The characterization of quantum processes, e.g. communication channels, is an essential ingredient for establishing quantum information systems. For quantum key distribution protocols, the amount of overall noise in the channel determines the rate at which secret bits are distributed between authorized partners. In particular, tomographic protocols allow for the full reconstruction, and thus characterization, of the channel. Here, we perform quantum process tomography of high-dimensional quantum communication channels with dimensions ranging from 2 to 5. We can thus explicitly demonstrate the effect of an eavesdropper performing an optimal cloning attack or an intercept-resend attack during a quantum cryptographic protocol. Moreover, our study shows that quantum process tomography enables a more detailed understanding of the channel conditions compared to a coarse-grained measure, such as quantum bit error rates. This full characterization technique allows us to optimize the performance of quantum key distribution under asymmetric experimental conditions, which is particularly useful when considering high-dimensional encoding schemes.
The characterization of quantum processes, e.g. communication channels, is an essential ingredient for establishing quantum information systems. For quantum key distribution protocols, the amount of overall noise in the channel determines the rate at which secret bits are distributed between authorized partners. In particular, tomographic protocols allow for the full reconstruction, and thus characterization, of the channel. Here, we perform quantum process tomography of high-dimensional quantum communication channels with dimensions ranging from 2 to 5. We can thus explicitly demonstrate the effect of an eavesdropper performing an optimal cloning attack or an intercept-resend attack during a quantum cryptographic protocol. Moreover, our study shows that quantum process tomography enables a more detailed understanding of the channel conditions compared to a coarse-grained measure, such as quantum bit error rates. This full characterization technique allows us to optimize the performance of quantum key distribution under asymmetric experimental conditions, which is particularly useful when considering high-dimensional encoding schemes.
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.
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 key distribution algorithms are considered secure because they leverage quantum phenomena to provide security. As such, eavesdroppers can be detected by analyzing the error rate in the shared key obtained by the parties performing the key exchange. Nevertheless, this paper developed and investigated a novel attack strategy capable of being undetected through error analysis of the shared key. Said attack entails an eavesdropper measuring the quantum channel (i.e., the channel used to transmit quantum particles between two parties) using a higher dimension than that used by the legitimate parties. By measuring a particle in a dimension that spans all possible states in a given quantum key distribution algorithm, the collapsed state of the measured particle should be undetectable when measured in the lower dimension. To analyze the proposed high-dimensional eavesdropping attack, the simulator Cirq was used to model the attack on BB84, a four-dimensional variant of BB84, and the Six-State Protocol. The results of these simulations show the efficiency of this attack, with an eavesdropper being undetectable through quantum bit error rate analysis in each algorithm This promotes the need for further analysis of the high-dimensional eavesdropping attack on physical hardware and other quantum key distribution algorithms
The security analysis of the Ekert 1991 (E91), Bennett 1992 (B92), six-state protocol, Scarani–Acín–Ribordy–Gisin 2004 (SARG04) quantum key distribution (QKD) protocols, and their variants have been studied in the presence of collective-rotation noise channels. However, besides the Bennett–Brassard 1984 (BB84) being the first proposed, extensively studied, and essential protocol, its security proof under collective-rotation noise is still missing. Thus, we aim to close this gap in the literature. Consequently, we investigate how collective-rotation noise channels affect the security of the BB84 protocol. Mainly, we study scenarios where the eavesdropper, Eve, conducts an intercept-resend attack on the transmitted photons sent via a quantum communication channel shared by Alice and Bob. Notably, we distinguish the impact of collective-rotation noise and that of the eavesdropper. To achieve this, we provide rigorous, yet straightforward numerical calculations. First, we derive a model for the collective-rotation noise for the BB84 protocol and parametrize the mutual information shared between Alice and Eve. This is followed by deriving the quantum bit error rate (QBER) for two intercept-resend attack scenarios. In particular, we demonstrate that, for small rotation angles, one can extract a secure secret key under a collective-rotation noise channel when there is no eavesdropping. We observe that noise induced by rotation of 0.35 radians of the prepared quantum state results in a QBER of 11%, which corresponds to the lower bound on the tolerable error rate for the BB84 QKD protocol against general attacks. Moreover, a rotational angle of 0.53 radians yields a 25% QBER, which corresponds to the error rate bound due to the intercept-resend attack. Finally, we conclude that the BB84 protocol is robust against intercept-resend attacks on collective-rotation noise channels when the rotation angle is varied arbitrarily within particular bounds.
Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scales exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. We make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography, enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.
The characterization of a decoherence process is among the central challenges in quantum physics. A major difficulty with current quantum process tomography methods is the enormous number of experiments needed to accomplish a tomography task. Here we present a highly efficient method for tomography of a quantum process that has a small number of significant elements. Our method is based on the compressed sensing techniques being used in information theory. In this new method, for a system with Hilbert space dimension n and a process matrix of dimension n × n with sparsity s, the required number of experimental configurations is O(s log n). This heralds a logarithmic advantage in contrast to other methods of quantum process tomography. More specifically, for q-qubits with n = 2, the scaling of resources is O(sq) — linear in the product of sparsity and number of qubits.