arXiv subjects
Publications and source records attributed to Nicholas Van Ryn.
We explore the relation between the von Neumann entropy and the Renyi entropies of integer orders for shift-invariant quasi-free Fermionic lattice systems. We investigate approximating the von Neumann entropy by a combination of integer-order Renyi entropies and give an estimate for the quality of such an approximation.
A recently proposed test of quantumness [R. Alicki and N. Van Ryn, J. Phys. A: Math. Theor. 41 062001 (2008)] is put into a broader mathematical and physical perspective. The notion of quantumness witness is introduced, in analogy to entanglement witness, and illustrated by examples of a single qubit and many-body systems with additive observables. We compare also our proposal with the quantumness test based on quantum correlations (entanglement) and Bell inequalities. A class of quantumness witnesses associated to the phase space representation is also discussed.
We propose a simple test of quantumness which can decide whether for the given set of accessible experimental data the classical model is insufficient. Take two observables $ A,B$ such that for any state $ψ$ their mean values satisfy $0\leq <ψ|A|ψ>\leq <ψ|B|ψ>\leq 1$. If there exists a state $ϕ$ such that the second moments fulfill the inequality $<ϕ|A^2|ϕ> ><ϕ|B^2|ϕ>$ then the system cannot be described by the classical probabilistic scheme. An example of an optimal triple $(A,B,ϕ)$ in the case of a qubit is given.