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arXiv:2104.12811 · Physical Review A

Classical model for measurements of an entanglement witness

Brian R. La Cour, E. C. G. Sudarshan

Published Sep 2, 2015• 4 citations
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Abstract

We describe a classical model that may serve as an analog for joint and local measurements of an entanglement witness. The analogous experimental procedure and data analysis protocol of the model follow those of a previous experiment to measure an entanglement witness with polarized photons prepared in a mixed state [Phys. Rev. Lett. 91, 227901 (2003)]. Numerical simulations show excellent agreement with both experimental results and quantum-mechanical predictions. This agreement is made possible by the fact that the model exhibits contextuality due to the postselection of coincident detection events.

DOI
10.1103/physreva.92.032302

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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.
We present a method to estimate entanglement measures in experiments. We show how a lower bound on a generic entanglement measure can be derived from the measured expectation values of any finite collection of entanglement witnesses. Hence witness measurements are given a quantitative meaning without the need of further experimental data. We apply our results to a recent multiphoton experiment [M. Bourennane, Phys. Rev. Lett. 92, 087902 (2004)], giving bounds on the entanglement of formation and the geometric measure of entanglement in this experiment.
Abstract Recent Einstein-Podolsky-Rosen-Bohm experiments [M. Giustinaet al. Phys. Rev. Lett. 115, 250401 (2015); L. K. Shalmet al. Phys. Rev. Lett. 115, 250402 (2015)] that claim to be loophole free are scrutinized. The combination of a digital computer and discrete-event simulation is used to construct a minimal but faithful model of the most perfected realization of these laboratory experiments. In contrast to prior simulations, all photon selections are strictly made, as they are in the actual experiments, at the local station and no other “post-selection” is involved. The simulation results demonstrate that a manifestly non-quantum model that identifies photons in the same local manner as in these experiments can produce correlations that are in excellent agreement with those of the quantum theoretical description of the corresponding thought experiment, in conflict with Bell’s theorem which states that this is impossible. The failure of Bell’s theorem is possible because of our recognition of the photon identification loophole. Such identification measurement-procedures are necessarily included in all actual experiments but are not included in the theory of Bell and his followers.