arXiv subjects

Artur Czerwinski

Publications and source records attributed to Artur Czerwinski.

36 records · Page 2Linked to original sources

arXiv2022

Quantum tomography of entangled qubits by time-resolved single-photon counting with time-continuous measurements

In this article, we introduce a framework for entanglement characterization by time-resolved single-photon counting with measurement operators defined in the time domain. For a quantum system with unitary dynamics, we generate time-continuous measurements by shifting from the Schrodinger picture to the Heisenberg representation. In particular, we discuss this approach in reference to photonic tomography. To make the measurement scheme realistic, we impose timing uncertainty on photon counts along with the Poisson noise. Then, the framework is tested numerically on quantum tomography of qubits. Next, we investigate the accuracy of the model for polarization-entangled photon pairs. Entanglement detection and precision of state reconstruction are quantified by figures of merit and presented on graphs versus the amount of time uncertainty.

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arXiv2022

Entanglement quantification enhanced by dark count correction

In this letter, we propose a method of dark count correction in quantum state tomography of entangled photon pairs. The framework is based on a linear model of dark counts, which is imposed on the measurement formalism. The method is tested on empirical data derived from an experiment on polarization-entangled photons. We demonstrate that the numerical approach to dark count correction guarantees more reliable state reconstruction compared with standard estimation. Most importantly, however, the conceptually simple theoretical approach proves to be more efficient at entanglement quantification than experimental techniques.

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arXiv2022

Efficiency of photonic state tomography affected by fiber attenuation

In this article, we investigate the efficiency of photonic state tomography in the presence of fiber attenuation. The theoretical formalism of the photon loss is provided by implementing methods from the theory of open quantum systems. The quantum state is reconstructed from photon counts obtained for symmetric informationally complete POVMs. The number of photons that reach the detectors is numerically modeled by the binomial distribution, which describes the loss of light caused by the medium. This approach allows us to study the quality of state tomography versus the length of the fiber. In particular, we focus on entangled qubits and qutrits, which are sent through fibers of different lengths. The amount of entanglement detected by the measurement scheme is quantified and presented on graphs. The results demonstrate how the quality of photonic tomography depends on the distance between the source and the receiver.

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arXiv2022

Quantum tomography of three-qubit generalized Werner states

In this article, we introduce a numerical framework for quantum tomography and entanglement quantification of three-qubit generalized Werner states. The scheme involves the single-qubit SIC-POVM, which is then generalized to perform three-qubit measurements. We introduce random errors into the scheme by imposing the Poisson noise on the measured photon counts. The precision of state estimation is quantified and presented on graphs. As a special case, we compare the efficiency of the framework for the pure three-qubit generalized Werner state and the W state. The reconstructed states are presented graphically and discussed.

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arXiv2022

Entanglement dynamics governed by time-dependent quantum generators

In the article, we investigate entanglement dynamics defined by time-dependent linear generators. We consider multilevel quantum systems coupled to an environment that induces decoherence and dissipation, such that the relaxation rates depend on time. By applying the condition of partial commutativity, one can precisely describe the dynamics of selected subsystems. More specifically, we investigate the dynamics of entangled states. The concurrence is used to quantify the amount of two-qubit entanglement in the time domain. The framework appears an efficient tool for investigating quantum evolution of entangled states driven by time-local generators. In particular, non-Markovian effects can be included to observe the restoration of entanglement in time.

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arXiv2021

Entanglement characterization by single-photon counting with random noise

In this article, we investigate the problem of entanglement characterization with polarization measurements combined with maximum likelihood estimation (MLE). A realistic scenario is considered with measurement results distorted by random experimental errors. In particular, by imposing unitary rotations acting on the measurement operators, we can test the performance of the tomographic technique versus the amount of noise. Then, dark counts are introduced to explore the efficiency of the framework in a multi-dimensional noise scenario. The concurrence is used as a figure of merit to quantify how well entanglement is preserved through noisy measurements. Quantum fidelity is computed to quantify the accuracy of state reconstruction. The results of numerical simulations are depicted on graphs and discussed.

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arXiv2021

Hamiltonian tomography by the quantum quench protocol with random noise

In this article, we introduce a framework for Hamiltonian tomography of multi-qubit systems with random noise. We adopt the quantum quench protocol to reconstruct a many-body Hamiltonian by local measurements that are distorted by random unitary operators and time uncertainty. In particular, we consider a transverse field Ising Hamiltonians describing interactions of two spins $1/2$ and three-qubit Hamiltonians of a heteronuclear system within the radio-frequency field. For a sample of random Hamiltonians, we report the fidelity of reconstruction versus the amount of noise quantified by two parameters. Furthermore, we discuss the correlation between the accuracy of Hamiltonian tomography and the number of pairs of quantum states involved in the framework. The results provide valuable insight into the robustness of the protocol against random noise.

