Frequency-Resolved Simulations of Highly Entangled Biphoton States: Beyond the Single-Pair Approximation. II. Application to Entanglement-based Quantum Key Distribution
We present time- and frequency-resolved simulations of quantum key distribution~(QKD) systems employing highly entangled biphoton quantum states. Our simulations are based on expansions of the covariance matrix and photon detection probabilities of biphoton states in terms of increasing orders of the joint spectral amplitude that were introduced in the first part of this series. Employing these expansions allows us to efficiently evaluate the impact of multi-pair events on the performance of the QKD systems while systematically taking into account effects from the photon spectra and many relevant imperfections of the setup. The results are shown to be in agreement with corresponding measurements of the key rates and quantum bit error rates.
We present time- and frequency-resolved simulations of quantum key distribution~(QKD) systems employing highly entangled biphoton quantum states. Our simulations are based on expansions of the covariance matrix and photon detection probabilities of biphoton states in terms of increasing orders of the joint spectral amplitude that were introduced in the first part of this series. Employing these expansions allows us to efficiently evaluate the impact of multi-pair events on the performance of the QKD systems while systematically taking into account effects from the photon spectra and many relevant imperfections of the setup. The results are shown to be in agreement with corresponding measurements of the key rates and quantum bit error rates.
The creation and manipulation of biphotons is important for many applications in quantum optics and quantum information. Topics that benefit from efficient biphoton sources range from the most fundamental quantum science experiments to the highly applied fields of quantum communication and quantum computation. Biphoton sources have long been hailed as one of the leading methods for creating entangled photon pairs for tests of Bell's inequality, creating heralded photon pairs that are used in on-demand single-photon sources and heralded measurement techniques, and for quantum communication protocols to name a few. Specifically for quantum communication, biphoton sources are commonly used for cutting edge quantum key distribution (QKD) protocols. In the first part of the thesis, I focus on realizing an efficient biphoton source that produces high yield photon pairs. More specifically, I develop an optimized biphoton source using the nonlinear optical process of spontaneous parametric down-conversion in a second-order nonlinear crystal. I develop a formalism for predicting the two important metrics of a biphoton source: the heralding efficiency and joint count rate. I show how, from a large parameter space, one can tailor the phase matching of the nonlinear interaction to create a high quality biphoton source that produces both high heralding efficiency and high joint count rate. I achieve heralding efficiencies of 86$\\pm5\\%$ and joint count rates of 2.58$\\pm0.6kHzpermWpumppower.Ishowthatusingacollinearnondegenerategeometryallowsforheraldingefficienciesofupto99.7\\%$ assuming no loss in the system. I verify the theoretical model with experimental results and find good agreement. In the second part of the thesis I turn to manipulating the single photons born from the biphoton source for applications in creating single-photon spectrometers and time-frequency QKD systems. The security of QKD is only guaranteed if the two parties have access to a set of states called mutually unbiased states. I create a set of these states in time and their conjugate states in the frequency basis and show that I can manipulate single photon correlations in time and frequency so that an eavesdropper can be detected if she localizes a photon to a 1 ns time interval. Additionally, in these experiments, I stretch a single photon wavepacket of 5-ps-width to a wavepacket of 8.3-ns-width and subsequently recompress it to at least the resolution of the detectors (sim 300 ps). This demonstrates a stretch factor of >1600 for a single-photon pulse using a group velocity dispersive material. To my knowledge, this is the largest reported stretch factor for a single-photon wavepacket produced by a biphoton source. The ability to stretch and recompress a single photon by this amount has applications in creating high-resolution, high-efficiency, single-photon spectrometers as well as advancing time-frequency QKD systems and other temporal pulse shaping applications.
