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

Encoding mutually unbiased bases in orbital angular momentum for quantum key distribution

Angela L. Dudley, Mhlambululi Mafu, Sandeep K. Goyal, Daniel Giovannini, Melanie G. McLaren, Thomas Konrad, Miles J. Padgett, Francesco Petruccione, Norbert Lütkenhaus, Andrew Forbes

Published Feb 25, 2014• 1 citation
Publisher

Abstract

We encode mutually unbiased bases (MUBs) using the higher-dimensional orbital angular momentum (OAM) degree of freedom and illustrate how these states are encoded on a phase-only spatial light modulator (SLM). We perform ( d - 1)- mutual unbiased measurements in both a classical prepare and measure scheme and on entangled photon pairs for dimensions ranging from d = 2 to 5. The calculated average error rate, mutual information and secret key rate show an increase in information capacity as well as higher generation rates as the dimension increases.

DOI
10.1117/12.2038362

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We encode mutually unbiased bases (MUBs) using the higher-dimensional orbital angular momentum (OAM) degree of freedom and illustrate how these states are encoded on a phase-only spatial light modulator (SLM). We perform ( d - 1)- mutual unbiased measurements in both a classical prepare and measure scheme and on entangled photon pairs for dimensions ranging from d = 2 to 5. The calculated average error rate, mutual information and secret key rate show an increase in information capacity as well as higher generation rates as the dimension increases.
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Quantum Key Distribution (QKD) systems usually exploit the polarization of light to encode bit values, thus limiting to 1 bit the amount of information carried by each photon and placing serious limits on the error rates tolerated. Here we propose the use of two mutually unbiased bases for high-dimensional QKD that exploit the transverse spatial structure and coherence properties of the light field, allowing for the transfer of more than 1 bit per photon. Our proposed method employs coherence modulation with an orthonormal basis of time delays (TD) and the corresponding mutually unbiased basis of wave trains (WT). We construct the mutually unbiased basis set WT using a linear combination of orbital angular momentum OAM modes. Through the use of a high-dimensional alphabet encoded in the TD and WT bases, we achieve a high channel capacity of bits per inspected photon. In addition to exhibiting increased channel capacity, multidimensional QKD systems based on spatiotemporal encoding may be more resilient against intercept-resend eavesdropping attacks. Numerical simulations are presented as tests of the proposed QKD system. Experiments remain to be conducted to verify the concept.
Measurements in mutually unbiased bases (MUBs) are integral to quantum science. An underlying principle of a set of MUBs is that a measurement in one such basis provides no information about a measurement in one of the others. This feature is especially relevant for quantum key distribution. We perform a complete set of mutually unbiased measurements for high-dimensional orbital angular momentum (OAM) states of light. For a two-photon entangled state we show that specific joint measurements provide the minimum number of experimental settings required to characterize the quantum state. From these measurements we reconstruct the density matrix describing the high-dimensional two-photon entangled state. The experimental procedure that we outline can be applied to many different multipartite and high-dimensional systems.
Orbital angular momentum (OAM) states of photons span a high-dimensional Hilbert space, and by using it, higher information capacity and enhanced security can be achieved for both classical communication and quantum key distribution. In this work, we propose a feasible basis-independent encoding scheme for OAM states and show its application in high-dimensional quantum secure direct communication, which enables direct transmission of meaningful messages, in addition to random secret key establishing. Imperfections of optical components may reduce the efficiency of the encoding scheme and, thus, the channel capacity. We discuss the optimal input distribution under realistic conditions to achieve maximal mutual information and an alternative solution using a different set of mutually unbiased bases in the case of a prime-dimensional quantum system.
There has been considerable interest recently in the generation of azimuthal phase functions associated with photon orbital angular momentum (OAM) for high-dimensional quantum key distribution. The generation of secure quantum keys requires not only this pure phase basis but also additional bases comprised of orthonormal superposition states formed from the pure states. These bases are also known as mutually unbiased bases (MUBs) and include quantum states whose wave functions are modulated in both phase and amplitude. Although modulo 2pi optical path control with high-resolution spatial light modulators (SLMs) is well suited to creating the azimuthal phases associated with the pure states, it does not introduce the amplitude modulation associated with the MUB superposition states. Using computer-generated holography (CGH) with the Leith-Upatnieks approach to hologram recording, however, both phase and amplitude modulation can be achieved. We present a description of the OAM states of a three-dimensional MUB system and analyze the construction of these states via CGH with a phase-modulating SLM. The effects of phase holography artifacts on quantum-state generation are quantified and a prescription for avoiding these artifacts by preconditioning the hologram function is presented. Practical effects associated with spatially isolating the first-order diffracted field are also quantified, and a demonstration utilizing a liquid-crystal SLM is presented.