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arXiv:quant-ph/0405155

Proposed experiment on the continuity of quantum entanglement

Masanori Sato

Published May 26, 2004• 2 citations
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Abstract

We propose experiments on quantum entanglement for investigating the Einstein Podolsky Rosen (EPR) problem with the polarization directions of photons. These experiments are performed to investigate whether the defined polarization directions in an entangled state are teleported between entangled photons. EPR-type sequential experiments are performed using a twin-photon beam and two pairs of linear polarization analyzers under the cross-Nicol condition (i.e., orthogonal to each other). If the third filter whose polarization angle is 45 degrees is set between the first cross-Nicol filters, the beam intensity is changed from 0 to 12.5 %, and at the second cross-Nicol filters, the beam intensity is changed from 0 to 25 %. In this experiment, we predict that the "continuity of quantum entanglement" under a pure Hamiltonian evolution is detected.

DOI
10.48550/arxiv.quant-ph/0405155

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We propose experiments on quantum entanglement for investigating the Einstein Podolsky Rosen (EPR) problem with the polarization directions of photons. These experiments are performed to investigate whether the defined polarization directions in an entangled state are teleported between entangled photons. EPR-type sequential experiments are performed using a twin-photon beam and two pairs of linear polarization analyzers under the cross-Nicol condition (i.e., orthogonal to each other). If the third filter whose polarization angle is 45 degrees is set between the first cross-Nicol filters, the beam intensity is changed from 0 to 12.5 %, and at the second cross-Nicol filters, the beam intensity is changed from 0 to 25 %. In this experiment, we predict that the "continuity of quantum entanglement" under a pure Hamiltonian evolution is detected.
We propose experiments of quantum entanglement for investigating the EPR problem with the polarization directions of photons. These experiments are performed to investigate whether or not the polarization directions in an entangled state are affected through quantum entanglement. EPR-type sequential experiments can be performed using a twin-photon beam and two pairs of linear polarization analyzers. If one of the linear polarization analyzers in the second pair is set at a different angle to the first one, it indicates that one of the entangled state photons has changed its polarization direction. In this experiment, we can predict the following two answers. (1) The first pair of linear polarization analyzers projects the entangled state on a nonentangled state, or (2) the "continuity of entanglement" under a pure Hamiltonian evolution is detected.
We generate and characterize continuous variable polarization entanglement between two optical beams. We first produce quadrature entanglement, and by performing local operations we transform it into a polarization basis. We extend two entanglement criteria, the inseparability criteria proposed by Duan et al (2000 Phys. Rev. Lett. 84 2722) and the Einstein–Podolsky–Rosen (EPR) paradox criteria proposed by Reid and Drummond (1988 Phys. Rev. Lett. 60 2731), to Stokes operators; and use them to characterize the entanglement. Our results for the EPR paradox criteria are visualized in terms of uncertainty balls on the Poincaré sphere. We demonstrate theoretically that using two quadrature entangled pairs it is possible to entangle three orthogonal Stokes operators between a pair of beams, although with a bound √3 times more stringent than for the quadrature entanglement.
A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for measurements with continuous variable outcomes is presented to establish criteria for the demonstration of the EPR paradox, for situations where the correlation between spatially separated subsystems is not perfect. Two types of criteria for EPR correlations are determined. The first type are based on measurements of the variances of conditional probability distributions and are necessary to reflect directly the situation of the original EPR paradox. The second weaker set of EPR criteria are based on the proven failure of (Bell-type) local realistic theories which could be consistent with a local quantum description for each subsystem. The relationship with criteria sufficient to prove entanglement is established, to show that any demonstration of EPR correlations will also signify entanglement. It is also shown how a demonstration of entanglement between two spatially separated subsystems, if not able to interpreted as a violation of a Bell-type inequality, may be interpreted as a demonstration of the EPR correlations. In particular it is explained how the experimental observation of two-mode squeezing using spatially separated detectors will signify not only entanglement but EPR correlations defined in a general sense.
Results of experiments recently performed are reported, in which two optical parametric amplifiers were set up to generate two independently quadrature squeezed continuous wave laser beams. The transformation of quadrature squeezed states into polarization squeezed states and into states with spatial quantum correlations is demonstrated. By utilizing two squeezed laser beams, a polarization squeezed state exhibiting three simultaneously squeezed Stokes operator variances was generated. Continuous variable polarization entanglement was generated and the Einstein-Podolsky-Rosen paradox was observed. A pair of Stokes operators satisfied both the inseparability criterion and the conditional variance criterion. Values of 0.49 and 0.77, respectively, were observed, with entanglement requiring values below unity. The inseparability measure of the observed quadrature entanglement was 0.44. This value is sufficient for a demonstration of quantum teleportation, which is the next experimental goal of the authors.
We report recent developments in our experiment to teleport light beams by utilizing Einstein-Podolsky-Rosen (EPR) entanglement for continuous quantum variables. We describe details of our experimental apparatus, including the generation of EPR entanglement from squeezed states of light. In addition, we have developed an explicit model for the teleportation of coherent states that includes the effect of diverse loss factors and limited degrees of entanglement, and that enables us to project the possibilities for achieving yet higher fidelities beyond the currently achieved value of 62% with our apparatus. Propects for other teleportation schemes will also be discussed.
The Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum nonlocality between entanglement and Bell nonlocality, which plays an important role in quantum information processing tasks. In the past few years, the investigations concerning the EPR steering have been demonstrated in a series of experiments. However, these studies rely on the relevant steering inequalities and the choices of measurement settings. Here, we experimentally verify the EPR steering via entanglement detection without using any steering inequality and measurement setting. By constructing two new states from a two-qubit state, we observe the EPR steering by detecting the entanglement of these new states. The results show that the entanglement of the newly constructed states can be regarded as an unusual kind of steering witness for these states. Compared to the results of Xiao et al. [Phys. Rev. Lett. 118, 140404 (2017)], we find that the ability to detect the EPR steering in our scenario is stronger than that of two-setting projective measurements, which can observe more steerable states. Hence, our demonstrations can deepen the understanding of the connection between the EPR steering and entanglement.