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arXiv:2409.10852 · Physical Review Research

Detecting and protecting entanglement through nonlocality, variational entanglement witness, and nonlocal measurements

Haruki Matsunaga, Le Bin Ho

Published Mar 4, 2025• 2 citations
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Abstract

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.

DOI
10.1103/physrevresearch.7.013239

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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-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.
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.
Entanglement in quantum mechanics contradicts local realism and is a manifestation of quantum nonlocality. Its presence can be detected through the violation of Bell, or Clauser-Horne-Shimony-Holt (CHSH) inequalities. Paradigmatic quantum systems provide examples of both, nonentangled and entangled states. Here, we consider a minimal complexity setup consisting of six Majorana zero modes. We find that any allowed state in the degenerate Majorana space is nonlocally entangled. We show how to measure (with available techniques) the CHSH-violating correlations using either intermediate strength or weak measurement protocols.
We propose and experimentally implement an efficient procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. This is an experimental determination of these quantities without quantum state tomography or continuous monitoring of all measurement bases in the usual CHSH inequality tests. We analyze how well the measured degrees of Bell nonlocality and other entanglement witnesses (including the fully entangled fraction and a nonlinear entropic witness) of an arbitrary two-qubit state can estimate its entanglement. In particular, we measure these witnesses and estimate the negativity of various two-qubit Werner states. Our approach could especially be useful for quantum communication protocols based on entanglement swapping.
Abstract Quantum entanglement and nonlocality are foundational to quantum technologies, driving quantum computation, communication, and cryptography innovations. To benchmark the capabilities of these quantum techniques, efficient detection and accurate quantification methods are indispensable. This paper examines the concept ‘detection length’—a metric that quantifies the minimum number of simultaneously measured particles required to detect entanglement or nonlocality. We extend the detection length framework to encompass various entanglement categories and nonlocality phenomena, providing a comprehensive analytical model to determine detection lengths for specified forms of entanglement. Furthermore, we exploit semidefinite programming techniques to design entanglement witnesses and Bell’s inequalities tailored to specific minimal detection lengths, offering an upper bound for detection lengths in given states. By assessing the noise robustness of these witnesses, we demonstrate that witnesses with shorter detection lengths can exhibit superior performance under certain conditions.