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. IntroductionFirst introduced in 1984 by Bennett and Brassard, quantum key distribution (QKD) is a method for distributing a secret key between two parties [1,2]. Due to a fundamental property of quantum physics known as the nocloning theorem, any attempt made by a third party to eavesdrop inevitably leads to errors that can be detected by the sender and receiver [3,4]. Modern QKD schemes conventionally use a qubit system for encoding information, such as the polarization of a photon. Such systems are easily implemented because technology for encoding and decoding information in a qubit state-space is readily available today, enabling system clock rates in the GHz regime [5][6][7]. Recently, the spatial degree of freedom of photons has been identified as an extremely useful resource for transferring information [8,9]. The information transfer capacity of classical communication links has been increased to more than one terabit per second using spatial-mode multiplexing [10]. In addition, it has been theoretically shown that employing multilevel quantum states (qudits) can increase the robustness of a QKD system against eavesdropping [11][12][13][14]. Although the majority of high-dimensional QKD schemes so far have employed time-bin encoding for increasing the alphabet size [15][16][17][18], it is expected that spatial-mode encoding can be alternatively used to enhance the performance of a QKD system considering the recent advances in free-space orbital angular momentum (OAM) communication, .The feasibility of high-dimensional QKD in the spatial domain has been previously demonstrated by encoding information in the transverse linear momentum and position bases [19,20]. While such encoding schemes provide a simple solution for increasing the information capacity, they are not suitable for long-haul optical links due to the cross-talk caused by diffraction. D...

We describe an experimental implementation of a free-space 11-dimensional communication system using orbital angular momentum (OAM) modes. This system has a maximum measured OAM channel capacity of 2.12 bits/photon. The effects of Kolmogorov thin-phase turbulence on the OAM channel capacity are quantified. We find that increasing the turbulence leads to a degradation of the channel capacity. We are able to mitigate the effects of turbulence by increasing the spacing between detected OAM modes. This study has implications for high-dimensional quantum key distribution (QKD) systems. We describe the sort of QKD system that could be built using our current technology.

We report a technique for encoding both amplitude and phase variations onto a laser beam using a single digital micro-mirror device (DMD). Using this technique, we generate Laguerre-Gaussian and vortex orbital-angular-momentum (OAM) modes, along with modes in a set that is mutually unbiased with respect to the OAM basis. Additionally, we have demonstrated rapid switching among the generated modes at a speed of 4 kHz, which is much faster than the speed regularly achieved by phase-only spatial light modulators (SLMs). The dynamic control of both phase and amplitude of a laser beam is an enabling technology for classical communication and quantum key distribution (QKD) systems that employ spatial mode encoding.

We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital angular momentum bases, is used to estimate angular rotations. This is done by an amplification of both the real and imaginary parts of the weak-value of a polarization operator that has been coupled to the pointer, which is a spatial mode, via a spin-orbit coupling. Our experiment demonstrates the first realization of weak-value amplification in the azimuthal degree of freedom. We have achieved effective amplification factors as large as 100, providing a sensitivity that is on par with more complicated methods that employ quantum states of light or extremely large values of orbital angular momentum.Comment: 5 pages, 3 figures, contains supplementary informatio

We wish to report a typographical error made in the preparation of our manuscript. Specifically, on line 10 of the second paragraph of page 5, we quote values of the parameters that we use to simulate the turbulence. The distances we quote are = z 171.7 1 m and = z 1.538 2 m. The first value is correct, but the second value should read = z 769 2 m. The correct value was used in our laboratory studies, and thus the conclusions of the paper are not modified.We thank Jeffery H Shapiro of MIT for pointing out to us an inconsistency in our published paper, which we subsequently traced to the incorrect value of z 2 quoted in the text. AbstractWe describe a procedure by which a long (≳1 km) optical path through atmospheric turbulence can be experimentally simulated in a controlled fashion and scaled down to distances easily accessible in a laboratory setting. This procedure is then used to simulate a 1 km long free-space communication link in which information is encoded in orbital angular momentum spatial modes. We also demonstrate that standard adaptive optics methods can be used to mitigate many of the effects of thick atmospheric turbulence.