Dynamic State Reconstruction of Quantum Systems Subject to Pure Decoherence

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.

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

“…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.…”

Quantum State Tomography of Four-Level Systems with Noisy Measurements

“…In particular, symmetric informationally complete POVMs (SIC-POVMs) can be considered optimal as far as the number of measurements is concerned [10][11][12]. Special attention should be paid to the methods which utilize dynamical maps in order to decrease the number of necessary measurement operators [13][14][15]. On the other hand, in * aczerwin@umk.pl practical realizations of QST protocols, there is a tendency to apply overcomplete sets of measurements in order to reduce the detrimental impact of experimental noise [16,17].…”

Entanglement characterization by single-photon counting with random noise

“…In particular, methods based on compressed sensing can decrease the number of measurement settings [9]. Special attention should also be paid to the methods which utilize dynamical maps in order to decrease the number of necessary measurement operators [10][11][12].…”