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Optics Express

High-dimensional encoding based on classical nonseparability

Pengyun Li, Bo Wang, Xiangdong Zhang

Published Jun 24, 2016• 46 citations
Publisher

Abstract

Based on the formal analogy between classical nonseparability and quantum entanglement, we present a multi-ary encoding protocol exploiting the nonseparability of orbital angular momentum (OAM) and polarization for a hybrid vector beam. Such an encoding can be realized in high-dimensional state space by transforming OAM of the vector beam under the assistance of polarization, which is called "high-dimensional" encoding. It is shown that N-ary encoding using N-dimensional non-separable basis can be obtained by manipulating N/2 different OAM modes, which is equivalent to encoding log2N bits of information. It is also shown that the decoding of vector beams can be realized with very low cross talk. Compared with the encoding protocol transforming OAM modes of scalar beams, our encoding scheme, based on classical nonseparability of vector beams, can encode much more information. This is of great benefit to the optical communication.

DOI
10.1364/oe.24.015143

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Based on the formal analogy between classical nonseparability and quantum entanglement, we present a multi-ary encoding protocol exploiting the nonseparability of orbital angular momentum (OAM) and polarization for a hybrid vector beam. Such an encoding can be realized in high-dimensional state space by transforming OAM of the vector beam under the assistance of polarization, which is called "high-dimensional" encoding. It is shown that N-ary encoding using N-dimensional non-separable basis can be obtained by manipulating N/2 different OAM modes, which is equivalent to encoding log2N bits of information. It is also shown that the decoding of vector beams can be realized with very low cross talk. Compared with the encoding protocol transforming OAM modes of scalar beams, our encoding scheme, based on classical nonseparability of vector beams, can encode much more information. This is of great benefit to the optical communication.
In this work, it is experimentally demonstrated that the nonseparability of vector beams (e.g., radial and azimuthal polarization) can be used to encode information for optical communication. By exploiting the nonseparability of a vector beam's space and polarization degrees of freedom using conventional wave plates, it is shown that 2 bits of information can be encoded when applying the identity and three Pauli operators to its polarization degree of freedom. It is also shown that vector beams can be efficiently decoded with as low as 2.7% cross talk using a Mach-Zehnder interferometer that exploits a higher-order Pancharatnam-Berry phase and liquid crystal q-plates.
Hybrid entangled states, having entanglement between different degrees-of-freedom (DoF) of a particle pair, are of great interest for quantum information science and communication protocols. Among different DoFs, the hybrid entangled states encoded with polarization and orbital angular momentum (OAM) allow the generation of qubit-qudit entangled states, macroscopic entanglement with very high quanta of OAM and improvement in angular resolution in remote sensing. Till date, such hybrid entangled states are generated by using a high-fidelity polarization entangled states and subsequent imprinting of chosen amount of OAM using suitable mode converters such as spatial light modulator in complicated experimental schemes. Given that the entangled sources have feeble number of photons, loss of photons during imprinting of OAM using diffractive optical elements limits the use of such hybrid states for practical applications. Here we report, on a simple generic experimental scheme to generate hybrid entangled states in polarization and OAM through direct transfer of classical non-separable states of the pump beam in parametric down conversion process. As a proof of principle, using local non-separable pump states of OAM mode l = 3, we have produced quantum hybrid entangled states with entanglement witness parameter of ~1.25 ± 0.03 violating by 8 standard deviation.
Hybrid entangled states, having entanglement between different degrees-of-freedom (DoF) of a particle pair, are of great interest for quantum information science and communication protocols. Among different DoFs, the hybrid entangled states encoded with polarization and orbital angular momentum (OAM) allow the generation of qubit-qudit entangled states, macroscopic entanglement with very high quanta of OAM and improvement in angular resolution in remote sensing. Till date, such hybrid entangled states are generated by using a high-fidelity polarization entangled state and subsequent imprinting of chosen amount of OAM using suitable mode converters such as spatial light modulator in complicated experimental schemes. Given that the entangled sources have feeble number of photons, loss of photons during imprinting of OAM using diffractive optical elements limits the use of such hybrid state for practical applications. Here we report, on a simple experimental scheme to generate hybrid entangled state in polarization and OAM through direct transfer of classical non-separable state of the pump beam in parametric down conversion process. As a proof of principle, using local non-separable pump state of OAM mode l=3, we have produced quantum hybrid entangled state with entanglement witness parameter of W-1.25 violating by 8 standard deviation. The generic scheme can be used to produce hybrid entangled state between two photons differing by any quantum number through proper choice of non-separable state of the pump beam.
The orbital angular momentum (OAM) carried by optical beams is a useful quantity for encoding information. This form of encoding has been incorporated into various works ranging from telecommunications to quantum cryptography, most of which require methods that can rapidly process the OAM content of a beam. Among current state-of-the-art schemes that can readily acquire this information are so-called OAM sorters, which consist of devices that spatially separate the OAM components of a beam. Such devices have found numerous applications in optical communications, a field that is in constant demand for additional degrees of freedom, such as polarization and wavelength, into which information can also be encoded. Here, we report the implementation of a device capable of sorting a beam based on its OAM and polarization content, which could be of use in works employing both of these degrees of freedom as information channels. After characterizing our fabricated device, we demonstrate how it can be used for quantum communications via a quantum key distribution protocol.