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Realization and Application of the Two-photon High Dimensional Hyperentangled State

Hongbo Xu, Kun Du, Cong‐Feng Qiao

Published Apr 2, 2012• 0 citations
OpenAlex

Abstract

We propose an experimentally feasible scheme for generating a two $2\times4\times4$ dimensional photons hyperentangled state, entangled in polarization, frequency and spatial mode. This scheme is mainly based on a parametric down-conversion source and cross-Kerr nonlinearities, which avoids the complicated uncertain post-selection. Our method can be easily expanded to the production of hyperentangled states with more photons in multi-dimension. Hence the expectation for vast quantities of information in quantum information processing will possibly come true. Finally, we put forward a realizable quantum key distribution (QKD) protocol based on the high dimensional hyperentangled state.

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Nowadays,the generation of multiphoton entangled states is almost realized by combining the coupled entangled photons emitted from spontaneous parametric down-conversion (SPDC) with the first-order term.In this case,one may focus mainly on the first-order term,and then avoid multipair emission events by restricting experimental parameters.On the other hand,for the higher-order terms in SPDC source,these emitted entangled photons have interesting features.For example,they are entangled maximally not only in photon number for the spatial modes,but also in polarization degree of freedom.In general,two photons,which are entangled in two or more degrees of freedom,are called hyperentangled pair of photons or hyperentangled state.We present a scheme to generate the four-photon hyperentangled state based on four indistinguishable photons emitted from SPDC source with the second-order term.Consider two SPDC sources with equal probability of emission of photons in respective spatial modes.With the passive linear optical devices,i.e., beam splitters,half wave plates,polarizing beam splitters,etc.,under the condition of registering a specified four-photon coincidence,we can obtain the four-photon hyperentangled state in which the photons are entangled in both polarization and spatial-mode degrees of freedom.Here,of course,for an arbitrary fourfold coincidence detection,one obtains a canonical four-photon Greenberger-Horne-Zeilinger (GHZ) state.Then we show the results of fourfold coincidence detections and the corresponding probabilities for the four-photon GHZ states,where the generation of the four-photon hyperentangled state is included as long as we are not to distinguish the two detectors located at the same locations. As a result,our scheme has two notable features.When we only consider the second-order emission,since it is not needed for us to distinguish between the two SPDC sources,the present scheme is simple and feasible.Also,based on the postselection with fourfold coincidence detection,our scheme is suitable for the normal first-order emission where we restrict the four photons emitted from the same source.In this sense,our scheme is efficient.In a word,we describe a method to generate the four-photon hyperentangled state with the second-order emission in SPDC source,which may contribute to the exploration of multipair entanglement with higher-order emissions from the SPDC source.

