On classical and quantum liftings

Abstract

We analyze the procedure of lifting in classical stochastic and quantum systems. It enables one to `lift' a state of a system into a state of `system+reservoir'. This procedure is important both in quantum information theory and the theory of open systems. We illustrate the general theory of liftings by a particular class related to so called circulant states.

25 pages

References in corpus (17)

• Quantum cloning
• Negative entropy and information in quantum mechanics
• Vanishing quantum discord is necessary and sufficient for completely positive maps
• Non-Markovian quantum dynamics: local versus non-local
• Completely Positive Maps and Classical Correlations
• Physical accessibility of non-completely positive maps
• Long-time memory in non-Markovian evolutions
• Bound entanglement in the magic simplex of two--qutrits
• On circulant states with positive partial transpose
• Constructing new optimal entanglement witnesses
• Entanglement, Quantum Entropy and Mutual Information
• Geometry of quantum states: new construction of positive maps
• Spectral conditions for entanglement witnesses vs. bound entanglement
• A class of positive atomic maps
• Generalized Circulant Densities and a Sufficient Condition for Separability
• States of quantum systems and their liftings
• Entanglements and compound states in quantum information theory