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Chinese Physics Letters

Six-State Quantum Key Distribution Using Photons with Orbital Angular Momentum

Li Jun-Lin, Chuan Xi Wang

Published Nov 1, 2010• 17 citations
Publisher

Abstract

A new implementation of high-dimensional quantum key distribution (QKD) protocol is discussed. Using three mutual unbiased bases, we present a d-level six-state QKD protocol that exploits the orbital angular momentum with the spatial mode of the light beam. The protocol shows that the feature of a high capacity since keys are encoded using photon modes in d-level Hilbert space. The devices for state preparation and measurement are also discussed. This protocol has high security and the alignment of shared reference frames is not needed between sender and receiver.

DOI
10.1088/0256-307x/27/11/110303

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A new implementation of high-dimensional quantum key distribution (QKD) protocol is discussed. Using three mutual unbiased bases, we present a d-level six-state QKD protocol that exploits the orbital angular momentum with the spatial mode of the light beam. The protocol shows that the feature of a high capacity since keys are encoded using photon modes in d-level Hilbert space. The devices for state preparation and measurement are also discussed. This protocol has high security and the alignment of shared reference frames is not needed between sender and receiver.
Quantum Key Distribution (QKD) guarantees the security of communication with quantum physics. Most of widely adopted QKD protocols currently encode the key information with binary signal format---qubit, such as the polarization states. Therefore the transmitted information efficiency of the quantum key is intrinsically upper bounded by 1 bit per photon. High dimensional quantum system is a potential candidate for increasing the capacity of single photon. However, due to the difficulty in manipulating and measuring high dimensional quantum systems, the experimental high dimensional QKD is still at its infancy. Here we propose a sort of practical high-speed high dimensional QKD using partial mutual unbiased basis (PMUB) of photon's orbital angular momentum (OAM). Different from the previous OAM encoding, the high dimensional Hilbert space we used is expanded by the OAM states with same mode order, which can be extended to considerably high dimensions and implemented under current state of the art. Because all the OAM states are in the same mode order, the coherence will be well kept after long-distance propagation, and the detection can be achieved by using passive linear optical elements with very high speed. We show that our protocol has high key generation rate and analyze the anti-noise ability under atmospheric turbulence. Furthermore, the security of our protocol based on PMUB is rigorously proved. Our protocol paves a brand new way for the application of photon's OAM in high dimensional QKD field, which can be a breakthrough for high efficiency quantum communications.
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.
We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform (d+1d+1d+1) mutually unbiased measurements in a classically simulated prepare-and-measure scheme and on a pair of entangled photons for dimensions ranging from d=2d=2d=2 to 5. In our analysis, we pay attention to the detection efficiency and photon pair creation probability. As security measures, we determine from experimental data the average error rate, the mutual information shared between the sender and receiver, and the secret key generation rate per photon. We demonstrate that increasing the dimension leads to an increased information capacity as well as higher key generation rates per photon. However, we find that the benefit of increasing the dimension is limited by practical implementation considerations, which in our case results in deleterious effects observed beyond a dimension of d=4d=4d=4.
Quantum key distribution (QKD) systems often rely on polarization of light for encoding, thus limiting the amount of information that can be sent per photon and placing tight bounds on the error rates that such a system can tolerate. Here we describe a proof-of-principle experiment that indicates the feasibility of high-dimensional QKD based on the transverse structure of the light field allowing for the transfer of more than 1 bit per photon. Our implementation uses the orbital angular momentum (OAM) of photons and the corresponding mutually unbiased basis of angular position (ANG). Our experiment uses a digital micro-mirror device for the rapid generation of OAM and ANG modes at 4 kHz, and a mode sorter capable of sorting single photons based on their OAM and ANG content with a separation efficiency of 93%. Through the use of a seven-dimensional alphabet encoded in the OAM and ANG bases, we achieve a channel capacity of 2.05 bits per sifted photon. Our experiment demonstrates that, in addition to having an increased information capacity, multilevel QKD systems based on spatial-mode encoding can be more resilient against intercept-resend eavesdropping attacks.
Here, we present a proof-of-principle high-dimensional quantum key distribution (QKD) protocol utilizing the position and momentum entanglement of photon pairs. The protocol exploits the fact that position and momentum form mutually unbiased bases, linked via a Fourier transform. One photon of the entangled pair is measured by the sender in a randomly chosen basis-either position or momentum-selected passively via a beam splitter. This projective measurement remotely prepares the partner photon in a corresponding spatial mode, which is sent to the receiver, who similarly performs a random measurement in one of the two bases. In this implementation, we achieve a photon information efficiency of 5.07 bits per photon using 90 spatial modes, and a maximum bit rate of 0.9 Kb/s with 361 modes. To assess the scalability of this spatial-mode encoding scheme, we theoretically show that using a brighter entangled photon source along with next-generation single-photon cameras - featuring improved quantum efficiency, timing and spatial resolution - this approach could achieve 9 bits per photon at 2000 spatial modes, and a bit rate of over 700 Mb/s at 4400 modes while accounting for finite-key effects. These results quantify the opportunities and performance bounds of spatially encoded, entanglement-based QKD and provide a benchmark for future high-dimensional quantum communication systems.
Quantum key distribution (QKD) systems often rely on polarization of light for encoding, thus limiting the amount of information that can be sent per photon and placing tight bounds on the error rates that such a system can tolerate. Here we describe a proof-of-principle experiment that indicates the feasibility of high-dimensional QKD based on the transverse structure of the light field allowing for the transfer of more than 1 bit per photon. Our implementation uses the orbital angular momentum (OAM) of photons and the corresponding mutually unbiased basis of angular position (ANG). Our experiment uses a digital micro-mirror device for the rapid generation of OAM and ANG modes at 4 kHz, and a mode sorter capable of sorting single photons based on their OAM and ANG content with a separation efficiency of 93%. Through the use of a seven-dimensional alphabet encoded in the OAM and ANG bases, we achieve a channel capacity of 2.05 bits per sifted photon. Our experiment demonstrates that, in addition to having an increased information capacity, multilevel QKD systems based on spatial-mode encoding can be more resilient against intercept-resend eavesdropping attacks.