Acta Physica Sinica•Jan 1, 2018•2 citations
We propose an experimentally feasible scheme for generating a two 2×4×42\times4\times42×4×4 dimensional photons hyperentangled state, entangled in polarization, frequency and spatial mode. This scheme is mainly based on a parametric down-conversion source and cross-Kerr nonlinearities, which avoids the complicated uncertain post-selection. Our method can be easily expanded to the production of hyperentangled states with more photons in multi-dimension. Hence the expectation for vast quantities of information in quantum information processing will possibly come true. Finally, we put forward a realizable quantum key distribution (QKD) protocol based on the high dimensional hyperentangled state.
We propose an experimentally feasible scheme for generating a two 2 × 4 × 4 dimensional photon hyperentangled state, entangled in polarization, frequency and spatial mode. This scheme is mainly based on a parametric down-conversion source and cross-Kerr nonlinearities, which avoids the complicated uncertain post-selection. Our method can be easily expanded to the production of hyperentangled states with more photons in multidimensions. Hence the expectation for vast quantities of information in quantum information processing will possibly come true. Finally, we put forward a realizable quantum key distribution (QKD) protocol based on the high dimensional hyperentangled state.
Nowadays, the nonlinear optical process of spontaneous parametric down-conversion is considered as the canonical approach for creating entangled-photon pairs. We consider three pairs of entangled photons emitted by the parametric down-conversion source, and introduce a setup for evolving these photons based on linear optics, which is composed of several polarizing beam splitters, beam splitters, and half wave plates. By using the parametric down-conversion source and the setup, we carefully design an efficient scheme for preparing six-photon hyperentangled states in both the polarization and the spatial degrees of freedom. Because we use almost all possible behaviors of the three pairs of entangled photons, the present scheme is efficient for creating six-photon hyperentangled states. Next, in the regime of weak nonlinearity we design a quantum nondemolition detection to distinguish the two cases of photons in two special spatial modes. It is worth pointing out that our scheme is much easier to realize, since the strength of the nonlinearities in the process of quantum nondemolition detection can be restricted to the scalable orders of magnitude in practicality.
Multiphoton hyperentangement is fundamental in optical quantum information processing. Existing theory and experiments usually focus on producing two-photon hyperentanglement and multiphoton entangled states encoded in a single degree of freedom. Multiphoton entangled states have until now relied on the outcome postselection, a procedure where only the measurement results corresponding to the desired state are considered. Such an approach severely limits the usefulness of the resulting entangled states. We present the protocols of direct production of three- and four-photon hyperentanglement and extend the approach to an arbitrary number of photons through a straightforward cascade of spontaneous parametric down-conversion (SPDC) sources. The generated multiphoton hyperentangled states are encoded in polarization-spatial modes and polarization-time bin degrees of freedom, respectively. Numerical calculation shows that if the average photon number $\ensuremath{\mu}$ is 1, the down-conversion efficiency is $7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and the repetition frequency of the laser is 109{10}^{9}109 Hz, the number of the generation of three-photon and four-photon hyperentanglement after cascading can reach about $5.78\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and $4.44\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ pairs per second, respectively. By eliminating the constraints of outcome postselection, our protocols may represent progresses for multiphoton hyperentangement generation and provide a pivotal role in future multiparty and high-capacity communication networks.
Entanglement in high-dimensional quantum systems, where one or more degrees of freedom of light are involved, offers increased information capacities and enables new quantum protocols.Here, we demonstrate a functional source of high-dimensional, noise-resilient hyperentangled states encoded in time-frequency and vector vortex structured modes, which in turn carry single-particle entanglement between polarization and orbital angular momentum.Pairing nonlinearity-engineered parametric downconversion in an interferometric scheme with spin-to-orbital-angular-momentum conversion, we generate highly entangled photon pairs at telecom wavelength that we characterize via two-photon interference and quantum state tomography, achieving near-unity visibilities and fidelities.While hyperentanglement has been demonstrated before in photonic qubits, here we present a rich entanglement structure involving spectrally and spatially structured light, where three different forms of entanglement coexist in the same biphoton state.
Nowadays,the generation of multiphoton entangled states is almost realized by combining the coupled entangled photons emitted from spontaneous parametric down-conversion (SPDC) with the first-order term.In this case,one may focus mainly on the first-order term,and then avoid multipair emission events by restricting experimental parameters.On the other hand,for the higher-order terms in SPDC source,these emitted entangled photons have interesting features.For example,they are entangled maximally not only in photon number for the spatial modes,but also in polarization degree of freedom.In general,two photons,which are entangled in two or more degrees of freedom,are called hyperentangled pair of photons or hyperentangled state.We present a scheme to generate the four-photon hyperentangled state based on four indistinguishable photons emitted from SPDC source with the second-order term.Consider two SPDC sources with equal probability of emission of photons in respective spatial modes.With the passive linear optical devices,i.e., beam splitters,half wave plates,polarizing beam splitters,etc.,under the condition of registering a specified four-photon coincidence,we can obtain the four-photon hyperentangled state in which the photons are entangled in both polarization and spatial-mode degrees of freedom.Here,of course,for an arbitrary fourfold coincidence detection,one obtains a canonical four-photon Greenberger-Horne-Zeilinger (GHZ) state.Then we show the results of fourfold coincidence detections and the corresponding probabilities for the four-photon GHZ states,where the generation of the four-photon hyperentangled state is included as long as we are not to distinguish the two detectors located at the same locations. As a result,our scheme has two notable features.When we only consider the second-order emission,since it is not needed for us to distinguish between the two SPDC sources,the present scheme is simple and feasible.Also,based on the postselection with fourfold coincidence detection,our scheme is suitable for the normal first-order emission where we restrict the four photons emitted from the same source.In this sense,our scheme is efficient.In a word,we describe a method to generate the four-photon hyperentangled state with the second-order emission in SPDC source,which may contribute to the exploration of multipair entanglement with higher-order emissions from the SPDC source.