When the assignment map is completely positive

Abstract

Finding the general set of system-environment states for which the reduced dynamics of the system is completely positive (CP) is the subject of some recent works. An advance in this context appeared in [X. Lu, Phys. Rev. A 93, 042332 (2016)], where the problem has been solved for the case of CP assignment map. Here, we restate this result using the framework introduced in [J. M. Dominy et al., Quantum Inf. Process. 15, 465 (2016)]. This, we think, clarifies the mentioned result better and so leads to a generalization of it, straightforwardly.

7 pages. arXiv admin note: substantial text overlap with arXiv:1608.07412

References in corpus (8)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Vanishing quantum discord is necessary and sufficient for completely positive maps
• Completely Positive Maps and Classical Correlations
• Vanishing quantum discord is not necessary for completely-positive maps
• Reduced dynamical maps in the presence of initial correlations
• Completely positive maps within the framework of direct-sum decomposition of state space
• Structure of correlated initial states that guarantee completely positive reduced dynamics
• Reference state for arbitrary U-consistent subspace

Cited by in corpus (3)

• Markovianity of the reference state, complete positivity of the reduced dynamics, and monotonicity of the relative entropy
• Requiring linearity leads to complete positivity
• Positivity of the assignment map implies complete positivity of the reduced dynamics