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Title: Quantum state tomography and fidelity estimation via Phaselift

Experiments of multi-photon entanglement have been performed by several groups. Obviously, an increase on the photon number for fidelity estimation and quantum state tomography causes a dramatic increase in the elements of the positive operator valued measures (POVMs), which results in a great consumption of time in measurements. In practice, we wish to obtain a good estimation of fidelity and quantum states through as few measurements as possible for multi-photon entanglement. Phaselift provides such a chance to estimate fidelity for entangling states based on less data. In this paper, we would like to show how the Phaselift works for six qubits in comparison to the data given by Pan’s group, i.e., we use a fraction of the data as input to estimate the rest of the data through the obtained density matrix, and thus goes beyond the simple fidelity analysis. The fidelity bound is also provided for general Schrödinger Cat state. Based on the fidelity bound, we propose an optimal measurement approach which could both reduce the copies and keep the fidelity bound gap small. The results demonstrate that the Phaselift can help decrease the measured elements of POVMs for six qubits. Our conclusion is based on the prior knowledgemore » that a pure state is the target state prepared by experiments.« less
Authors:
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Publication Date:
OSTI Identifier:
22451212
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 360; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY MATRIX; PHOTONS; PURE STATES; QUANTUM ENTANGLEMENT; QUANTUM SYSTEMS; QUBITS; TOMOGRAPHY