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Entanglement detection of two-qubit Werner states

Artur Czerwiński

Published Apr 15, 2021• 0 citations
OpenAlex

Abstract

In this article, we introduce a framework for entanglement detection 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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In this article, we introduce a framework for entanglement detection 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.
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.
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.
Entanglement detection by local measurements, which can possibly be performed by far distant observers, are of particular interest for applications in quantum key distribution and quantum communication. In this paper sufficient conditions for arbitrary dimensional bipartite entanglement detection based on correlation matrices and joint probability distributions of such local measurements are investigated. In particular, their dependence on the nature of the local measurements is explored for typical bipartite quantum states and for measurements involving local orthonormal hermitian operators bases (LOOs) or generalized measurements based on informationally complete positive operator valued measures of the recently introduced (N,M)(N,M)(N,M)-type ((N,M)(N,M)(N,M)-POVMs) \cite{NMPOVM}. It is shown that symmetry properties of (N,M)(N,M)(N,M)-POVMs imply that sufficient conditions for bipartite entanglement detection exhibit peculiar scaling properties relating different equally efficient local entanglement detection scenarios. For correlation-matrix based bipartite local entanglement detection, for example, this has the consequence that LOOs and all informationally complete (N,M)(N,M)(N,M)-POVMs are equally powerful. With the help of a hit-and-run Monte-Carlo algorithm the effectiveness of local entanglement detection of typical bipartite quantum states is explored numerically. For this purpose Euclidean volume ratios between locally detectable entangled states and all bipartite quantum states are determined.