Related papers: Entanglement and perfect quantum error correction
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…
In the setting of entanglement-assisted quantum error-correcting codes (EAQECCs), the sender and the receiver have access to pre-shared entanglement. Such codes promise better information rates or improved error handling properties.…
The errors that arise in a quantum channel can be corrected perfectly if and only if the channel does not decrease the coherent information of the input state. We show that, if the loss of coherent information is small, then approximate…
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…
We provide a self-contained introduction for entanglement-assisted quantum error-correcting codes in this book chapter.
We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…
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…
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…
From the set of operators for errors and its correction code, we introduce the so-called complete unitary transformation. It can be used for encoding while the inverse of it can be applied for correcting the errors of the encoded qubit. We…
Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we…
Measurements are central in all quantitative sciences, and a fundamental challenge is to make observations without systematic measurement errors. This holds in particular for quantum information processing, where other error sources, such…
Quantum state exclusion is the task of determining which states from a given set a system was not prepared in. We provide a complete solution to optimal quantum state exclusion for arbitrary sets of pure states generated by finite groups,…
Entanglement-assisted quantum error-correcting codes (EAQECCs) to desired rate, error-correcting capability and maximum shared entanglement are constructed. Thus for a required rate $R$, required error-correcting capability to correct $t$…
We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…
We present a theoretical framework for state-adaptive quantum error correction that bridges the gap between quantum computing and error correction paradigms. By incorporating knowledge of quantum states into the error correction process, we…
We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and…
We show why and when entanglement is needed for quantum-enhanced precision measurements, and which type of entanglement is useful. We give a simple, intuitive construction that shows how entanglement transforms parallel estimation…
Entanglement-assisted quantum error correcting codes (EAQECCs) are a simple and fundamental class of codes. They allow for the construction of quantum codes from classical codes by relaxing the duality condition and using pre-shared…
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…
The concept of entanglement is at the core of the theory of quantum information. In this paper a criterion for unentanglement of quantum states is proposed and proved. This criterion is natural, practical and easy to check.