相关论文: Two families of Entanglement-assisted Quantum MDS …
In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes additive codes. We study MDS codes in this setting and define…
This work explores entanglement-assisted communication, where quantum entanglement resources enable the transmission of classical information at an enhanced rate. We consider a scenario where entanglement is distributed ahead of time based…
Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…
Brun, Devetak, and Hsieh [Science 314, 436 (2006)] demonstrated that pre-shared entanglement between sender and receiver enables quantum communication protocols that have better parameters than schemes without the assistance of…
Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is--paradoxically--itself prone to errors. Decoherence free subspaces, on the other hand,…
There is a connection between classical codes, highly entangled pure states (called k-uniform or absolutely maximally entangled (AME) states), and quantum error correcting codes (QECCs). This leads to a systematic method to construct…
Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the…
Under two-party deterministic dense-coding, Alice communicates (perfectly distinguishable) messages to Bob via a qudit from a pair of entangled qudits in pure state |Psi>. If |Psi> represents a maximally entangled state (i.e., each of its…
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 investigate additive codes, defined as $\mathbb{F}_q$-linear subspaces $C \subseteq \mathbb{F}_{q^h}^n$ of length $n$ and dimension $r$ over $\mathbb{F}_q$. An additive code is said to be of type $[n, r/h, d]_q^h$, where $d$ denotes the…
The hull of linear codes plays an important role in quantum information and coding theory. In the present paper, by investigating the Galois hulls of generalized Reed-Solomon (GRS) codes and extended GRS codes over the finite field Fq, we…
It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this…
We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and…
For a linear code $C$ over a finite field, if its dual code $C^{\perp}$ is equivalent to itself, then the code $C$ is said to be {\it isometry-dual}. In this paper, we first confirm a conjecture about the isometry-dual MDS elliptic codes…
In this paper, a linear $\ell$-intersection pair of codes is introduced as a generalization of linear complementary pairs of codes. Two linear codes are said to be a linear $\ell$-intersection pair if their intersection has dimension…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
We construct quantum MDS codes with parameters $ [\![ q^2+1,q^2+3-2d,d ]\!] _q$ for all $d \leqslant q+1$, $d \neq q$. These codes are shown to exist by proving that there are classical generalised Reed-Solomon codes which contain their…
We introduce two dual, purely quantum protocols: for entanglement distillation assisted by quantum communication (``mother'' protocol) and for entanglement assisted quantum communication (``father'' protocol). We show how a large class of…
New families of maximum distance separable (MDS) codes are constructed from elliptic curves by exploiting their group structures. In contrast to classical constructions based on divisors supported at a single rational point, the proposed…
The development of quantum networks (QNs) relies on efficient mechanisms for distributing entanglement among multiple quantum users (QUs) under practical system constraints. This paper investigates the problem of entanglement rate…