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arXiv:1210.1054

Entanglement verification via nonlinear witnesses

Megan Agnew, Jeff Z. Salvail, Jonathan Leach, Robert W. Boyd

Published Oct 3, 2012• 2 citations
arXivHTMLPDF

Abstract

The controlled generation of entangled states and their subsequent detection are integral aspects of quantum information science. In this work, we analyse the application of nonlinear witnesses to the verification of entanglement, and we demonstrate experimentally that nonlinear witnesses perform significantly better than linear witnesses. Specifically, we demonstrate that a single non- linear entanglement witness is able to determine to a high degree of certainty that a mixed state containing orbital angular momentum (OAM) entanglement of specific forms is entangled for any relative phase and sufficient fidelity. This is a significant improvement over linear witnesses, which cannot provide the same level of performance. We envisage that nonlinear witnesses and our method of state preparation will have further uses in areas of quantum science such as superdense coding and quantum key distribution.

DOI
10.48550/arxiv.1210.1054

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The controlled generation of entangled states and their subsequent detection are integral aspects of quantum information science. In this work, we analyse the application of nonlinear witnesses to the verification of entanglement, and we demonstrate experimentally that nonlinear witnesses perform significantly better than linear witnesses. Specifically, we demonstrate that a single non- linear entanglement witness is able to determine to a high degree of certainty that a mixed state containing orbital angular momentum (OAM) entanglement of specific forms is entangled for any relative phase and sufficient fidelity. This is a significant improvement over linear witnesses, which cannot provide the same level of performance. We envisage that nonlinear witnesses and our method of state preparation will have further uses in areas of quantum science such as superdense coding and quantum key distribution.
The controlled generation of entangled states and their subsequent detection are integral aspects of quantum information science. In this Letter, we implement a simple and precise technique that produces any of the four Bell states in the orbital angular momentum degree of freedom. We then use these states to perform the first experimental demonstration of an accessible nonlinear entanglement witness. Such a witness determines entanglement by using the same measurements as required for a linear witness but can detect, in this case, twice as many states as a single linear witness can. We anticipate that our method of state preparation and nonlinear witnesses will have further uses in areas of quantum science, such as superdense coding and quantum key distribution.
Verification of entanglement is an important tool to characterize sources and devices for use in quantum computing and communication applications. In a vast majority of experiments entanglement witnesses (EWs) are used in order to prove the presence of entanglement in a quantum state. EWs can be constructed from available measurement results and do not require a reconstruction of the whole density matrix (full tomography), which is especially valuable for high-dimensional systems. We provide a method to construct accessible nonlinear EWs, which incorporate two important properties. First, they improve on linear EWs in the sense that each nonlinear EW detects more entangled states than its linear counterpart and therefore allows the verification of entanglement without critical dependence on having found the ``right'' linear witness. Second, they can be evaluated using exactly the same data as for the evaluation of the original linear witness. This allows a reanalysis of published experimental data to strengthen statements about entanglement verification without the requirement to perform additional measurements. These particular properties make the accessible nonlinear EWs attractive for the implementations in current experiments, for they can also enhance the statistical significance of the entanglement verification.
Demonstration of entanglements of mobile electrons in solid state conductors using minimal entanglement linear witness from electrical current correlations has been given. However, detection of maximally entangled states and some mixed states is lacking if the witness is based on two cross correlation measurements only. This thesis is trying to detect them with the same number of measurements by investigating nonlinear witnesses which, in principle, should be able to detect more states than a linear witness. This is done theoretically with a generic entangler-detector setup. We found that all entangled states are detectable when considering pure states only but when considering mixed states, there is no improvement compared to a linear witness. This was done using the symmetries between the two operators corresponding to each measurement.
Abstract Entanglement witnesses (EWs) are one of the most effective methods to detect entanglement. It is known that nonlinear EW provide better entanglement detection than their linear counterparts, in that the former detect a strictly larger subset of entangled states than the latter. Whether linear or nonlinear, the method is measurement-device dependent, so that imperfect measurements may cause false certification of entanglement in a shared state. Measurement-device-independent EW provide an escape from such measurement dependence of the entanglement detection for linear EW. Here we present measurement-device-independent nonlinear EW for non-positive partial transpose entangled states as well as for bound entangled states with positive partial transpose. Although the witness considered herein does not detect a larger set of entangled states than other nonlinear EW, it is more efficient in that it never leads to a false detection corresponding to wrong measurements. The constructed measurement-device-independent nonlinear EW certify the entanglement of the same sets of entangled states as their device-dependent parents do, and therefore are better than the linear EW, device-independent or otherwise.
Single photons with helical phase structures may carry a quantized amount of orbital angular momentum (OAM), and their entanglement is important for quantum information science and fundamental tests of quantum theory. Because there is no theoretical upper limit on how many quanta of OAM a single photon can carry, it is possible to create entanglement between two particles with an arbitrarily high difference in quantum number. By transferring polarization entanglement to OAM with an interferometric scheme, we generate and verify entanglement between two photons differing by 600 in quantum number. The only restrictive factors toward higher numbers are current technical limitations. We also experimentally demonstrate that the entanglement of very high OAM can improve the sensitivity of angular resolution in remote sensing.
Hybrid entangled states, having entanglement between different degrees-of-freedom (DoF) of a particle pair, are of great interest for quantum information science and communication protocols. Among different DoFs, the hybrid entangled states encoded with polarization and orbital angular momentum (OAM) allow the generation of qubit-qudit entangled states, macroscopic entanglement with very high quanta of OAM and improvement in angular resolution in remote sensing. Till date, such hybrid entangled states are generated by using a high-fidelity polarization entangled states and subsequent imprinting of chosen amount of OAM using suitable mode converters such as spatial light modulator in complicated experimental schemes. Given that the entangled sources have feeble number of photons, loss of photons during imprinting of OAM using diffractive optical elements limits the use of such hybrid states for practical applications. Here we report, on a simple generic experimental scheme to generate hybrid entangled states in polarization and OAM through direct transfer of classical non-separable states of the pump beam in parametric down conversion process. As a proof of principle, using local non-separable pump states of OAM mode l = 3, we have produced quantum hybrid entangled states with entanglement witness parameter of ~1.25 ± 0.03 violating by 8 standard deviation.