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arXiv2021

Quantum state tomography of qutrits by single-photon counting with imperfect measurements

In this article, we introduce a framework for quantum state tomography of qutrits by projective measurements. The framework is based on photon-counting with measurement results distorted due to the Poisson noise and dark counts. Two different measurement schemes are investigated numerically and compared in terms of their efficiency for distinct numbers of photons per measurement. The accuracy of state reconstruction is quantified by figures of merit which are presented on graphs versus the amount of noise.

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arXiv2021

Quantifying entanglement of two-qubit Werner states

In this article, we introduce a framework for entanglement quantification of photon pairs represented by two-qubit Werner states. The measurement scheme is based on the symmetric informationally complete POVM. To make the framework realistic, we impose the Poisson noise on the measured two-photon coincidences. For various settings, numerical simulations were performed to evaluate the efficiency of the framework.

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arXiv2021

Phase estimation of time-bin qudits by time-resolved single-photon counting

We present a comprehensive framework for quantum state tomography (QST) of time-bin qudits sent through a fiber. Starting from basic assumptions, we define a positive-operator valued measure (POVM) which is then applied to the quantum state reconstruction problem. A realistic scenario is considered where the time uncertainty of the detector is treated as a source of experimental noise. The performance of the quantum tomography framework is examined through a series of numerical simulations conducted for different parameters describing the apparatus. The quality of state recovery, quantified by the notion of minimum fidelity, is depicted on graphs for a range of fiber lengths. Special attention is paid to relative phase reconstruction for qubits and qutrits. The results present relevant interdependence between the fiber length and the detector jitter.

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arXiv2021

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

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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arXiv2021

Quantum State Tomography of Four-Level Systems with Noisy Measurements

In this article, we investigate the problem of state reconstruction of four-level quantum systems. A realistic scenario is considered with measurement results distorted by random unitary operators. Two frames which define injective measurements are applied and compared. By introducing arbitrary rotations, we can test the performance of the framework versus the amount of experimental noise. The results of numerical simulations are depicted on graphs and discussed. In particular, a class of entangled states is reconstructed. The concurrence is used as a figure of merit in order to quantify how well entanglement is preserved through noisy measurements.

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arXiv2021

Quantum Tomography of Pure States with Projective Measurements Distorted by Experimental Noise

The article undertakes the problem of pure state estimation from projective measurements based on photon counting. Two generic frames for qubit tomography are considered -- one composed of the elements of the SIC-POVM and the other defined by the vectors from the mutually unbiased bases (MUBs). Both frames are combined with the method of least squares in order to reconstruct a sample of input qubits with imperfect measurements. The accuracy of each frame is quantified by the average fidelity and purity. The efficiency of the frames is compared and discussed. The method can be generalized to higher-dimensional states and transferred to other fields where the problem of complex vectors reconstruction appears.

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arXiv2020

Open quantum systems integrable by partial commutativity

The article provides a framework to solve linear differential equations based on partial commutativity which is introduced by means of the Fedorov theorem. The framework is applied to specific types of three-level and four-level quantum systems. The efficiency of the method is evaluated and discussed. The Fedorov theorem appears to answer the need for methods which allow to study dynamical maps corresponding with time-dependent generators. By applying this method, one can investigate countless examples of dissipative systems such that the relaxation rates depend on time.

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arXiv2020

Tomography of time-bin quantum states using time-resolved detection

We present a method for measuring quantum states encoded in the temporal modes of photons. The basis for the multilevel quantum states is defined by the use of modes propagating in a dispersive medium, which is a fiber in this case. The propagation and time-resolved single photon detection allow us to define a positive-operator valued measure (POVM). The POVM depends on the amount of dispersion and the characteristics of a detector. This framework is numerically tested by performing quantum state tomography on a large number of states for a set of realistic experimental settings. Finally, the average fidelity between the expected and reconstructed states is computed for qubits, qutrits and entangled qubits.

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arXiv2020

Quantum state tomography for qutrits subject to laser cooling

In this article we propose a dynamic quantum state tomography model for qutrits subject to laser cooling. We prove that one can reduce the number of distinct measurement setups required for state reconstruction by employing the stroboscopic approach. The results are in line with current advances in quantum tomography where there is a strong tendency to investigate the optimal criteria for state reconstruction. We believe that the stroboscopic approach can be considered an efficient tool for density matrix identification since it allows to determine the minimal number of distinct observables needed for quantum state tomography.

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arXiv2020

Dynamic state reconstruction of quantum systems subject to pure decoherence

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: Open Syst. Inf. Dyn. 23, 1650019 (2016). In the current 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 the optimal criteria for quantum tomography of entangled qubits. Finally, we prove two universal theorems concerning the minimal number of distinct observables required for quantum tomography of qudits. We believe that dynamic state reconstruction schemes bring significant advancement and novelty to quantum tomography since they allow to reduce the number of distinct measurements required to solve the problem, which is important from the experimental point of view.

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arXiv2020

Dynamic Quantum Tomography Model for Phase-Damping Channels

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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