Markov property and Strong additivity of von Neumann entropy for graded quantum systems
نویسنده
چکیده
It is easily verified that the quantum Markov property is equivalent to the strong additivity of von Neumann entropy for graded quantum systems. However, the structure of Markov states for graded systems is different from that for tensor-product systems which have trivial grading. For three-composed graded systems we have U(1)-gauge invariant Markov states whose restriction to the marginal pair of subsystems is non-separable.
منابع مشابه
Monotonicity of quantum relative entropy revisited
Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences as the strong sub-additivity of von Neumann entropy, the Golden-Thompson trace inequality and the monotonicity of the Holevo quantitity. The relation to quantum Markov states is briefly ind...
متن کاملMonotonicity of quantum relative entropy revisited 1
Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences as the strong sub-additivity of von Neumann entropy, the Golden-Thompson trace inequality and the monotonicity of the Holevo quantitity. The relation to quantum Markov states is briefly ind...
متن کاملReiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras
متن کامل
The minimum Renyi entropy output of a quantum channel is locally additive
We show that the minimum Renyi entropy output of a quantum channel is locally additive for Renyi parameter α > 1. While our work extends the results of [11] (in which local additivity was proven for α = 1), it is based on several new techniques that incorporate the multiplicative nature of `p-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that ...
متن کاملOn estimation of the entropy infimum for the output of the Weyl channels being covariant with respect to the maximum commutative group of unitaries
We estimate the von Neumann entropy infimum for the output of the Weyl channels being covariant with respect to the maximum commutative group. In qubit case, such the class includes the quantum depolarizing channel and the ”two-Pauli” channel as well. For the dimesion d = 2 our approach allows to prove the additivity conjecture for the Holevo-Schumacher-Westmoreland bound. Our method is based u...
متن کامل