Minimal number of operators for observability ofN-level quantum systems

Jamiołkowski

2016

Open Syst. Inf. Dyn.

In this article we propose a dynamic quantum tomography model for open quantum systems with evolution given by phase-damping channels. Mathematically, these channels correspond to completely positive trace-preserving maps defined by the Hadamard product of the initial density matrix with a time-dependent matrix which carries the knowledge about the evolution. Physically, there is a strong motivation for considering this kind of evolution because such channels appear naturally in the theory of open quantum systems. The main idea behind a dynamic approach to quantum tomography claims that by performing the same kind of measurement at some time instants one can obtain new data for state reconstruction. Thus, this approach leads to a decrease in the number of distinct observables which are required for quantum tomography; however, the exact benefit for employing the dynamic approach depends strictly on how the quantum system evolves in time. Algebraic analysis of phase-damping channels allows one to determine optimal criteria for quantum tomography of systems in question. General theorems and observations presented in the paper are accompanied by a specific example, which shows step by step how the theory works. The results introduced in this article can potentially be applied in experiments where there is a tendency a look at quantum tomography from the point of view of economy of measurements, because each distinct kind of measurement requires, in general, preparing a separate setup

Section: An Example For Dimh = 2 -Dephasingsupporting

confidence: 70%

Section: S(qmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic Quantum Tomography Model for Phase-Damping Channels

Jamiołkowski

2016

Open Syst. Inf. Dyn.

“…In this paper we follow yet another approach to quantum tomography -the stroboscopic tomography (or stroboscopic observability) which initiated in 1983 in the article [7]. This approach was developed in further papers, such as [8,9].…”

Section: Introductionmentioning

confidence: 99%

Minimal number of observables for quantum tomography of systems with evolution given by double commutators

Quantum Stud.: Math. Found.

2017

In this paper, we analyze selected evolution models of N -level open quantum systems to find the minimal number of observables (Hermitian operators) such that their expectation values at some time instants determine the accurate representation of the quantum system. The assumption that lies at the foundation of this approach to quantum tomography claims that time evolution of an open quantum system can be expressed by the KossakowskiLindblad equation of the formρ = Lρ, which is the most general type of Markovian and time-homogeneous master equation which preserves trace and positivity. We consider the cases when the generator of evolution can be presented by means of two or more double commutators. Determining the minimal number of observables required for quantum tomography can be the first step towards optimal tomography models for N -level quantum systems.

Applications of the Stroboscopic Tomography to Selected 2-Level Decoherence Models

2015

Int J Theor Phys

In the paper we discuss possible applications of the so-called stroboscopic tomography (stroboscopic observability) to selected decoherence models of 2-level quantum systems. The main assumption behind our reasoning claims that the time evolution of the analyzed system is given by a master equation of the formρ = Lρ and the macroscopic information about the system is provided by the mean values m i (t j The goal of the stroboscopic tomography is to establish the optimal criteria for observability of a quantum system, i.e. minimal value of r and p as well as the properties of the observables {Q i } r i=1 .