Related papers: Entanglement-assisted quantum error-correcting cod…
Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting codes (AEAQECCs) from Calderbank-Shor-Steane (CSS) construction. In general, it's difficult to determine the required number of…
We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as…
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…
Entanglement-assisted quantum (QUENTA) 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 traditional…
In this dissertation, I present a general method for studying quantum error correction codes (QECCs). This method not only provides us an intuitive way of understanding QECCs, but also leads to several extensions of standard QECCs,…
Entanglement-assisted concatenated quantum codes (EACQCs), constructed by concatenating two quantum codes, are proposed. These EACQCs show several advantages over the standard concatenated quantum codes (CQCs). Several families of EACQCs…
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,…
We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is $c$, the…
Though the entanglement-assisted formalism provides a universal connection between a classical linear code and an entanglement-assisted quantum error-correcting code (EAQECC), the issue of maintaining large amount of pure maximally…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
This paper develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum…
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…
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is defined from the orthogonal group of a simplified stabilizer group. From the Poisson summation formula, this duality leads to the MacWilliams identities and…
We study the subfield subcodes of projective Reed-Solomon codes and their duals: we provide bases for these codes and estimate their parameters. With this knowledge, we can construct symmetric and asymmetric entanglement-assisted quantum…
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…
Absolutely maximally entangled (AME) states are pure multi-partite generalizations of the bipartite maximally entangled states with the property that all reduced states of at most half the system size are in the maximally mixed state. AME…
We introduce a Steane-like enlargement procedure for entanglement-assisted quantum error-correcting codes (EAQECCs) obtained by considering Euclidean inner product. We give formulae for the parameters of these enlarged codes and apply our…
A new type of link between geometry of symplectic group and entanglement-assisted (EA) quantum error-correcting codes (EAQECCs) is presented. Relations of symplectic subspaces and quaternary additive codes concerning parameters of EAQECCs…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to…