the CSS construction of quantum codes [Ketkar et al. 2006]. The important parameters are (1) the codimension, (2) the…
In this paper, we provide a framework for constructing entanglement-assisted quantum error-correcting codes (EAQECCs) from classical additive codes over a finite commutative local Frobenius ring $\mathcal{R}$. At the heart of the framework,…
Reed--Solomon codes are a well--studied code class which fulfill the Singleton bound with equality. However, their length is limited to the size $q$ of the underlying field $\mathbb{F}_q$. In this paper we present a code construction which…
We study compression strategies for multipartite entanglement distribution under uncertainty in the partitioning of the quantum state. When the partition is not known at the time of state preparation, we show that a joint design of the…
We define a virtual projection of a Reed-Solomon code $RS(q^{l},n,k)$ to an $RS(q,n,k)$ Reed-Solomon code. A new probabilistic decoding algorithm that can be used to perform fractional decoding beyond the $\alpha$- decoding radius is…
Mutually unbiased bases have been extensively studied in the literature and are simple and effective in quantum key distribution protocols, but they are not optimal. Here equiangular spherical codes are introduced as a more efficient and…
Multiple photonic degrees of freedom can be explored to generate high-dimensional quantum states; commonly referred to as `qudits'. Qudits offer several advantages for quantum communications, including higher information capacity, noise…
Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains…
Superdense coding proved that entanglement-assisted quantum communications can improve the data transmission rates compared to classical systems. It allows sending 2 classical bits between the parties in exchange of 1 quantum bit and a…
We study covering problems in Hamming and Grassmann spaces through a unified coding-theoretic and information-theoretic framework. Viewing covering as a form of quantization in general metric spaces, we introduce the notion of the average…
We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two new methods to achieve this, the first method involving…
With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by…