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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Multiphoton entanglement

Mohamed Bourennane, Manfred Eibl, Sascha Gaertner, Nikolai Kiesel, Christian Kurtsiefer, Marek Żukowski, Harald Weinfurter

Published Sep 11, 2002• 1 citation
Publisher

Abstract

Multiphoton entanglement is the basis of many quantum communication schemes, quantum cryptographic protocols, and fundamental tests of quantum theory. Spontaneous parametric down-conversion is the most effective source for polarization entangled photon pairs. Here we show, that a entangled 4-photon state can be directly created by parametric down-conversion. This state exhibit perfect quantum correlations and a high robustness of entanglement against photon loss. We have used this state for four-particle test of local realistic theories. Therefore this state can be used for new types of quantum communication. We also report on possibilities for the experimentally realization of a 3-photon entangled state, the so called W-state, and discuss some of its properties.

DOI
10.1117/12.483039

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Multiphoton entanglement is the basis of many quantum communication schemes, quantum cryptographic protocols, and fundamental tests of quantum theory. Spontaneous parametric down-conversion is the most effective source for polarization entangled photon pairs. Here we show, that a entangled 4-photon state can be directly created by parametric down-conversion. This state exhibit perfect quantum correlations and a high robustness of entanglement against photon loss. We have used this state for four-particle test of local realistic theories. Therefore this state can be used for new types of quantum communication. We also report on possibilities for the experimentally realization of a 3-photon entangled state, the so called W-state, and discuss some of its properties.
Abstract Multiphoton entanglement is the basis of many quantum communication schemes, quantum cryptographic protocols, and fundamental tests of quantum theory. Spontaneous parametric down‐conversion is the most effective source for polarization entangled photon pairs. Here we show, that a class of entangled 4‐photon states can be directly created by parametric down‐conversion. These states exhibit perfect quantum correlations and a high robustness of entanglement against photon loss. Therefore these states are well suited for new types of quantum communication.
Multiphoton entanglement is the basis of many quantum communication schemes, quantum cryptographic protocols, and fundamental tests of quantum theory. For entangled three-qubit states it has been shown that there are two inequivalent classes of states, under stochastic local operations and classical communications. The classes are represented by the GHZ- and W-state. The GHZ-state has been used to prove Bell's theorem without inequality. Contrary to the GHZ-state, the W-state shows high robustness of entanglement against photon loss. Here we show the first experimental results on the observation of the polarization entangled three-photon W-state from spontaneous parametric down-conversion.
Multiphoton entanglement in the same polarization has been shown theoretically to be obtainable by type-I spontaneous parametric downconversion (SPDC), which can generate bright pulses more easily than type-II SPDC. A new quantum cryptographic protocol utilizing polarization pairs with the detected type-I entangled multiphotons is proposed as quantum key distribution. We calculate the information capacity versus photon number corresponding to polarization after considering the transmission loss inside the optical fiber, the detector efficiency, and intercept-resend attacks at the level of channel error. The result compares favorably with all other schemes employing entanglement.
Multi-particle entangled states are becoming more and more interesting for different applications in quantum information, such as quantum multi-particle teleportation, entangled based cryptography and quantum communication schemes based on multi-particle states, but also for fundamental reasons such as testing local realism by means of the Greenberger-Horne-Zeilinger states (GHZ) arguments . The advantage of multiparticle entanglement versus the most common two particle one lies in the fact that the greater the number of particles involved in the entangled state, the more clearly the quantum effects are exhibited. Our final goal is to exploit the multi-photon entangled states for quantum metrology. By the interaction of those states with nanostructures (mostly nanoholes, but in a future also nanospheres), we expect to reach sub-wavelength sensitivity phase measurements beating the Standard Quantum Limit as well as to detect plasmonic effects. In this thesis we present our work consisting on designing and building an experimental setup for the generation of states of 4-photon entangled in the transverse linear momentum. In the first part we explain some basics in the form of a technical introduction. We then adapt a general theoretical model to our particular case, explaining the physics of the process of generation of entangled states of photons. We proceed explaining the details of our setup, as well as the procedure of measurement. We then present the results of our tests in a "standard" 2-photon regime to show the correct functioning of the setup itself. Some more sophisticated measurements using structured light in the form of a first-order Hermite-Gaussian mode has been performed to generate entanglement in higher spatial modes are also presented. We conclude with theoretical and experimental details regarding the 4-photon experiments feasible with our setup. Our source is based on Spontaneous Parametric Down-Conversion (SPDC). In the last two decades it has been extensively studied for the generation of two-photon entangled states, since Kwiat et al. published in 1995 the new scheme based on polarization entangled photons. Most of the studies regarding entangled states involving more than two photons are indeed based on quantum correlations in the polarization or in the path of the down converted beams. The great advantage of entangling a spatial degree of freedom (as we do) is related to the dimensionality of the Hilbert space in which the state is defined. In the particular case of linear momentum, which is a continuous variable, we are dealing with infinite dimensions. Since in each dimension of the state one quanta of information can be encoded, the advantage of having multidimension entanglement for the field of quantum communication and computing is clear. The specs of our setup include a periodically-poled KTP crystals offering high conversion efficiency and cut for type-0 SPDC. The photons generated are well known to be inherently entangled in different degrees of freedom such as polarization, energy-time, linear momentum, and orbital angular momentum. Since each single SPDC event generates one photon pair, in order to reach four photon we entangle two consecutive SPDC events per each state. Furthermore, it is possible to manipulate (to enhance) the dimensionality of the entanglement by properly tailoring the pump spatial profile. The key point for the generation of four-photon entangled states is that, under some conditions, two consecutive pairs generated via SPDC cannot be described as two independent pairs but necessarily as a four-photon state showing genuine entanglement. This can happen when using a pulsed laser to generate the entangled photons; in particular, in the regime in which the coherence time of the down-converted photons τc is (much) longer than the temporal length of the pumping pulse Δt. In this condition the emission of a second pair is stimulated by the presence of the first one. That effect can be ultimately seen as a constructive multi-particle interference effect, the deep origin of which has to be sought in the boson statistic of photons.
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.