Quantum Correlations, Local Interactions and Error Correction

Abstract

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 nonlocal 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 it non-local interactions.

submitted to The Physical Review A

References in corpus (10)

• Mixed State Entanglement and Quantum Error Correction
• Elementary gates for quantum computation
• Concentrating Partial Entanglement by Local Operations
• Good Quantum Error-Correcting Codes Exist
• Quantum privacy amplification and the security of quantum cryptography over noisy channels
• Multiple Particle Interference and Quantum Error Correction
• Information-theoretic aspects of quantum inseparability of mixed states
• Quantum Physics and Computers
• Quantum error correction in the presence of spontaneous emission
• Error Correction in Quantum Communication

Cited by in corpus (6)

• Entanglement Measures and Purification Procedures
• The Role of Relative Entropy in Quantum Information Theory
• Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
• Basics of Quantum Computation
• Landauer's erasure, error correction and entanglement
• Quantum Euler relation for local measurements