Related papers: Entanglement and perfect quantum error correction
The key realisation which lead to the emergence of the new field of quantum information processing is that quantum mechanics, the theory that describes microscopic particles, allows the processing of information in fundamentally new ways.…
It is shown that, if the loss of entanglement along a quantum channel is sufficiently small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. Explicit bounds are obtained for…
We analyze the effect of a quantum error correcting code on the entanglement of encoded logical qubits in the presence of a dephasing interaction with a correlated environment. Such correlated reservoir introduces entanglement between…
We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…
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…
Creation of entanglement is considered theoretically and numerically in an ensemble of spin chains with dipole-dipole interaction between the spins. The unwanted effect of the long-range dipole interaction is compensated by the optimal…
The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be…
Entanglement is essential for quantum computation. However, disentanglement is also necessary. It can be achieved without the need of classical operations (measurements). Two examples are analyzed: the discrete Fourier transform and error…
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…
A simple and unifying method to show the perfect error-correcting condition is provided based on the quantum mutual information. The one-to-one parameterization of quantum operations and the properties of the quantum relative entropy are…
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 provide a systematic way of constructing entanglement-assisted quantum error-correcting codes via graph states in the scenario of preexisting perfectly protected qubits. It turns out that the preexisting entanglement can help beat the…
The ``entanglement of formation'' of a mixed state of a bipartite quantum system can be defined in terms of the number of pure singlets needed to create the state with no further transfer of quantum information. We find an exact formula for…
We show how procedures which can correct phase and amplitude errors can be directly applied to correct errors due to quantum entanglement. We specify general criteria for quantum error correction, introduce quantum versions of the Hamming…
Two new expressions for the entanglement fidelity recently introduced by Schumacher (LANL e-print quant-ph/9604023, to appear in Phys. Rev. A) are derived. These expressions show that it is the entanglement fidelity which must be maximized…
An important measure of bipartite entanglement is the entanglement of formation, which is defined as the minimum average pure state entanglement of all decompositions realizing a given state. A decomposition which achieves this minimum is…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems. A major benefit of our presentation is a rigorous description of entanglement of formation. In particular,…
Quantum error correction in general is experimentally challenging as it requires significant expansion of the size of quantum circuits and accurate performance of quantum gates to fulfill the error threshold requirement. Here we propose a…
We show how entanglement can be used to improve the estimation of an unknown transformation. Using entanglement is always of benefit, in improving either the precision or the stability of the measurement. Examples relevant for applications…