Related papers: New entanglement-assisted quantum codes from negac…
We explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer code uses CSS-type quantum Reed-Solomon code and the inner code uses a set of special quantum codes. In the field 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,…
The hypergraph product (HGP) construction of quantum error-correcting codes (QECC) offers a general and explicit method for building a QECC from two classical codes, thereby paving the way for the discovery of good quantum low-density…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…
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…
Entanglement purification protocols (EPP) and quantum error-correcting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some…
Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a…
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
A fundamental requirement for enabling fault-tolerant quantum information processing is an efficient quantum error-correcting code (QECC) that robustly protects the involved fragile quantum states from their environment. Just as classical…
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…
New families of classical and quantum optimal negacyclic convolutional codes are constructed in this paper. This optimality is in the sense that they attain the classical (quantum) generalized Singleton bound. The constructions presented in…
It is commonly believed that logical states of quantum error-correcting codes have to be highly entangled such that codes capable of correcting more errors require more entanglement to encode a qubit. Here, we show that the validity of this…
Demonstrating how long-range entangled states are born from product states has gained much attention, which is not only important for quantum technology but also provides an unconventional tool in characterizing and classifying exotic…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
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…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…
We introduce the notion of entanglement of subspaces as a measure that quantify the entanglement of bipartite states in a randomly selected subspace. We discuss its properties and in particular we show that for maximally entangled subspaces…
Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum…