In this thesis, Quantum Key Distribution and quantum communication methods based on high-dimensional spatial coding of light are developed. Their security is based on the fundamental quantum nature of light and profits from the highdimensional Hilbert spaces offered intrinsically by imaging optics. An overview of classical information theory and quantum information is given to introduce the field of quantum cryptography. The advantages of larger dimensional alphabets and the security of the standard two-bases BB84 protocol is shown. The spatial states used for encoding are introduced. An analytic expression for the upper bound on the mutual information for these states is derived, including multiphoton states, detector noise and beam broadening. High-dimensional encoding of single photons is experimentally realized, reaching 10.5 bit per received photon. The dependence of the mutual information on the number of detector pixels is discussed and the experimental values are compared with the theoretical upper bound. It was shown that a standard error-correcting LDPC code is sufficient to achieve practically error-free communication. By adding a second mutually unbiased basis, a large-alphabet QKD system is experimentally realized and characterized. The security of this BB84-like protocol is analyzed in terms of intercept-resend and collective attacks. The key rate after postprocessing is analyzed under realistic circumstances, including finite key length. Finally, a new quantum communication method is demonstrated, which is based on encoding information into wavefronts decomposed over guided modes of a multimode fiber. At the end a step back is made and the similarities and differences of several quantum authentication and quantum cryptography schemes as well as Quantum Data Locking are discussed. This involves comparison of the characteristics of the classical channel, the quantum channel and the necessary dimension of the Hilbert space.
In this thesis, Quantum Key Distribution and quantum communication methods based on high-dimensional spatial coding of light are developed. Their security is based on the fundamental quantum nature of light and profits from the highdimensional Hilbert spaces offered intrinsically by imaging optics. An overview of classical information theory and quantum information is given to introduce the field of quantum cryptography. The advantages of larger dimensional alphabets and the security of the standard two-bases BB84 protocol is shown. The spatial states used for encoding are introduced. An analytic expression for the upper bound on the mutual information for these states is derived, including multiphoton states, detector noise and beam broadening. High-dimensional encoding of single photons is experimentally realized, reaching 10.5 bit per received photon. The dependence of the mutual information on the number of detector pixels is discussed and the experimental values are compared with the theoretical upper bound. It was shown that a standard error-correcting LDPC code is sufficient to achieve practically error-free communication. By adding a second mutually unbiased basis, a large-alphabet QKD system is experimentally realized and characterized. The security of this BB84-like protocol is analyzed in terms of intercept-resend and collective attacks. The key rate after postprocessing is analyzed under realistic circumstances, including finite key length. Finally, a new quantum communication method is demonstrated, which is based on encoding information into wavefronts decomposed over guided modes of a multimode fiber. At the end a step back is made and the similarities and differences of several quantum authentication and quantum cryptography schemes as well as Quantum Data Locking are discussed. This involves comparison of the characteristics of the classical channel, the quantum channel and the necessary dimension of the Hilbert space.
Quantum communication aims to provide absolutely secure transmission of secret information. Existing methods encode symbols into single photons or coherent light with much less than one photon on average. Here we propose and demonstrate an original method that is fundamentally secure with weak coherent light even when several photons per symbol are used. Our method does not require a change of measurement basis and works with a high-dimensional alphabet in a simple practical setup. Moreover, it sends information in a deterministic way, allowing direct decoding at the receiver end. This feature makes the method suitable for both quantum key distribution (QKD) as well as quantum secure direct communication (QSDC). The key element of our method is the combination of wavefront shaping with a multimode fiber channel. Since it is based on an optical fiber, our method allows to naturally extend secure communication to larger distances.
Quantum Key Distribution (QKD) provides a secure way of generating shared cryptographic keys between a sender (Alice) and a receiver (Bob). The original BB84 protocol uses a two-dimensional polarization basis, limiting the information content of a single photon to 1 bit. Using the transverse position of single photons as one basis and the Fourier space as a second basis, one can construct a pair of mutually unbiased higher-dimensional bases. This improves not only the security of the protocol, but also the key generation rate. We present experimental results with a Spatial-Light-Modulator-based encoding scheme employing two nearly orthogonal alphabets with on the order of 103symbols each and an information content of about 10 bit.