The paper addresses the development of quantum networks (QNs) with entanglementbased Quantum Key Distribution (QKD) protocols.The entanglement (the correlation among the quantum states of several particles) is an essential principle of quantum mechanics.This property has a major impact on the fields of application of QKD systems, the secured cryptographic key exchange and passive attack detection, while it can also be applied in quantum teleportation.Starting from the existing achievements in Europe (a QN for connecting several cities in Randstad, one of the main metropolitan regions in the Netherlands), a case study for a simulated entanglement-based QN is presented, including an ideal scenario (with noiseless QKD) and a nonideal one (with noisy QKD).The experimental settings are differentiated through the link and node fidelity.The simulation process produces general statistics, sender statistics, receiver statistics, the QBER (Quantum Bit Error Rate) and also the raw keys as generated by the entanglement-based protocol.No post-processing (non-quantic) phase is considered for the analyzed setting.Such simulations are useful for properly adjusting the design of a QN while taking into account its expected performance with respect to the non-ideal use-cases with errors that could be caused by an imperfect hardware or by potential eavesdropping actions.
Quantum information is transforming modern society with concepts like entanglement, crucial for communication, computing and sensing. To mainstream these technologies, improved efficiency in encoding, transmission and information processing is required, especially in quantum key distribution (QKD). This method aims to securely distribute encryption keys while improving key rates and overcoming propagation loss and noise. Photons serve as ideal carriers due to their various properties for encoding information and minimal environmental interaction, making them vital for the global internet. High-dimensional and hyper-entanglement offer advantages over traditional two-mode encoding methods, including increase noise tolerance and information capacity. However, practical implementation is often limited by measurement device complexities and errors. Frequencies, or photon colours, present a promising approach to boost quantum communication thanks to their compatibility with existing telecommunications infrastructure and naturally occurs in photon pair generation. This thesis explores the frequency degree of freedom for applications in QKD, utilizing efficient all-fiber photon-pair sources to generate hyper-entangled states in polarization and frequency. The incorporation of fast modulators allows for high-speed operation while maintaining high entanglement fidelity. Reconfigurable spectral filters enable tailored spectro-temporal properties to fulfil requirements in multi-user networks and protocols beyond QKD, such as quantum secret sharing. To maximize quantum information capacity, methods for efficiently characterizing frequency entanglement are developed, achieving a certification of 35 modes, a record for the time and frequency degrees of freedom. Finally, estimates of secure key rates and a discussion of noise effects is shown. This foundation supports broadband and flexible quantum networks that effectively utilize frequency encoding in the future quantum internet.
A method for photon-efficient quantum key distribution (QKD) is proposed and analyzed theoretically. The technique is based on nested encoding of multiple logical qubits into the discretized temporal degree of freedom of a single photon. The states of individual logical qubits are measured using a cascade of interferometric stages followed by time-resolved photon counting. The method may be useful in implementations of entanglement-based QKD protocols whose performance is limited by the brightness of onboard sources of nonclassical light, based e.g. on spontaneous parametric down-conversion. Numerical optimization taking into account the presence of background noise indicates the potential of multiqubit encoding for a nearly tenfold increase of the attainable key rate for entanglement-based LEO satellite QKD systems.
For secure practical systems, quantum key distribution (QKD) must provide high key rates over long distances. Time-entanglement-based QKD promises to increase the secret key rate and distribution distances compared to other QKD implementations. This article describes the major steps in QKD protocols, focusing on the nascent QKD technology based on high-dimensional time-bin entangled photons. We overview state-of-the-art from the information and coding theory perspective. In particular, we discuss the key rate loss due to single-photon detector imperfections. We hope the open questions posed and discussed in this paper will inspire information and coding theorists to contribute to and impact fledgling quantum applications and influence future quantum communication systems.
We formulate quantum optics to include frequency dependence in the modeling of optical networks. Entangled light pulses available for quantum cryptography are entangled not only in polarization but also, whether one wants it or not, in frequency. We model effects of the frequency spectrum of faint polarization-entangled light pulses on detection statistics. For instance, we show how polarization entanglement combines with frequency entanglement in the variation of detection statistics with pulse energy. Attention is paid not only to single-photon light states but also to multi-photon states. These are needed (1) to analyze the dependence of statistics on energy and (2) to help in calibrating fiber couplers, lasers and other devices, even when their desired use is for the generation of single-photon light.