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.
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.
Abstract Most quantum key distribution protocols using a two-dimensional basis, such as HV polarization as first proposed by Bennett and Brassard in 1984, are limited to a key generation density of 1 bit per photon. We increase this key density by encoding information in the transverse spatial displacement of the used photons. Employing this higher-dimensional Hilbert space together with modern single-photon-detecting cameras, we demonstrate a proof-of-principle large-alphabet quantum key distribution experiment with 1024 symbols and a shared information between sender and receiver of 7 bit per photon.
Quantum Key Distribution (QKD) systems usually exploit the polarization of light to encode bit values, thus limiting to 1 bit the amount of information carried by each photon and placing serious limits on the error rates tolerated. Here we propose the use of two mutually unbiased bases for high-dimensional QKD that exploit the transverse spatial structure and coherence properties of the light field, allowing for the transfer of more than 1 bit per photon. Our proposed method employs coherence modulation with an orthonormal basis of time delays (TD) and the corresponding mutually unbiased basis of wave trains (WT). We construct the mutually unbiased basis set WT using a linear combination of orbital angular momentum OAM modes. Through the use of a high-dimensional alphabet encoded in the TD and WT bases, we achieve a high channel capacity of bits per inspected photon. In addition to exhibiting increased channel capacity, multidimensional QKD systems based on spatiotemporal encoding may be more resilient against intercept-resend eavesdropping attacks. Numerical simulations are presented as tests of the proposed QKD system. Experiments remain to be conducted to verify the concept.
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.
Here, we present a proof-of-principle high-dimensional quantum key distribution (QKD) protocol utilizing the position and momentum entanglement of photon pairs. The protocol exploits the fact that position and momentum form mutually unbiased bases, linked via a Fourier transform. One photon of the entangled pair is measured by the sender in a randomly chosen basis-either position or momentum-selected passively via a beam splitter. This projective measurement remotely prepares the partner photon in a corresponding spatial mode, which is sent to the receiver, who similarly performs a random measurement in one of the two bases. In this implementation, we achieve a photon information efficiency of 5.07 bits per photon using 90 spatial modes, and a maximum bit rate of 0.9 Kb/s with 361 modes. To assess the scalability of this spatial-mode encoding scheme, we theoretically show that using a brighter entangled photon source along with next-generation single-photon cameras - featuring improved quantum efficiency, timing and spatial resolution - this approach could achieve 9 bits per photon at 2000 spatial modes, and a bit rate of over 700 Mb/s at 4400 modes while accounting for finite-key effects. These results quantify the opportunities and performance bounds of spatially encoded, entanglement-based QKD and provide a benchmark for future high-dimensional quantum communication systems.
Quantum key distribution (QKD) exploits the quantum nature of light to share provably secure keys, allowing secure communication in the presence of an eavesdropper. The first QKD schemes used photons encoded in two states, such as polarization. Recently, much effort has turned to large-alphabet QKD schemes, which encode photons in high-dimensional basis states. Compared to binary-encoded QKD, large-alphabet schemes can encode more secure information per detected photon, boosting secure communication rates, and also provide increased resilience to noise and loss. High-dimensional encoding may also improve the efficiency of other quantum information processing tasks, such as performing Bell tests and implementing quantum gates. Here, we demonstrate a large-alphabet QKD protocol based on high-dimensional temporal encoding. We achieve record secret-key rates and perform the first field demonstration of large-alphabet QKD. This demonstrates a new, practical way to optimize secret-key rates and marks an important step towards transmission of high-dimensional quantum states in deployed networks.
Quantum key distribution (QKD) protocols most often use two conjugate bases in order to verify the security of the quantum channel. In the majority of protocols, these bases are mutually unbiased to one another, which is to say they are formed from balanced superpositions of the entire set of states in the opposing basis. Here, we introduce a high-dimensional QKD protocol using qubit-like states, referred to as Fourier-qubits (or F-qubits). In our scheme, each F-qubit is a superposition of only two computational basis states with a relative phase that can take d distinct values, where d is the dimension of the computational basis. This non-mutually-unbiased approach allows us to bound the information leaked to an eavesdropper, maintaining security in high-dimensional quantum systems despite the states’ seemingly two-dimensional nature. By simplifying state preparation and measurement, our protocol offers a practical alternative for secure high-dimensional quantum communications. We experimentally demonstrate this protocol for a noisy high-dimensional QKD channel using the orbital angular momentum degree of freedom of light and discuss the potential benefits for encoding in other degrees of freedom. High dimensional quantum key distribution (QKD) systems will allow for higher key generation rate, but with added complexity for creating and detecting high dimensional quantum states. The authors demonstrate a QKD protocol using “qubit-like” qudit states, “F-qubits”, with simpler generation and detection, maintaining the benefits of high dimensional QKD protocols.