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Quantum Electronics and Laser Science Conference

Experimentally measuring the purity of a state without state tomography

Lynden K. Shalm, Robert B. A. Adamson, Aephraim M. Steinberg

Published Dec 10, 2005• 0 citations
Publisher

Abstract

We present an experiment that determines the purity of a state without the need for state tomography. We rely instead on a Bell-basis measurement on a pair of particles.
DOI
10.1109/qels.2005.1548853

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The process of quantum tomography of polarization-entangled photon pairs was simulated on quantum computers of different generations of the IBM Q Experience platform. The simulation was carried out for all four two-qubit Bell states. It turned out that the contribution of basis states that are absent in Bell states does not exceed 10 %\%% even on quantum computers of the first generations, and is reduced to several percent on quantum computers of the latest generation. The simulation quality was evaluated using Fidelity. The Fidelity values were in a range of 68.6–94.9 %\%% , depending on the generation of computers. It was shown that for Bell states Fidelity can be calculated using three tomographic measurements instead of the nine required for determination of the density matrix using quantum state tomography.
Many experiments in quantum information aim at creating graph states. Quantifying the purity of an experimentally achieved graph state could in principle be accomplished using full-state tomography. This method requires a number of measurement settings growing exponentially with the number of constituents involved. Thus, full-state tomography becomes experimentally infeasible even for a moderate number of qubits. In this paper we present a method to estimate the purity of experimentally achieved graph states with simple measurements. The observables we consider are the stabilizers of the underlying graph. Then, we formulate the problem as: "What is the state with the least purity that is compatible with the measurement data?" We solve this problem analytically and compare the obtained bounds with results from full-state tomography for simulated data.