Abstract
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.
Highlights
Quantum communication and quantum computation require well-defined resources in order to encode quantum information [1,2,3]
We contribute to the search for optimal methods of quantum tomography as we introduce a framework for dynamic generation of informationally complete set of measurement operators
We have showed that, for qubits subject to dephasing, one can start with two positive operators and dynamically generate an IC-Positive Operator-Valued Measure (POVM) by double measurement of probabilities corresponding with these operators
Summary
Quantum communication and quantum computation require well-defined resources in order to encode quantum information [1,2,3]. For this reason, the ability to characterize quantum objects based on measurements is crucial in these fields [4,5]. There is quantum measurement tomography which allows one to determine the characteristics of the actual operators governing the measurements [9]. We focus on quantum state tomography, assuming that the dynamics of the system and measurement operators are well characterized
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