相关论文: Two families of Entanglement-assisted Quantum MDS …
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…
We consider classical message transmission under entanglement assistance for compound memoryless and arbitrarily varying quantum channels. In both cases, we prove general coding theorems together with corresponding weak converse bounds. In…
Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to…
The main conjecture on maximum distance separable (MDS) codes states that, execpt for some special cases, the maximum length of a q-ary linear MDS code is q+1. This conjecture does not hold true for near maximum distance separable codes…
Entanglement-assisted quantum error-correcting (EAQEC) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the…
We consider $(n,k)$ MDS-coded distributed storage over $\mathbb{F}_q$ with per-node storage $\alpha$ symbols. For the oblivious update problem, where a single message symbol changes and neither helpers nor the stale node know which, the…
A precise physical description and understanding of the classical dual content of quantum theory is necessary in many disciplines today: from concepts and interpretation to quantum technologies and computation. In this paper we investigate…
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We show that if no entanglement is envolved then…
In this paper, we show how to construct non-binary entanglement-assisted stabilizer quantum codes by using pre-shared entanglement between the sender and receiver. We also give an algorithm to determine the circuit for non-binary…
Recent advances have led towards first prototypes of quantum networks in which entanglement is distributed by sources producing bipartite entangled states. This raises the question of which states can be generated in quantum networks based…
Linear programming approaches have been applied to derive upper bounds on the size of classical codes and quantum codes. In this paper, we derive similar results for general quantum codes with entanglement assistance, including nonadditive…
Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum…
The mds (maximum distance separable) conjecture claims that a nontrivial linear mds $[n,k]$ code over the finite field $GF(q)$ satisfies $n \leq (q + 1)$, except when $q$ is even and $k = 3$ or $k = q- 1$ in which case it satisfies $n \leq…
Given a finite dimensional pure state transformation restricted by entanglement assisted local operations and classical communication (ELOCC), we derive minimum and maximum bounds on the entanglement of an ancillary catalyst that allows…
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…
For each odd prime power $q$, let $4 \leq n\leq q^{2}+1$. Hermitian self-orthogonal $[n,2,n-1]$ codes over $GF(q^{2})$ with dual distance three are constructed by using finite field theory. Hence, $[[n,n-4,3]]_{q}$ quantum MDS codes for $4…
The intersection ${\bf C}\bigcap {\bf C}^{\perp_H}$ of a linear code ${\bf C} \subset {\bf F}_{q^2}$ and its Hermitian dual ${\bf C}^{\perp_H}$ is called the Hermitian hull of this code. A linear code ${\bf C} \subset {\bf F}_{q^2}$…
For two non-communicating parties, quantum theory can give rise to probability distributions of outcomes that no local classical model can reproduce without communication. However, in the case of two-dimensional systems ($d=2$), it is known…
Over the past few decades, significant progress has been made in quantum information technology, from theoretical studies to experimental demonstrations. Revolutionary quantum applications are now in the limelight, showcasing the advantages…
In this paper, we study the Hermitian hulls of generalized Reed-Solomon (GRS) codes over finite fields. For a given class of GRS codes, by extending the length, increasing the dimension, and extending the length and increasing the dimension…