Related papers: On Protected Realizations of Quantum Information
Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
We introduce the notion of trace-norm isometric encoding and explore its implications for passive and active methods to protect quantum information against errors. Beside providing an operational foundations to the "subsystems principle"…
Encoding and manipulation of quantum information by means of topological degrees of freedom provides a promising way to achieve natural fault-tolerance that is built-in at the physical level. We show that this topological approach to…
Operator quantum error-correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error-correction, and provides a unified framework for topics such as quantum…
In certain situations the state of a quantum system, after transmission through a quantum channel, can be perfectly restored. This can be done by 'coding' the state space of the system before transmission into a 'protected' part of a larger…
Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system's ability to…
Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be…
Noiseless subsystems offer a general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. A paradigmatic class of error models displaying non-trivial symmetries emerges under…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the…
We incorporate active and passive quantum error-correcting techniques to protect a set of optical information modes of a continuous-variable quantum information system. Our method uses ancilla modes, entangled modes, and gauge modes (modes…
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment.…
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
We give a short introduction to operator quantum error correction. This is a new protocol for error correction in quantum computing that has brought the fundamental methods under a single umbrella, and has opened up new possibilities for…
This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known…