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Physical Review Letters

Experimental Methods for Detecting Entanglement

Joseph B. Altepeter, Evan R. Jeffrey, Paul G. Kwiat, Sébastien Tanzilli, Nicolas Gisin, Antonio Acín

Published Jul 15, 2005• 67 citations
Publisher

Abstract

Here we present experimental realizations of two new entanglement detection methods: a three-measurement Bell inequality inequivalent to the Clauser-Horne-Shimony-Holt inequality and a nonlinear Bell-type inequality based on the negativity measure. In addition, we provide an experimental and theoretical comparison between these new methods and several techniques already in use: the traditional Clauser-Horne-Shimony-Holt inequality, the entanglement witness, and complete state tomography.

DOI
10.1103/physrevlett.95.033601

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Here we present experimental realizations of two new entanglement detection methods: a three-measurement Bell inequality inequivalent to the Clauser-Horne-Shimony-Holt inequality and a nonlinear Bell-type inequality based on the negativity measure. In addition, we provide an experimental and theoretical comparison between these new methods and several techniques already in use: the traditional Clauser-Horne-Shimony-Holt inequality, the entanglement witness, and complete state tomography.
We propose a new method for detecting entanglement of two qubits and discuss its relation with the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. Without the need for full quantum tomography for the density matrix we can experimentally detect the entanglement by measuring less than 9 local observables for any given state. We show that this test is stronger than the CHSH-Bell inequality and also gives an estimation for the degree of entanglement. If prior knowledge is available we can further greatly reduce the number of required local observables. The test is convenient and feasible with present experimental technology.
An entangled state of a two-particle system is a quantum state that cannot be separated-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 to violate these inequalities.However, there are other, more efficient 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.We present the theory of witness operators, and an undergraduate experiment that measures an entanglement witness for the joint polarization state of two photons.We are able to produce states for which the expectation value of the witness operator is entangled by more than 160 standard deviations.
All previous tests of local realism have studied correlations between single-particle measurements. In the present experiment, we have performed a Bell experiment on three particles in which one of the measurements corresponds to a projection onto a maximally entangled state. We show theoretically and experimentally that correlations between these entangled measurements and single-particle measurements are too strong for any local-realistic theory and are experimentally exploited to violate a Clauser-Horne-Shimony-Holt-Bell inequality by more than 5 standard deviations. We refer to this possibility as "entangled entanglement."
We propose an innovative method to enhance the detection and protection of quantum entanglement, a cornerstone of quantum mechanics with applications in computing, communication, and beyond. While entanglement can be represented through nonlocal correlations detectable by the Clauser-Horne-Shimony-Holt (CHSH) inequality, this method does not fully capture all entangled states. To address this limitation, we introduce a variational entanglement witness (VEW) that optimizes the probabilities of detection and improves the efficiency of distinguishing between separable and entangled states. Additionally, we propose a nonlocal measurement framework that enables the assessment of both CHSH inequalities and the VEW while preserving the entanglement. Our approach enhances the reliability of entanglement detection while maintaining the entanglement of quantum states, offering significant advancements for quantum technologies.
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.
In this review, we introduce some methods for detecting or measuring entanglement. Several nonlinear entanglement witnesses are presented. We derive a series of Bell inequalities whose maximally violations for any multipartite qubit states can be calculated by using our formulas. Both the nonlinear entanglement witnesses and the Bell inequalities can be operated experimentally. Thus they supply an effective way for detecting entanglement. We also introduce some experimental methods to measure the entanglement of formation, and the lower bound of the convex-roof extension of negativity.