Abstract
The article introduces efficient quantum state tomography schemes for qutrits and entangled qubits subject to pure decoherence. We implement the dynamic state reconstruction method for open systems sent through phase-damping channels, which was proposed in: Czerwinski and Jamiolkowski Open Syst. Inf. Dyn. 23, 1650019 (2016). In the present article we prove that two distinct observables measured at four different time instants suffice to reconstruct the initial density matrix of a qutrit with evolution given by a phase-damping channel. Furthermore, we generalize the approach in order to determine criteria for quantum tomography of entangled qubits. Finally, we prove two universal theorems concerning the number of observables required for quantum state tomography of qudits subject to pure decoherence. We believe that dynamic state reconstruction schemes bring advancement and novelty to quantum tomography since they utilize the Heisenberg representation and allow to define the measurements in time domain.
Highlights
Quantum state tomography, i.e. the problem of reconstructing the accurate representation of a physical system from measurements, is crucial for quantum information and computation
The goal of this section is to demonstrate that the effectiveness of quantum state tomography can be significantly improved if we assume that the evolution of the quantum system is given by a phase-damping channel
In this article we have proved that the dynamic approach to quantum tomography can be an effective method of state reconstruction for qutrits and entangled qubits which are sent through phase-damping channels
Summary
I.e. the problem of reconstructing the accurate representation of a physical system from measurements, is crucial for quantum information and computation. Among many different methods of quantum tomography, special attention should be paid to the so-called stroboscopic approach, which was originally introduced in 1983 by Andrzej Jamiolkowski [10] This approach aims to reconstruct the initial density matrix by the lowest possible number of distinct observables due to the utilization of the knowledge about the evolution of a quantum system (encoded, for example, in a GKSL equation [11, 12]). We give the upper bound for the number of distinct observables required for the quantum state tomography of N −level open systems subject to pure decoherence. MN (C) shall denote the vector space of N × N complex matrices
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