Over the last few decades, quantum cryptography has been one of the most important quantum technologies developed. It holds the promise of communicating secure information over untrusted channels. In particular, quantum cryptography is immune to the eventual threats posed by large-scale quantum computers, which is not the case for our current classical cryptography infrastructures. In a world where information, communication and privacy are of paramount importance, the development of secure quantum communication infrastructures becomes imperative. So far, most of the quantum cryptographic systems developed to date are based on two-dimensional encoding schemes, analogous to classical bits, known as qubits. Nevertheless, other than for the polarization of light, photonic degrees of freedom, i.e. position, momentum, time and frequency, naturally occur as high-dimensional quantum systems. Moreover, by considering high-dimensional encoding schemes beyond qubits, advantages in terms of information capacity and noise tolerance are predicted in theory. In this thesis, the basic components of a high-dimensional quantum cryptographic system are investigated. We begin by reviewing important developments in quantum cryptography and high-dimensional quantum information. As a starting point, two different quantum information tasks, i.e. optimal quantum cloning and quantum metrology, are experimentally investigated for high-dimensional quantum systems in order to demonstrate the numerous advantages of performing quantum tasks beyond qubits. The photonic degree of freedom used in these experiments, known as transverse spatial modes, is obtained by combining the position and momentum photonics degrees of freedom. Thus, we develop a novel method to measure high-dimensional quantum states encoded in arbitrary spatial modes. Using a similar characterization technique, several high-dimensional quantum communication channels are characterized to perform high-dimensional quantum cryptography. The tools developed in the laboratory are then brought to realistic conditions in order to test the feasibility of high-dimensional quantum cryptography. Two different types of quantum channels are experimentally investigated, namely an intra-city 300 m long free-space link and a short 3 m outdoor underwater link. Finally, we investigate and compare novel high-dimensional protocols to overcome current limitations.
Quantum communication aims to provide absolutely secure transmission of secret information. State-of-the-art methods encode symbols into single photons or coherent light with much less than one photon on average. For long-distance communication, typically a single-mode fiber is used and significant effort has been devoted already to increase the data carrying capacity of a single optical line. Here we propose and demonstrate a fundamentally new concept for remote key establishment. Our method allows high-dimensional alphabets using spatial degrees of freedom by transmitting information through a light-scrambling multimode fiber and exploiting the no-cloning theorem. Eavesdropper attacks can be detected without using randomly switched mutually unbiased bases. We prove the security against a common class of intercept-resend and beam-splitting attacks with single-photon Fock states and with weak coherent light. Since it is optical fiber based, our method allows to naturally extend secure communication to larger distances. We experimentally demonstrate this new type of key exchange method by encoding information into a few-photon light pulse decomposed over guided modes of an easily available multimode fiber.
The manipulation of high-dimensional degrees of freedom provides new opportunities for more efficient quantum information processing. It has recently been shown that high-dimensional encoded states can provide significant advantages over binary quantum states in applications of quantum computation and quantum communication. In particular, high-dimensional quantum key distribution enables higher secret-key generation rates under practical limitations of detectors or light sources, as well as greater error tolerance. Here, we demonstrate high-dimensional quantum key distribution capabilities both in the laboratory and over a deployed fiber, using photons encoded in a high-dimensional alphabet to increase the secure information yield per detected photon. By adjusting the alphabet size, it is possible to mitigate the effects of receiver bottlenecks and optimize the secret-key rates for different channel losses. This work presents a strategy for achieving higher secret-key rates in receiver-limited scenarios and marks an important step toward high-dimensional quantum communication in deployed fiber networks.
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography performance. This fundamental trade-off between correctness and secrecy motivates the search for quantum high-dimensional encoding approaches for cryptography. Here, we introduce state embeddings that use a k -symbol subset within a d -dimensional Hilbert space, tailored to the channel's error structure. We demonstrate the advantage of our scheme in realistic quantum channels, producing a higher secure key rate. We validate our approach using d = 25 quantum key distribution (QKD) experimental data, derive closed-form expressions for the key rate and threshold, and determine the optimum at k = 5 . These findings advance high-dimensional QKD and pave the way for error correction and modulation for quantum cryptography.