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arXiv:quant-ph/0307003 · Physical Review Letters

Detection of Entanglement with Polarized Photons: Experimental Realization of an Entanglement Witness

Marco Barbieri, F. De Martini, G. Di Nepi, Paolo Mataloni, Giacomo Mauro D’Ariano, Chiara Macchiavello

Published Nov 24, 2003• 192 citations
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Abstract

We report on the first experimental realization of an entanglement witness, a method to detect entanglement with few local measurements. The present demonstration has been performed with polarized photons in Werner states, a well-known family of mixed states that can be either separable or nonseparable. The Werner states are generated by a novel high brilliance source of bipartite entangled states by which the state mixedness can be easily adjusted.

DOI
10.1103/physrevlett.91.227901

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We report on the first experimental realization of an entanglement witness, a method to detect entanglement with few local measurements. The present demonstration has been performed with polarized photons in Werner states, a well-known family of mixed states that can be either separable or nonseparable. The Werner states are generated by a novel high brilliance source of bipartite entangled states by which the state mixedness can be easily adjusted.
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.
Multipartite entangled states are key elements for quantum information processing. Here we experimentally investigate the particular properties of a polarization-entangled four-photon state, which can be generated directly by second order parametric down-conversion. The perfect correlations and the invariance under local transformations enable one to encode one qubit of quantum information in a decoherence-free subspace and thus to communicate it safely over noisy quantum channels. Furthermore, we present an experimental method to detect genuine fourpartite entanglement using entanglement witness operators. The implementation of such operators requires only of few local polarization measurements but uniquely proves the genuine multipartite entanglement.
We experimentally demonstrate a method for detection of entanglement via construction of entanglement witnesses from a limited fixed set of local measurements ( M ). Such a method does not require a priori knowledge about the form of the entanglement witnesses. It is suitable for a scenario where a full state tomography is not available, but the only resource is a limited set of M . We demonstrate the method on pure two-qubit entangled states and mixed two-qubit entangled states, which emerge from photonic implementation of controllable quantum noisy channels. The states we select are motivated by realistic experimental conditions, and we confirm it works well for both cases. Furthermore, possible generalizations to higher-dimensional bipartite systems have been considered, which can potentially detect both decomposable and indecomposable entanglement witnesses. Our experimental results show perfect validity of the method, which indicates that even a limited set of local measurements can be used for quick entanglement detection and further provide a practical test bed for experiments with entanglement witnesses.
An entangled state of a two-particle system is a quantum state that cannot be separated, meaning it cannot be written as the product of states of the individual particles. One way to tell if a system is entangled is to use it to violate a Bell inequality (such as the Clauser-Horne-Shimony-Holt, CHSH, inequality), because entanglement is necessary for such a violation. However, there are other, easier-to-perform measurements that determine whether or not a system is entangled. An operator that corresponds to such a measurement is referred to as an entanglement witness. Here, we present the theory of witness operators and an undergraduate experiment that measures entanglement witnesses for the joint polarization state of two photons. We are able to produce states for which the expectation value of a witness operator is entangled by more than 300 standard deviations. In order to further examine the performance of these witness operators, we present a simple way to generate states that closely approximate Werner states, which have a controllable degree of entanglement.