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

Czerwinski, Artur

doi:10.1007/s10773-015-2703-2

Cited by 13 publications

(24 citation statements)

References 9 publications

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“…One can notice that the result (42) is equivalent to the result concerning dephasing published in [18], where the author followed the stroboscopic approach as introduced in [11]. The fact that both results are practically identical confirms that the new approach outlined in the current article is correct.…”

Section: An Example For Dimh = 2 -Dephasingsupporting

confidence: 71%

“…Whereas in the current article we need to employ different algebraic methods to consider the dynamical map as introduced in (4). Therefore, though seemingly the current article resembles previous works on stroboscopic tomography [11,12,13,14,18], it actually brings a significant contribution to the field because it differs with the main assumption concerning evolution and mathematical methods used to solve this problem. Morover, the current approach can be applied to more general evolution models with time-dependent generators.…”

Section: Introductionmentioning

confidence: 90%

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Dynamic Quantum Tomography Model for Phase-Damping Channels

Czerwinski

Jamiołkowski

2016

Open Syst. Inf. Dyn.

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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

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Section: An Example For Dimh = 2 -Dephasingsupporting

confidence: 71%

Section: Introductionmentioning

confidence: 90%

Dynamic Quantum Tomography Model for Phase-Damping Channels

Czerwinski

Jamiołkowski

2016

Open Syst. Inf. Dyn.

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“…Finally, in this section we may refer to the one-parametric non-degenerate family of Kraus operators {K i (t; a)} 2 i=0 which was introduced in [21]. It has the following form.…”

Section: Optimal Evolution Models For 2-level Systemsmentioning

confidence: 99%

“…In [21] it was proved that such a family is a one-parametric non-degenerate family of Kraus operators iff a ∈ R and a ∈ (0; 2). One can easily notice that the family proposed in [21] is a special case of the three-parametric non-degenerate family for a 1 = a 3 , a 2 = 2−a 3 , a 3 = 0. In this section it has been proved that there exists a non-degenerate family of Kraus operators that depends on three parameters (a 1 , a 2 , a 3 ) which have to satisfy 12 and 13.…”

Section: Optimal Evolution Models For 2-level Systemsmentioning

confidence: 99%

Optimal evolution models for quantum tomography

Czerwinski¹

2016

J. Phys. A: Math. Theor.

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The research presented in this article concerns the stroboscopic approach to quantum tomography, which is an area of science where quantum Physics and linear algebra overlap. In this article we introduce the algebraic structure of the parametric-dependent quantum channels for 2-level and 3-level systems such that the generator of evolution corresponding with the Kraus operators has no degenerate eigenvalues. In such cases the index of cyclicity of the generator is equal 1, which physically means that there exists one observable the measurement of which performed sufficient number of times at distinct instants provides enough data to reconstruct the initial density matrix and, consequently, the trajectory of the state. Necessary conditions for the parameters and relations between them are introduced. The results presented in this paper seem to have considerable potential applications in experiments due to the fact that one can perform quantum tomography by conducting only one kind of measurement. Therefore, the analyzed evolution models can be considered optimal in the context of quantum tomography. Finally, we also introduce some remarks concerning optimal evolution models in case of n−dimensional Hilbert space.

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“…Another possibility to implement a feasible framework for state reconstruction is based on measurements defined by the mutually unbiased bases (MUBs) [20,21]. There are also tomographic techniques which solve the density matrix reconstruction problem by means of expectation values of Hermitian operators [22][23][24]. Finally, contemporary quantum state tomography methods usually utilize the concept of generalized quantum measurements, which is the focus of this article.…”

Section: Introductionmentioning

confidence: 99%

Quantum state tomography with informationally complete POVMs generated in the time domain

Czerwinski

2021

Quantum Inf Process

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The article establishes a framework for dynamic generation of informationally complete POVMs in quantum state tomography. Assuming that the evolution of a quantum system is given by a dynamical map in the Kraus representation, one can switch to the Heisenberg picture and define the measurements in the time domain. Consequently, starting with an incomplete set of positive operators, one can obtain sufficient information for quantum state reconstruction by multiple measurements. The framework has been demonstrated on qubits and qutrits. For some types of dynamical maps, it suffices to initially have one measurement operator. The results demonstrate that quantum state tomography is feasible even with limited measurement potential.

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

Cited by 13 publications

References 9 publications

Dynamic Quantum Tomography Model for Phase-Damping Channels

Dynamic Quantum Tomography Model for Phase-Damping Channels

Optimal evolution models for quantum tomography

Quantum state tomography with informationally complete POVMs generated in the time domain

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