Quantum cryptography with structured photons through a vortex fiber
Alicia Sit, Robert Fickler, Fatimah Alsaiari, Frédéric Bouchard, Hugo Larocque, Patrick Gregg, Lu Yan, Robert W. Boyd, Siddharth Ramachandran, Ebrahim Karimi
Optical fiber links and networks are integral components within and between cities' communication infrastructures. Implementing quantum cryptographic protocols on either existing or new fiber links will provide information-theoretical security to fiber data transmissions. However, there is a need for ways to increase the channel bandwidth. Using the transverse spatial degree of freedom is one way to transmit more information and increase tolerable error thresholds by extending the common qubit protocols to high-dimensional quantum key distribution (QKD) schemes. Here we use one type of vortex fiber where the transverse spatial modes serves as an additional channel to encode quantum information by structuring the spin and orbital angular momentum of light. In this proof-of-principle experiment, we show that two-dimensional structured photons can be used in such vortex fibers in addition to the common two-dimensional polarization encryption, thereby paving the path to QKD multiplexing schemes.
Optical fiber links and networks are integral components within and between cities' communication infrastructures. Implementing quantum cryptographic protocols on either existing or new fiber links will provide information-theoretical security to fiber data transmissions. However, there is a need for ways to increase the channel bandwidth. Using the transverse spatial degree of freedom is one way to transmit more information and increase tolerable error thresholds by extending the common qubit protocols to high-dimensional quantum key distribution (QKD) schemes. Here we use one type of vortex fiber where the transverse spatial modes serves as an additional channel to encode quantum information by structuring the spin and orbital angular momentum of light. In this proof-of-principle experiment, we show that two-dimensional structured photons can be used in such vortex fibers in addition to the common two-dimensional polarization encryption, thereby paving the path to QKD multiplexing schemes.
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.
Abstract The ability to engineer the spatial wavefunction of photons has enabled a variety of quantum protocols for communication, sensing, and information processing. These protocols exploit the high dimensionality of structured light enabling the encoding of multiple bits of information in a single photon, the measurement of small physical parameters, and the achievement of unprecedented levels of security in schemes for cryptography. Unfortunately, the potential of structured light has been restrained to free-space platforms in which the spatial profile of photons is preserved. Here, we make an important step forward to using structured light for fiber optical communication. We introduce a classical encryption protocol in which the propagation of high-dimensional spatial modes in multimode fibers is used as a natural mechanism for encryption. This provides a secure communication channel for data transmission. The information encoded in spatial modes is retrieved using artificial neural networks, which are trained from the intensity distributions of experimentally detected spatial modes. Our on-fiber communication platform allows us to use single spatial modes for information encoding as well as the high-dimensional superposition modes for bit-by-bit and byte-by-byte encoding respectively. This protocol enables one to recover messages and images with almost perfect accuracy. Our classical smart protocol for high-dimensional encryption in optical fibers provides a platform that can be adapted to address increased per-photon information capacity at the quantum level, while maintaining the fidelity of information transfer. This is key for quantum technologies relying on structured fields of light, particularly those that are challenged by free-space propagation.
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.
Quantum key distribution (QKD) promises information-theoretically secure communication, and is already on the verge of commercialization. Thus far, different QKD protocols have been proposed theoretically and implemented experimentally [1, 2]. The next step will be to implement high-dimensional protocols in order to improve noise resistance and increase the data rate [3-7]. Hitherto, no experimental verification of high-dimensional QKD in the single-photon regime has been conducted outside of the laboratory. Here, we report the realization of such a single-photon QKD system in a turbulent free-space link of 0.3 km over the city of Ottawa, taking advantage of both the spin and orbital angular momentum photonic degrees of freedom. This combination of optical angular momenta allows us to create a 4-dimensional state [8]; wherein, using a high-dimensional BB84 protocol [3, 4], a quantum bit error rate of 11\% was attained with a corresponding secret key rate of 0.65 bits per sifted photon. While an error rate of 5\% with a secret key rate of 0.43 bits per sifted photon is achieved for the case of 2-dimensional structured photons. Even through moderate turbulence without active wavefront correction, it is possible to securely transmit information carried by structured photons, opening the way for intra-city high-dimensional quantum communications under realistic conditions.
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.
The ability to engineer the spatial wavefunction of photons has enabled a variety of quantum protocols for communication, sensing, and information processing. These protocols exploit the high dimensionality of structured light enabling the encodinng of multiple bits of information in a single photon, the measurement of small physical parameters, and the achievement of unprecedented levels of security in schemes for cryptography. Unfortunately, the potential of structured light has been restrained to free-space platforms in which the spatial profile of photons is preserved. Here, we make an important step forward to using structured light for fiber optical communication. We introduce a smart high-dimensional encryption protocol in which the propagation of spatial modes in multimode fibers is used as a natural mechanism for encryption. This provides a secure communication channel for data transmission. The information encoded in spatial modes is retrieved using artificial neural networks, which are trained from the intensity distributions of experimentally detected spatial modes. Our on-fiber communication platform allows us to use spatial modes of light for high-dimensional bit-by-bit and byte-by-byte encoding. This protocol enables one to recover messages and images with almost perfect accuracy. Our smart protocol for high-dimensional optical encryption in optical fibers has key implications for quantum technologies relying on structured fields of light, particularly those that are challenged by free-space propagation.