arXiv subjects

Dénes Petz

Publications and source records attributed to Dénes Petz.

3 recordsLinked to original sources

arXiv2015

Optimal quantum-state tomography with known parameters

It is a well-known fact that the optimal POVM for quantum state tomography is the symmetric, informationally complete, positive operator valued measure (SIC-POVM). We investigate the same problem only in the case when there are some a priori information about the state, specifically when some parameters are known. In this paper we mainly focus on solving a 3-dimensional optimization problem, which gives us a non-trivial example for the so-called conditional SIC- POVMs, a straightforward generalization of the concept of SIC-POVMs. We also present other special cases to show further applications of the proposed numerical methods and to illustrate the complexity of this topic.

quant-ph↗

arXiv2015

Some inequalities for quantum Tsallis entropy related to the strong subadditivity

In this paper we investigate the inequality $S_q(ρ_{123})+S_q(ρ_2)\leq S_q(ρ_{12})+S_q(ρ_{23}) \, (*)$ where $ρ_{123}$ is a state on a finite dimensional Hilbert space $\mathcal{H}_1\otimes \mathcal{H}_2\otimes \mathcal{H}_3,$ and $S_q$ is the Tsallis entropy. It is well-known that the strong subadditivity of the von Neumnann entropy can be derived from the monotonicity of the Umegaki relative entropy. Now, we present an equivalent form of $(*)$, which is an inequality of relative quasi-entropies. We derive an inequality of the form $S_q(ρ_{123})+S_q(ρ_2)\leq S_q(ρ_{12})+S_q(ρ_{23})+f_q(ρ_{123})$, where $f_1(ρ_{123})=0$. Such a result can be considered as a generalization of the strong subadditivity of the von Neumnann entropy. One can see that $(*)$ does not hold in general (a picturesque example is included in this paper), but we give a sufficient condition for this inequality, as well.

math-ph↗

arXiv2014

A characterization theorem for matrix variances

Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of observables and we present a necessary and sufficient condition for the decomposition of the matrix variances.

math.FA↗