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International Conference on Information Technology and Nanotechnology (ITNT)

Symmetric encryption algorithm using “twisted” light

Бурлов С. А., Alexander V. Gorokhov

Published Jan 1, 2017• 0 citations
Publisher

Abstract

An algorithm for applying a ”twisted” light for constructing an encryption scheme is described. Our approach is founded on famous classical symmetric permutation algorithm based on NP-full task for ”Knapsack Problem” with changes taken into account the quantum origin of the information carrier. As a measuring device for selection of pure states from a mixed one, the Mach-Zehnder interferometer cascade is supposed to use, which allows sorting the parity of the mixed state of the orbital angular momentum (OAM) of photons.

DOI
10.18287/1613-0073-2017-1900-136-139

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An algorithm for applying a ”twisted” light for constructing an encryption scheme is described. Our approach is founded on famous classical symmetric permutation algorithm based on NP-full task for ”Knapsack Problem” with changes taken into account the quantum origin of the information carrier. As a measuring device for selection of pure states from a mixed one, the Mach-Zehnder interferometer cascade is supposed to use, which allows sorting the parity of the mixed state of the orbital angular momentum (OAM) of photons.
Twisted light, or light with orbital angular momentum (OAM), plays an emerging role in both classical and quantum science, with important applications in areas as diverse as biophotonics, micromachines, spintronics, or quantum information. It offers fascinating opportunities for exploring new fundamental ideas in physics, as well as for being used as a tool for practical applications. One important point is to determine how to generate single photons, and two-photon states, with an appropriate OAM content. Here we describe the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) in different non-collinear geometries. These geometries introduce a variety of new features. In particular, we find the OAM of entangled pairs generated in purely transverse-emitting configurations, where the entangled photons counter-propagate perpendicularly to the direction of propagation of the pump beam. The spatial walk-off of all interacting waves in the parametric process also determines the OAM content of the down-converted photons, and here its influence is also revealed.
We report the experimental implementation of quantum permutation algorithm using polarization and orbital angular momentum of the classical optical beam. The easy-handling optical setup to realize all eight cyclic permutation transformations for an input four-dimensional system has been constructed. The two-to-one speed-up ratio to determine the parity of each permutation has been demonstrated. Moreover, we have theoretically discussed the extension to the case with eight elements, and the limitations on the generalization of our proposal to higher-dimensional cases. Our scheme exhibits outstanding stability and demonstrates that optical quantum computation is possible using classical states of light.
We investigate two-photon entangled states using two important degrees of freedom of the electromagnetic field, namely orbital angular momentum (OAM) and spin angular momentum. For photons propagating in the same direction we apply the idea of entanglement duality and develop schemes to do entanglement sorting based on either OAM or polarization. In each case the entanglement is tested using appropriate witnesses. We finally present generalizations of these ideas to three- and four-photon entangled states.
Summary form only given. The orbital angular momentum (OAM) of light has raised a great deal of applications [1], ranging from the trapping of particles, the driving of optical micromachines to applications in astrophysics studies. In quantum optics, twisted single-photons have also been identified as promising carriers for the implementation of various quantum information protocols. They indeed offer the possibility to encode and process information in high-dimensional Hilbert spaces and could enable to reach higher efficiencies and enhanced information capacity. For further applications in quantum networks involving light-matter interfaces, a critical capability is the ability to reversibly map OAM into and out of atomic memories. While the storage of bright beams of light in Laguerre-Gaussian modes has been reported in the past few years [2, 3], we report here the first demonstration of storage in the single-photon regime [4]. The experimental realization proceeds in the following way. First, LG modes are generated using a spatial light modulator. These modes, which are weak coherent states at the single-photon level, are then mapped into an ensemble of cold cesium atoms in a magneto-optical trap using the dynamic electromagnetically-induced transparency (EIT) protocol. The signal quantum properties, including its OAM, are expected to be transferred to the atomic medium and can be stored for a programmable time, limited by the lifetime of the atomic coherence. After this reversible storage, unlike for bright beams, the detection of twisted single-photons cannot be performed by imaging on a CCD camera. Here we have chosen to work with a combination of a computergenerated hologram, which adds or subtracts one unity of OAM, and a single-mode fiber to implement a mode discriminator. In our experiment, the output mode is actually split on a 50/50 beam splitter and one discriminator is installed in each of the two output paths so that we can quantify both the LG+1 and LG-1 components of the retrieved light. We stored and retrieved LG+1 and LG-1 modes. As can be seen in fig. 1, detection events in the detection path with l opposite to the one of the incoming mode are negligible, within the distinction ratio. For both modes, the overall storage and retrieval efficiency is (16 ± 2%). We thus demonstrated that such pulses carrying OAM can be stored in the single-photon regime into and out the ensemble with preserved handedness of the helical phase structure. Mapping of a TEM10 mode, i.e. an equal-weight superposition of LG+1 and LG-1 modes was also performed. Within our experimental precision, the achieved storage and retrieval efficiency is the same here each LG components than for the individual storage presented previously. Further works should include reconstruction of a full density matrix, including coherences not measured here, and the calculation of process fidelity. We implemented a sophisticated detection technique based on a Mach-Zehnder interferometer. Preliminary results will be reported. Extensions to higher alphabets for the realization of high-dimensional quantum information networks is also work for future.
Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light's orbital angular momentum degree of freedom. By exploiting the spatial mode of photons, our scheme provides a more elegant way to understand the principle of quantum permutation algorithm and shows that the high dimension characteristic of light's orbital angular momentum may be useful in quantum algorithms. Our scheme can be extended to higher dimension by introducing more spatial modes and it paves the way to trace the source of quantum speedup.
The efficient separation of the orbital angular momentum (OAM) is essential to both the classical and quantum applications with twisted photons. Here we devise and demonstrate experimentally an efficient method of mimicking the Faraday rotation to sort the OAM based on the OAM-to-polarization coupling effect induced by a modified Mach-Zehnder interferometer. Our device is capable of sorting the OAM of positive and negative numbers, as well as their mixtures. Furthermore, we report the first experimental demonstration to sort optical vortices of noninteger charges. The possibility of working at the photon-count level is also shown using an electron-multiplying CCD camera. Our scheme holds promise for quantum information applications with single-photon entanglement and for high-capacity communication systems with polarization and OAM multiplexing.