Related papers: Entanglement-assisted Coding Theory
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard…
The theory of entanglement-assisted quantum error-correcting codes (EAQECCs) is a generalization of the standard stabilizer quantum error-correcting codes, which can be possibly constructed from any classical codes by relaxing the duality…
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 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…
Code concatenation combines two or more component codes to design larger codes with greater noise resilience. Introducing entanglement assistance to concatenated codes provides a further advantage in terms of improved error rates and…
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…
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,…
The entanglement-assisted stabilizer formalism provides a useful framework for constructing quantum error-correcting codes (QECC), which can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting…
We study a linear computation problem over a quantum multiple access channel (LC-QMAC), where $S$ servers share an entangled state and separately store classical data streams $W_1,\cdots, W_S$ over a finite field $\mathbb{F}_d$. A user aims…
The entanglement-assisted (EA) formalism allows arbitrary classical linear codes to transform into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this…
We provide a self-contained introduction for entanglement-assisted quantum error-correcting codes in this book chapter.
Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing entanglement-assisted quantum maximum distance separable…
In the previous research by Grassl, Huber and Winter, they proved a theorem which can make entanglement-assisted quantum error-correcting codes (EAQECC) from general quantum error-correcting codes (QECC). In this paper, we prove that the…
Entanglement-assisted quantum error-correcting (EAQEC) codes make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQEC code from any classical linear code,…
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is the code resulting from exchanging the original code's information qubits with its ebits. To introduce this notion, we show how entanglement-assisted (EA)…
Using convex optimization, we propose entanglement-assisted quantum error correction procedures that are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error correction method achieves…
Quantum error correction is fundamentally important for quantum information processing and computation. Quantum error correction codes have been studied and constructed since the pioneering papers of Shor and Steane. Optimal (called MDS)…
In this paper we introduce a universal operator theoretic framework for quantum fault tolerance. This incorporates a top-down approach that implements a system-level criterion based on specification of the full system dynamics, applied at…
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…
By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality…