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Latin America Optics and Photonics Conference

Entanglement witnesses and detection of nonlocal superpositions

A. J. Gutiérrez-Esparza, Wanderson M. Pimenta, Breno Marques, A. A. Matoso, J. L. Lucio M., Jan Sperling, W. Vogel, Sebastião Pádua

Published Jan 1, 2014• 0 citations
Publisher

Abstract

A complete characterization of entanglement in a two-qutrit state generated using the transverse spatial correlations of two parametric down-converted photons is discussed. We verify entanglement for a particular case via entanglement witness operators which are decomposed into a sum of local observables. Experimentally, these operators are accomplished by using a spatial light modulator and a polarizing beam splitter. The quantification of entanglement is computed by the negativity. We also realize an experiment for the verification of the Schmidt number of quantum correlated photons. This measure of entanglement counts the number of global superpositions of product states which are needed to describe a compound quantum system. For unraveling a certain value of this measure, a family of entanglement and Schmidt number tests is constructed.

DOI
10.1364/laop.2014.lm2b.2

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A complete characterization of entanglement in a two-qutrit state generated using the transverse spatial correlations of two parametric down-converted photons is discussed. We verify entanglement for a particular case via entanglement witness operators which are decomposed into a sum of local observables. Experimentally, these operators are accomplished by using a spatial light modulator and a polarizing beam splitter. The quantification of entanglement is computed by the negativity. We also realize an experiment for the verification of the Schmidt number of quantum correlated photons. This measure of entanglement counts the number of global superpositions of product states which are needed to describe a compound quantum system. For unraveling a certain value of this measure, a family of entanglement and Schmidt number tests is constructed.
We present an experimental technique for a complete characterization of entanglement in a two-qutrit state generated using transverse spatial correlations of two parametric down-converted photons. We verify entanglement for a particular case via entanglement witness operators which are decomposed into a sum of local observables of single path and superposition projection operators. Experimentally, these operators are accomplished by using a spatial light modulator and a polarizing beam splitter which allow to modulate the amplitude of individually chosen path states. The quantification of entanglement is computed by the negativity obtained from the expectation values of the entanglement witnesses implemented.
We study in theory and experiment the verification of the Schmidt number of quantum correlated radiation fields. This measure of entanglement counts the number of global superpositions of product states which are needed to describe a compound quantum system. For unraveling a certain value of this measure, a family of entanglement and Schmidt number tests is constructed. The measurement of the whole class of witnesses is realized. By generating a path entangled two-photon state, we demonstrate the feasibility to directly count quantum superpositions.
This thesis deals with methods of the detection of entanglement.After recalling some facts and definitions concerning entanglement and separability, we investigate two methods of the detection of entanglement.In the first part of this thesis we consider so-called entanglement witnesses, mainly in view of the detection of multipartite entanglement.Entanglement witnesses are observables for which a negative expectation value indicates entanglement.We first present a simple method to construct these witnesses.Since witnesses are nonlocal observables, they are not easy to measure in a real experiment.However, as we will show, one can circumvent this problem by decomposing the witness into several local observables which can be measured separately.We calculate the local decompositions for several interesting witnesses for two, three and four qubits.Local decompositions can be optimized in the number of measurement settings which are needed for an experimental implementation.We present a method to prove that a given local decomposition is optimal and discuss with this the optimality of our decompositions.Then we present another method of designing witnesses which are by construction measurable with local measurements.Finally, we shortly report on experiments where some of the witnesses derived in this part have been used to detect three-and four-partite entanglement of polarized photons.The second part of this thesis deals with separability criteria which are written in terms of uncertainty relations.There are two different formulations of uncertainty relations since one can measure the uncertainty of an observable by its variance as well as by entropic quantities.We show that both formulations are useful tools for the derivation of separability criteria for finite-dimensional systems and investigate the resulting criteria.Our results in this part exhibit also some more fundamental properties of entanglement: We show how known separability criteria for infinitedimensional systems can be translated to finite-dimensional systems.Furthermore, we prove that any entropic uncertainty relation on one part of the system gives rise to a separability criterion on the composite system.
Quantum mechanics predicts the existence of correlations between composite systems that, although puzzling to our physical intuition, enable technologies not accessible in a classical world. Notwithstanding, there is still no efficient general method to theoretically quantify and experimentally detect entanglement of many qubits. Here we propose to detect entanglement by measuring the statistical response of a quantum system to an arbitrary nonlocal parametric evolution. We witness entanglement without relying on the tomographic reconstruction of the quantum state, or the realization of witness operators. The protocol requires two collective settings for any number of parties and is robust against noise and decoherence occurring after the implementation of the parametric transformation. To illustrate its user friendliness we demonstrate multipartite entanglement in different experiments with ions and photons by analyzing published data on fidelity visibilities and variances of collective observables.
The certification of entanglement is a vital task in quantum technology. To theoretically quantify and experimentally detect entanglement of many qubits, we suggest to identify quantum entanglement by measuring the statistical response of a quantum system to an arbitrary nonlocal parametric evolution. Our suggestion does not basing on the tomographic reconstruction of the quantum state, or the realization of witness operators. The protocol requires two collective settings for any number of parties and is robust against noise and decoherence occurring after the implementation of the parametric transformation. The bounds for witnessing quantum entanglement with strength of nonlocal interaction are shown with the help of Ising nonlocal Hamiltonian. Furthermore to illustrate its user friendliness we demonstrate multipartite entanglement in different experiments with ions and photons by analyzing published data on fidelity visibilities and variances of collective observables.
We characterize entanglement in two-qubit pure states encoded in transverse momenta of twin photons obtained from spontaneous parametric down-conversion. Two alternate methods are employed: (i) measurement of conditional interference patterns and (ii) measurement of the marginal probability that yields the single-photon interference pattern. Both methods are local with classical communication and rely on Schmidt decomposition of the quantum state, which is generated by letting the photons propagate through an appropriate lens system. In both cases we can obtain the concurrence either through the Schmidt coefficients in the first method or directly relating the concurrence to the visibility of the interference pattern in the second one.