aqora

Quantum correlations, local interactions and error correction

Vlatko Vedral, M. A. Rippin, Martin Bodo Plenio

We consider the effects of local interactions upon quantum mechanically entangled systems. In particular we demonstrate that non-local correlations cannot increase through local operations on any of the subsystems, but that through the use of quantum error correction methods, correlations can be maintained. We provide two mathematical proofs that local general measurements cannot increase correlations, and also derive general conditions for quantum error correcting codes. Using these we show that local quantum error correction can preserve non-local features of entangled quantum systems. We also demonstrate these results by use of specific examples employing correlated optical cavities interacting locally with resonant atoms. By way of counter example, we also describe a mechanism by which correlations can be increased, which demonstrates the need for non-local interactions.We consider the effects of local interactions upon quantum mechanically entangled systems. In particular we demonstrate that non-local correlations cannot increase through local operations on any of the subsystems, but that through the use of quantum error correction methods, correlations can be maintained. We provide two mathematical proofs that local general measurements cannot increase correlations, and also derive general conditions for quantum error correcting codes. Using these we show that local quantum error correction can preserve non-local features of entangled quantum systems. We also demonstrate these results by use of specific examples employing correlated optical cavities interacting locally with resonant atoms. By way of counter example, we also describe a mechanism by which correlations can be increased, which demonstrates the need for non-local interactions.

arXiv:quant-ph/9608030Journal of Modern OpticsNov 1, 199713 citations

Quantum Error Correction of Time-correlated Errors

Feng Lu, Dan Cristian Marinescu

arXiv:quant-ph/0605226Quantum Information ProcessingJul 7, 20077 citations

Non-Equilibrium Thermo Field Dynamics and Its Application to Error-Correction for Spatially Correlated Quantum Errors

Toshihico Arimitsu

The framework of the canonical operator formalism for dissipative and/or stochastic quantum systems named non-equilibrium thermo field dynamics (NETFD) is presented in a self-contained manner. As an application of the formalism, a model of noisy-channel which is under the influence of spatially correlated quantum Brownian motion is investigated within the framework of NETFD. It is shown that errors due to spatially correlated noises can be corrected by the quantum error-correction code and error-correction procedure prepared for those for independent noises.The framework of the canonical operator formalism for dissipative and/or stochastic quantum systems named non-equilibrium thermo field dynamics (NETFD) is presented in a self-contained manner. As an application of the formalism, a model of noisy-channel which is under the influence of spatially correlated quantum Brownian motion is investigated within the framework of NETFD. It is shown that errors due to spatially correlated noises can be corrected by the quantum error-correction code and error-correction procedure prepared for those for independent noises.

Interdisciplinary Information SciencesJan 1, 20091 citation

Efficient quantum error correction for fully correlated noise

Chi-Kwong Li, Mikio Nakahara, Yiu‐Tung Poon +2 more

arXiv:1104.4750Physics Letters AJul 25, 201118 citations

Error Correction for Continuous Quantum Variables

Samuel L. Braunstein

Springer eBooksJan 1, 199814 citations

Title: Universal Quantum Error Correction for Non-Linear Quantum Systems

Jincheng Zhang

The inherent fragility of quantum systems necessitates robust error correction to ensure reliable computation. Current error correction techniques often struggle with complex, non-linear quantum systems, demanding substantial overhead and hindering performance. This paper proposes a novel quantum error correction scheme predicated on entanglement and quantum correlations, aiming to minimize overhead while preserving high accuracy. The core mechanism centers around a dynamically adjusted encoding scheme that leverages these correlations to proactively detect and correct errors. We present a theoretical framework outlining the scheme's operation, including key mathematical operations and analysis. We demonstrate the effectiveness of this approach through simulations, illustrating significant reductions in overhead compared to existing methods for specific non-linear quantum systems. The study also explores the potential for adaptation and scalability to larger systems.The inherent fragility of quantum systems necessitates robust error correction to ensure reliable computation. Current error correction techniques often struggle with complex, non-linear quantum systems, demanding substantial overhead and hindering performance. This paper proposes a novel quantum error correction scheme predicated on entanglement and quantum correlations, aiming to minimize overhead while preserving high accuracy. The core mechanism centers around a dynamically adjusted encoding scheme that leverages these correlations to proactively detect and correct errors. We present a theoretical framework outlining the scheme's operation, including key mathematical operations and analysis. We demonstrate the effectiveness of this approach through simulations, illustrating significant reductions in overhead compared to existing methods for specific non-linear quantum systems. The study also explores the potential for adaptation and scalability to larger systems.

Aug 31, 20260 citations

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