Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its interpretation has historically been a subject of confusion. Here, a pragmatic introduction to the weak value in terms of measurable quantities is presented, along with an explanation of how it can be determined in the laboratory. Further, its application to three distinct experimental techniques is reviewed. First, as a large interaction parameter it can amplify small signals above technical background noise. Second, as a measurable complex value it enables novel techniques for direct quantum state and geometric phase determination. Third, as a conditioned average of generalized observable eigenvalues it provides a measurable window into nonclassical features of quantum mechanics. In this selective review, a single experimental configuration is used to discuss and clarify each of these applications.
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...
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