Florian Kanitschar

High-dimensional (HD) entanglement promises both enhanced key rates and overcoming obstacles faced by modern-day quantum communication. However, modern convex optimization-based security arguments are limited by computational constraints; thus, accessible dimensions are far exceeded by progress in HD photonics, bringing forth a need for efficient methods to compute key rates for large encoding dimensions. In response to this problem, we present a flexible analytic framework facilitated by the dual of a semi-definite program and diagonalizing operators inspired by entanglement-witness theory, enabling the efficient computation of key rates in high-dimensional systems. To facilitate the latter, we show how matrix completion techniques can be incorporated to effectively yield improved, computable bounds on the key rate in paradigmatic high-dimensional systems of time- or frequency-bin entangled photons and beyond, revealing the potential for very high dimensions to surpass low dimensional protocols already with existing technology. In our accompanying work, we show how our findings can be used to establish finite-size security against coherent attacks for general HD-QKD protocols both in the fixed- and variable-length scenario and we examine the performance under realistic conditions. Detailed manuscripts for Refs. [1] and [2] can be found attached.

In our work, we developed an optical CVQKD system that uses polarization-based QPSK modulation designed for atmospheric quantum communication and a corresponding post-processing pipeline including error correction and privacy amplification. In a first laboratory experiment, we applied the security statement of a recently published security proof to calculate composable key rates with a total security parameter of ε = 1e-10 in the finite size regime against i.i.d. collective attacks. We also used the post-processing pipeline to study the effect of error correction and frame errors on the actual key extraction in a finite-size system – finding that the common approach of going to high frame errors to increase the ECC efficiency β does not optimize the extractable key length.Furthermore, we deployed the system over an ad-hoc atmospheric channel of 1.7 km in Mai 2023 in the city of Jena, Germany. In a first proof-of-principle study, we were able to apply the full optical and post-processing pipeline to extract pseudo-asymptotic keys and discuss the further steps necessary to move the system to the finite-size regime. To the best of our knowledge, this is the first CVQKD demonstration over a real atmospheric channel combining both the new class of DMCVQKD security proofs without Gaussian optimality and error correction steps.

The conventional point-to-point setting of a Quantum Key Distribution (QKD) protocol typically considers two directly connected remote parties that aim to establish secret keys. This work proposes a natural generalization of a well-established point-to-point discrete-modulated continuous-variable (CV) QKD protocol to the point-to-multipoint setting. We explore four different trust levels among the communicating parties and provide secure key rates for the loss-only channel and the lossy & noisy channel both in the asymptotic limit and in the finite-size regime. We experimentally demonstrate the feasibility of our protocols in an access network topology with 10 km-long access links, achieving a key rate of $7.09 \times 10^{-3}$ bits per symbol or of 0.866 Mbit/s. Our study shows that discrete-modulated CV-QKD is a suitable candidate to connect several dozens of users in a point-to-multipoint network, achieving high rates at a reduced cost, using off-the-shelf components employed in modern communication infrastructure.

Quantum key distribution (QKD) provides information-theoretic security guaranteed by the laws of quantum mechanics, making it resistant to future computational threats, including quantum computers. While QKD technology shows great promise, its widespread adoption depends heavily on its usability and viability, with key rate performance and cost-effectiveness serving as critical evaluation metrics. In this work, we report an integrated silicon photonics-based QKD system that achieves a secret key rate of 1.213 Gbps over a metropolitan distance of 10 km with polarization multiplexing. Our contributions are twofold. First, in the quantum optical layer, we developed an on-chip quantum transmitter and an efficient quantum receiver that operate at 40 Gbaud/s at room temperature. Second, we designed a discrete-modulated continuous variable (DM CV) QKD implementation with efficient information reconciliation based on polar codes, enabling potentially high-throughput real-time data processing. Our results demonstrate a practical QKD solution that combines high performance with cost efficiency. We anticipate this research will pave the way for large-scale quantum secure networks.

Discrete-Modulated Continuous-Variable Quantum Key Distribution (DMCVQKD) protocols are amenable for deployment in quantum communication networks due to their experimental simplicity, but pose theoretical challenges impeding their tight security analyses. Major progress has recently been made in the finite-size regime against independent and identical (iid) collective attacks (Kanitschar, F. et. al., (2023), PRX Quantum, 4(4), p.040306). However, a complete and rigorous analysis must take into account correlated rounds of attack beyond the iid-collective assumption, and must not assume a photon-number cutoff on the signal states. The difficulty of achieving this lies in the absence of an information-theoretic framework for proving security that handles infinite dimensional multipartite quantum states that are a priori unstructured, i.e., beyond the asymptotic iid setting. We present a composable security proof against coherent attacks in the finite-size regime for a general DMCVQKD protocol. We introduce a framework to handle states that are in part iid and in part unstructured (almost iid) in infinite dimensional Hilbert spaces. We use a de Finetti reduction for infinite dimensional almost iid states (Renner, R., Cirac, J. I., Phys. Rev. Lett. 102, 110504 (2009)), and generalise the acceptance test and the energy test to almost iid states handling Eve’s correlated infinite dimensional side information. As work in progress, we address the issue of a missing chain rule that formulates an explicit key rate expression. Numerical simulation of key rates (Winick, A. et. al., Quantum 2, 77 (2018)) can then be performed, demonstrating the efficacy of the security proof.

