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Quantum Electronics and Laser Science Conference

Quantum cloning and multi-photon quantum cryptography

D. Boumeester

Published Aug 24, 2005• 0 citations
Publisher

Abstract

Summary form only given. Multi-photon states from stimulated parametric down~canverrionc an be entangled both in polarization and photon number. Maximally high-dimemion entanglement can be concentrated from these states via photon-counting. We show experimental results for the concentration of a ratational symmetric four-photon entangled state obtained by stimulated emission of the familiar anti-symmetric two-particle Bell state.

DOI
10.1109/qels.2002.1031291

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Summary form only given. Multi-photon states from stimulated parametric down~canverrionc an be entangled both in polarization and photon number. Maximally high-dimemion entanglement can be concentrated from these states via photon-counting. We show experimental results for the concentration of a ratational symmetric four-photon entangled state obtained by stimulated emission of the familiar anti-symmetric two-particle Bell state.
We introduce the notion of laser-like operation for polarization entangled photons. The proposed device has a two-mode output which contains quantum correlations both between the polarization degree of freedom for particles in separate modes and between the photon numbers in the modes. The proposed device will operate in the new and virtually unexplored regime of many-particle entanglement. We present the design and provide experimental data in support of the main operation mechanism. In particular we show the generation of a rotational symmetric four-photon entangled state obtained by stimulated emission of the familiar antisymmetric two-particle Bell state. The produced states allow for novel quantum cryptography and quantum information protocols and for tests of spin-s Bell inequalities.
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.
We propose an experiment where a photon is first cloned by stimulated parametric down-conversion, making many (imperfect) copies, and then the cloning transformation is inverted, regenerating the original photon while destroying the copies. Focusing on the case where the initial photon is entangled with another photon, we study the conditions under which entanglement can be proven in the final state. The proposed experiment would provide a clear demonstration that quantum information is preserved in quantum cloning. It would furthermore allow a definitive experimental proof for micro-macro entanglement in the intermediate multiphoton state, which is still an outstanding challenge. Finally, it might provide a quantum detection technique for small differences in transmission (e.g., in biological samples), whose sensitivity scales better with the number of photons used than a classical transmission measurement.
Summary form only given. Quantum cryptography uses single photons to allow secure distribution of secret key material to sender and receiver, without the possibility of an undetected eavesdropper. In the protocol suggested by Ekert, each photon of a quantum-mechanically entangled pair is sent to the sender and receiver, who randomly measure the polarization in various bases. If the bases are the same, then sender and receiver will have completely correlated measurement results, which become the shared secret key. Other combinations of measurements are used to test Bell's inequalities, which limit the possible correlations achievable with any local realistic theory. The presence of an intermediate eavesdropper can be readily detected by an inability to violate Bell's inequality. Using the polarization-entangled photon pairs from a novel spontaneous parametric down-conversion source, we have experimentally implemented. Ekert's proposal.
Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement-a highly nonclassical correlation-remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two-photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.