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Nonlocal Polarization Interferometry and Entanglement Detection

Brian P. Williams

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

At present, quantum entanglement is a resource, distributed to enable a variety of quantum information applications such as quantum key distribution, superdense coding, and teleportation. Necessarily, the distribution and characterization of entanglement is fundamental to its application. This dissertation details three research efforts to enable nonlocal entanglement detection, distribution, and characterization. Foremost of these efforts, we present the theory and demonstration of a nonlocal polarization interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer’s unique correlation dependence on the anti-diagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. Second, we propose a nonlocal method of interferometrically mapping time-entangled photons to polarization entangled states, capitalizing on the strengths of both the robust temporal degree of freedom and the “easy to measure” polarization degree of freedom. Finally, we propose a method of estimating and representing correlation probabilities in nonlocal two-photon experiments using Bayes’ rule. Numerical simulations confirm that a vigorous consideration of the available information offers a correlation characterization superior to the standard approach.

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At present, quantum entanglement is a resource, distributed to enable a variety of quantum information applications such as quantum key distribution, superdense coding, and teleportation. Necessarily, the distribution and characterization of entanglement is fundamental to its application. This dissertation details three research efforts to enable nonlocal entanglement detection, distribution, and characterization. Foremost of these efforts, we present the theory and demonstration of a nonlocal polarization interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer’s unique correlation dependence on the anti-diagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. Second, we propose a nonlocal method of interferometrically mapping time-entangled photons to polarization entangled states, capitalizing on the strengths of both the robust temporal degree of freedom and the “easy to measure” polarization degree of freedom. Finally, we propose a method of estimating and representing correlation probabilities in nonlocal two-photon experiments using Bayes’ rule. Numerical simulations confirm that a vigorous consideration of the available information offers a correlation characterization superior to the standard approach.
Quantum state interferography has recently been proposed as an interference-based technique for the measurement of the general qubit and pure qudit states [Phys. Rev. Lett. 125, 123601 (2020)]. This interferometric method exploits the relationship between the off-diagonal elements of the density matrix and the expectation values of non-Hermitian spin ladder operators. The extension of this method to a composite system is however nontrivial, as it involves the measurement of both single-photon and nonlocal multiphoton interferences. In this work, we present the theoretical analysis of the two-photon quantum state interferography of an arbitrary quantum state. We show that complete state information could in principle be obtained with two measurement settings and by recording six interferograms, using a single-photon sensitive imaging device. We then experimentally demonstrate two-photon nonlocal quantum state interferography of polarization-entangled photon pairs generated with type-I spontaneous parametric down conversion. Quantum state interferography of all four Bell states is performed. An upper bound on the separability of the bipartite states is established in terms of the visibility, phase average intensity, and phase shift of the interference patterns related to the antidiagonal elements of the matrix. Each of the four Bell states can be distinguished by the violation of these bounds uniquely.
We review methods that allow one to detect and characterize quantum correlations in many-body systems, with a special focus on approaches which are scalable. Namely, those applicable to systems with many degrees of freedom, without requiring a number of measurements or computational resources to analyze the data that scale exponentially with the system size. We begin with introducing the concepts of quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality in the bipartite scenario, to then present their multipartite generalization. We review recent progress on characterizing these quantum correlations from partial information on the system state, such as through data-driven methods or witnesses based on low-order moments of collective observables. We then review state-of-the-art experiments that demonstrate the preparation, manipulation and detection of highly-entangled many-body systems. For each platform (e.g. atoms, ions, photons, superconducting circuits) we illustrate the available toolbox for state preparation and measurement, emphasizing the challenges that each system poses. To conclude, we present a list of timely open problems in the field.
Summary form only given. Photon pairs entangled in different degrees of freedom are of great interest for quantum communication. In long distance fiber based communications, time-energy entanglement [1] is preferred over polarization entanglement due to its robustness against polarization mode dispersion due to the fiber propagation. On the other hand, the measurement of time-energy entanglement is more complex than that of polarization. In this work we convert the quantum correlation of time -energy entangled photons into polarization entanglement using unbalanced Michelson interferometers. Time correlated photons are generated thorough spontaneous parametric down conversion of a laser of wavelength 405nm in a second order nonlinear crystal (β-barium borate). Correlated photons carrying horizontal polarization are converted to diagonal polarization and send to a Michelson interferometer (Fig. la) with a polarizing beam splitter. In both arms of the interferometer, one quarter -wave plate oriented at 45° is kept so that the returning photons are converted from horizontal to vertical and vice -versa. The output of the interferometer yields co -polarized photons (HUI and VV) with the same relative time of arrival. The anti -correlated photons (HV and VH) exit the interferometer with different relative arrival time due to the unbalanced interferometer arms. A coincidence window less than the photon travel time for the path length difference will fi lter out the anti -correlated photons. We ensure that the coherence length of the pump laser is larger than the path length difference such that the co -polarized bi-photon state coherently adds up to the so called Bell state.
Quantum entanglement, quantum steering and Bell nonlocality, as significant quantum resources in the field of quantum information science, can achieve variously valuable quantum information tasks. Among of them, quantum entanglement and Bell nonlocality are the weakest and strongest nonlocal correlations, respectively. One can capture the quantum steering and Bell nonlocality via violating steering inequality and Bell inequality, respectively. In general, the detections of quantum steering and Bell nonlocality are strictly harder than entanglement detection. Here, based on steering inequality test and quantum state tomography, we attain various nonlocal correlations and experimentally demonstrate that the estimations of quantum steering and Bell nonlocality can be realized according to the quantum entanglement of the prepared two-photon test states. The estimated efficiency of quantum steering is stronger than the one of Bell nonlocality in this scenario, i.e., more steerable two-photon test states can be verified through quantum entanglement. In addition, quantum steering and Bell nonlocality are bounded by the corresponding upper and lower bounds, and these bounds cannot be punctured by all prepared two-photon states in experiment. These results are conducive to understand the relations among these nonlocal correlations.