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arXiv:2104.11258 · International Journal of Modern Physics B

Quantum tomography of three-qubit generalized Werner states

Artur Czerwiński

Published May 26, 2022• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/s0217979222501089

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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.
Abstract In this paper, we establish a new quantum state tomography model that fits the real environment very well. In our model, the number of photons emitted by the photon source is a random number of Gaussian distribution. The emitted photons are attenuated by a fiber, resulting in a binomial distribution of photons arriving at the detector. In the process of measurement, we impose Poisson noise, which makes the number of photons measured each time assume Poisson distribution. The quantum states are reconstructed from photon counts obtained for symmetric informationally complete positive operator-valued measures, and consider the influence of noise on the measurement operators. We study the quantum tomography efficiency of any two-qubit Werner state in our model. We obtained the relationship between the tomographic efficiency and multiple variables of the model through numerical simulation. PACS numbers: 03.67.Mn, 03.65.Ud, 03.67.-a
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It is a well-known fact that the optimal positive operator valued measure (POVM) for quantum-state tomography is the symmetric, informationally complete POVM (SIC-POVM). We investigate the same problem only in the case when there is some a priori information about the state, specifically when some parameters are known. In this paper, we mainly focus on solving a three-dimensional optimization problem, which gives us a non-trivial example for the so-called conditional SIC-POVMs, a straightforward generalization of the concept of SIC-POVMs. We also present other special cases to show further applications of the proposed numerical methods and to illustrate the complexity of this topic.