Markov property and strong additivity of von Neumann entropy for graded quantum systems

Abstract

It is easy to verify the equivalence of the quantum Markov property and the strong additivity of entropy for graded quantum systems as well. However, the structure of Markov states for graded systems is different from that for tensor product systems. For three-composed graded systems there are U(1)-gauge invariant Markov states whose restriction to the pair of marginal subsystems is non-separable.

14 pages, to appear J. Math. Phys

References in corpus (8)

• Universality of Entropy Scaling in 1D Gap-less Models
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Monotonicity of quantum relative entropy revisited
• Sufficiency in quantum statistical inference
• Equilibrium Statistical Mechanics of Fermion Lattice Systems
• Structure of sufficient quantum coarse-grainings
• Validity and failure of some entropy inequalities for CAR systems
• Markov states on the CAR algebra

Cited by in corpus (2)

• Entropy of Quantum Markov states on Cayley trees
• The structure of strongly additive states and Markov triplets on the CAR algebra