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Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the…
Shared entanglement can significantly amplify classical correlations between systems interacting over a limited quantum channel. A natural avenue is to use entanglement of the same dimension as the channel because this allows for unitary…
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…
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…
If entanglement is available, the error-correcting ability of quantum codes can be increased. We show how to optimize the minimum distance of an entanglement-assisted quantum error-correcting (EAQEC) code, obtained by adding ebits to a…
Construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic…
We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to an arbitrary entanglement-assisted block…
We investigate the problem of enhancement of mutual information by encoding classical data into entangled input states of arbitrary length and show that while there is a threshold memory or correlation parameter beyond which entangled…
We develop the theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional…
We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum…
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…
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,…
Finding the optimal encoding strategies can be challenging for communication using quantum channels, as classical and quantum capacities may be superadditive. Entanglement assistance can often simplify this task, as the…
We introduce a construction for entanglement-assisted quantum error-correcting codes (EAQECCs) that saturates the classical Singleton bound with less shared entanglement than any known method for code rates below $ \frac{k}{n} = \frac{1}{3}…
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…
The entanglement-assisted classical capacity of a quantum channel is known to provide the formal quantum generalization of Shannon's classical channel capacity theorem, in the sense that it admits a single-letter characterization in terms…
We consider the problem of transmitting classical and quantum information reliably over an entanglement-assisted quantum channel. Our main result is a capacity theorem that gives a three-dimensional achievable rate region. Points in the…
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…
Phenomena induced by the existence of entanglement, such as nonlocal correlations, exhibit characteristic properties of quantum mechanics distinguishing from classical theories. When entanglement is accompanied by classical communication,…
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)…