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...

Orbital angular momentum (OAM) of light is an attractive degree of freedom for fundamental studies in quantum mechanics. In addition, the discrete unbounded state-space of OAM has been used to enhance classical and quantum communications. Unambiguous measurement of OAM is a key part of all such experiments. However, state-of-the-art methods for separating single photons carrying a large number of different OAM values are limited to a theoretical separation efficiency of about 77%. Here we demonstrate a method which uses a series of unitary optical transformations to enable the measurement of light's OAM with an experimental separation efficiency of 492%. Furthermore, we demonstrate the separation of modes in the angular position basis, which is mutually unbiased with respect to the OAM basis. The high degree of certainty achieved by our method makes it particularly attractive for enhancing the information capacity of multi-level quantum cryptography systems.

The measurement of a quantum state poses a unique challenge for experimentalists. Recently, the technique of 'direct measurement' was proposed for characterizing a quantum state in situ through sequential weak and strong measurements. While this method has been used for measuring polarization states, its real potential lies in the measurement of states with a large dimensionality. Here we show the practical direct measurement of a highdimensional state vector in the discrete basis of orbital angular momentum. Through weak measurements of orbital angular momentum and strong measurements of angular position, we measure the complex probability amplitudes of a pure state with a dimensionality, d ¼ 27. Further, we use our method to directly observe the relationship between rotations of a state vector and the relative phase between its orbital-angular-momentum components. Our technique has important applications in high-dimensional classical and quantum information systems and can be extended to characterize other types of large quantum states.

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.

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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.

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The energy damping time in a mechanical resonator is critical to many precision metrology applications, such as timekeeping and force measurements. We present measurements of the phonon lifetime of a microwave-frequency, nanoscale silicon acoustic cavity incorporating a phononic bandgap acoustic shield. Using pulsed laser light to excite a colocalized optical mode of the cavity, we measured the internal acoustic modes with single-phonon sensitivity down to millikelvin temperatures, yielding a phonon lifetime of up to τph,0≈1.5 seconds (quality factor Q=5×1010) and a coherence time of τcoh,0≈130 microseconds for bandgap-shielded cavities. These acoustically engineered nanoscale structures provide a window into the material origins of quantum noise and have potential applications ranging from tests of various collapse models of quantum mechanics to miniature quantum memory elements in hybrid superconducting quantum circuits.