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arXiv:1206.3548

Quantum Key Distribution with Fibonacci Orbital Angular Momentum States

David S. Simon, Nate Lawrence, Jacob Trevino, Luca Dal Negro, Alexander V. Sergienko

Published Jun 15, 2012• 5 citations
arXivHTMLPDF

Abstract

Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to protect the security of shared encryption keys. Here we present a new and fundamentally different approach to high-capacity, high-efficiency QKD by exploiting interplay between cross-disciplinary ideas from quantum information and light scattering of aperiodic photonic media. The novelty of the proposed approach relies on a unique type of entangled-photon source and a new physical mechanism for efficiently sharing keys. The new source produces entangled photons with orbital angular momenta (OAM) randomly distributed among Fibonacci numbers. Combining entanglement with the mathematical properties of Fibonacci sequences leads to a new QKD protocol. This Fibonacci protocol is immune to photon-number-splitting attacks and allows secure generation of long keys from few photons. Unlike other protocols, reference frame alignment and active modulation of production and detection bases are unnecessary, since security does not require use of non-orthogonal polarization measurements.

DOI
10.48550/arxiv.1206.3548

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Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to protect the security of shared encryption keys. Here we present a new and fundamentally different approach to high-capacity, high-efficiency QKD by exploiting interplay between cross-disciplinary ideas from quantum information and light scattering of aperiodic photonic media. The novelty of the proposed approach relies on a unique type of entangled-photon source and a new physical mechanism for efficiently sharing keys. The new source produces entangled photons with orbital angular momenta (OAM) randomly distributed among Fibonacci numbers. Combining entanglement with the mathematical properties of Fibonacci sequences leads to a new QKD protocol. This Fibonacci protocol is immune to photon-number-splitting attacks and allows secure generation of long keys from few photons. Unlike other protocols, reference frame alignment and active modulation of production and detection bases are unnecessary, since security does not require use of non-orthogonal polarization measurements.
Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to securely share encryption keys between two parties. Here, we present an approach to high-capacity, high-efficiency QKD by exploiting cross-disciplinary ideas from quantum information theory and the theory of light scattering of aperiodic photonic media. We propose a unique type of entangled-photon source, as well as a physical mechanism for efficiently sharing keys. The key-sharing protocol combines entanglement with the mathematical properties of a recursive sequence to allow a realization of the physical conditions necessary for implementation of the no-cloning principle for QKD, while the source produces entangled photons whose orbital angular momenta (OAM) are in a superposition of Fibonacci numbers. The source is used to implement a particular physical realization of the protocol by randomly encoding the Fibonacci sequence onto entangled OAM states, allowing secure generation of long keys from few photons. Unlike in polarization-based protocols, reference frame alignment is unnecessary, while the required experimental setup is simpler than other OAM-based protocols capable of achieving the same capacity and its complexity grows less rapidly with increasing range of OAM used.
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.
It has been widely recognized that the underlying principles of quantum mechanics could be used to enable secure communications, without any additional conventional cryptographic systems, while utilizing the properties of the photons. Considerable research efforts have been invested to develop an efficient quantum key distribution (QKD) scheme over either free-space optical or fiber-optics channels. Most of these research efforts have been focused on a two-dimensional QKD, commonly realized by the use of the polarization state of photons. However, the data rates for the quantum key exchange in two-dimensional QKD are still low, while transmission distance is limited. On the other hand, it is well known that photons can carry both the spin angular momentum (SAM) and the orbital angular momentum (OAM), associated with the polarization and azimuthal phase of the complex electric field, respectively. Accordingly, we can define the combined-OAM-SAM state of a photon as |l, σ〉, where l and σ correspond to OAM and SAM indexes, respectively. Since the OAM eigenstates are orthogonal, an arbitrary number of bits per single photon can be transmitted, which could considerably increase the total secure bit rate. To improve secure data rates, we propose two types of protocols, namely, nonentangled-based (such as weak coherent state) and entanglement-assisted protocols, both employing the photon combined-OAM-SAM state, which can be used for secure key distribution over free-space optical and few-mode fiber channels. Two types of entanglement-assisted protocols are described, namely, two-basis and (D + 1)-basis protocols ( D is dimensionality of corresponding Hilbert space). We further describe how to implement the qudit gates required for implementation of these protocols. Finally, we discuss the security issues of the proposed protocols and determine both infinite and finite secret key fraction rates.
We propose an improved quantum key distribution (QKD) protocol based on orbital angular momentum (OAM) entangled states. Three Lucas-valued OAM entangled photons are generated by two cascaded spontaneous parameter down-conversion processes. Two photons are detained and detected by Alice, while the other is transmitted to Bob and then detected. A new scheme is designed to sift the original key bits. Compared to existing protocols, we believe our protocol greatly improves coding efficiency and is verifiable. The analysis results show that our protocol is immune to the photon-number-splitting attack, the intercept-resend attack and the classical information leakage. This work provides an efficient path to high-dimensional QKD systems.
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.