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arXiv:2104.07653 · Communications in Theoretical Physics

Quantifying entanglement of two-qubit Werner states

Artur Czerwiński

Published May 17, 2021• 9 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
10.1088/1572-9494/ac01e1

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Abstract 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.
In this paper, we introduce a numerical framework for quantum tomography and entanglement quantification of three-qubit generalized Werner states. The scheme involves the single-qubit symmetric, informationally complete, positive operator-valued measure (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.
In this article, we introduce a framework for two-qutrit Werner states tomography with Gaussian noise. The measurement scheme is based on the symmetric, informationally complete positive operator-valued measure. To make the framework realistic, we impose the Gaussian noise on the measured states numbers. Through numerical simulation, we successfully reconstructed the two-qutrit Werner states in various experimental scenarios and analyzed the optimal scenario from four aspects: fidelity, purity, entanglement, and coherence.
Abstract 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 Schrödinger 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.
Conventional methods of measuring entanglement in a two-qubit photonic mixed state require detection of both qubits. We generalize a recently introduced method which does not require detection of both qubits, by extending it to cover a wider class of entangled states. Specifically, we present a detailed theory that shows how to measure entanglement in a family of two-qubit mixed states, obtained by generalizing Werner states, without detecting one of the qubits. Our method is interferometric and does not require any coincidence measurement or postselection. We also perform a quantitative analysis of anticipated experimental imperfections. We show that the method is resistant to a decrease in the interference visibility resulting from such imperfections.
Multipartite entanglement is a key concept in quantum mechanics for which, despite the experimental progress in entangling three or more quantum devices, there is still no general quantitative theory that exists. In order to characterize the robustness of multipartite entanglement, one often employs generalized Werner states, that is, mixtures of a Greenberger-Horne-Zeilinger (GHZ) state and the completely unpolarized state. While two-qubit Werner states have been instrumental for various important advancements in quantum information, as of now there is no quantitative account for such states of more than two qubits. By using the GHZ symmetry introduced recently, we find exact results for tripartite entanglement in three-qubit generalized Werner states and, moreover, the entire family of full-rank mixed states that share the same symmetries.