The conventional point-to-point setting of Quantum Key Distribution (QKD) typically considers two directly connected remote parties that aim to establish secret keys. However, almost all digital communication tasks involve multiple nodes and complex network architectures. Thus, it is essential to adapt and integrate QKD protocols and their security analyses to accommodate these complex environments and ensure secure communication across interconnected systems. This work proposes a natural generalization of a well-established point-to-point discrete modulated (DM) continuous-variable (CV) QKD protocol to the multi-party setting. We explore four different trust levels among the communicating parties and provide secure key rates in lossy and noisy channels. Our study shows that discrete modulated CV-QKD is a suitable candidate to connect several dozens of users in a point-to-multipoint network, achieving high rates at low cost, using off-the-shelf components employed in modern communication infrastructure.

High-dimensional entanglement promises not only increased key rates but overcoming some of the obstacles faced by modern-day quantum communication. Typically, key rates are computed via convex optimization procedures, which inherently limits the dimensionality one can analyze through computational constraints. Recent progress in high-dimensional photonics far exceeds these limitations and brings forth a need for (semi-)analytic methods to compute key rates in the regime of large encoding dimensions. We present a flexible analytic framework facilitated by the dual of a semi-definite program, enabling the computation of key rates in high-dimensional systems. This method, whether purely analytical or semi-numerical, hinges on diagonalizing specific operators influenced by entanglement witnesses and efficiently solving an optimization problem. To facilitate the latter, we show how matrix completion techniques can be incorporated to yield effective and computable bounds on the key rate in paradigmatic high-dimensional systems of time- or frequency-bin entangled photons and beyond.

In our work, we provide a clean security analysis of a new high-dimensional QKD setup with a Franson interferometer in the asymptotic limit and calculate secure key rates using a recent method developed. We argue that our new protocol is not only experimentally easier, as it does not require tomography of the polarization degree of freedom, but also allows for a clean security analysis without assumptions that were implicitly hidden in earlier analyses of similar and related protocols. We build a realistic noise model that takes environmental photons, dark counts, channel losses and non-unit detection efficiency into account and show that our new protocol allows secure key rates for twice as many environmental photons than comparable protocols available in literature. We want to highlight that while the security analysis of our protocol is rigorous and clean, the compared key rates for the compared protocol are actually only an upper bound (due to the assumptions implicitly hidden described earlier), so our new protocol outperforms previous settings by at least a factor of 2. Current free-space QKD implementations are only operable during night when environmental photons are low, but fail to provide secure keys during twilight and daytime, which is a major obstacle towards broad practical usage. Thus, doubling the robustness against environmental photons marks an important step forwards towards daylight-independent Quantum Key Distribution implementations.

In our work, we explore various multi-user scenarios for Continuous Variable Quantum Key Distribution with discrete modulation. We propose and analyse DM CV-QKD protocols for various different multi-user scenarios such as * One Alice to $n$ Bobs, where the Bobs do not trust each other, * One Alice to $n$ Bobs, where $m<n$ Bobs trust each other, * Conference Key Agreement between one Alice and $n$ Bobs. One common feature of all protocols that we study is that Alice's source does not need any additional expensive components except state-of-the-art beamsplitters, therefore we call it `cheap source'. This makes the transmitter of our proposed protocols easily implementable in experiments and demonstrations. In our work, we calculate asymptotic secret key rates for a range of parameters and different trust scenarios and show that in the asymptotic limit multi-user DM CV-QKD is possible for distances relevant for mid-sized urban area networks between at least 16 user. This highlights, that DM CV-QKD can be extended to the multi-user scenario and remains a feasible candidate also for early implementations of Quantum Key Distribution in local networks.

Besides discrete-variable QKD, where single photon detection is used, continuous-variable (CV) protocols are using homodyne detection and are thus promising to be compatible with existing classical coherent communication technology. Originally, the research on CV QKD protocols mostly focused on Gaussian modulation (see review [1]), where one assumes that Alice can continuously displace coherent states according to a 2D Gaussian distribution. This modulation allows the security proofs to take advance of Gaussian optimality conditions, but experimental implementations can only reach this pattern up to some finite discretization. Another approach is to directly use a discrete-modulated (DM) CV QKD protocol. Here, Alice is required to prepare a finite number of displaced coherent states, aiming for a higher experimental simplicity, with the drawback of higher theoretical complexity. Recently, new security proofs such as [2] and corresponding experiments [3,4] could show the feasibility of systems using quadrature amplitude modulation (QAM) with 64 and 256 displaced states. However, the security proof was limited to the asymptotic regime and since the experiments did not use implemented error correction codes, one could only estimate the achievable key rates, but could not generate the secret key itself. In this poster, we demonstrate experiments with a protocol with a smaller constellation size of four coherent states that share the same amplitude but are shifted by 90° in phase (QPSK modulation). We exploit a recently published security proof providing tight secret key rates for collective attacks even in the finite size regime [5]. Furthermore, we show that the QPSK data is compatible with our implemented low density parity check (LDPC) codes for binary symmetric channels. This allows us to perform the full QKD protocol from experimental quantum state exchange to classical post processing and to generate a secret key shared between Alice and Bob. For this purpose, we use a laboratory system based on polarization encoding in the Stokes parameters which is equivalent to a QPSK pattern in phase space. This scheme is designed to cope with the challenges of a turbulent atmospheric channel. While the fluctuating nature of such a channel can be targeted by sub-binning the transmission channels [6], the atmosphere is in general non-birefringent, allowing for atmospheric quantum communications [7]. [1] F. Laudenbach et al., Adv. Quantum Technol. 1, 1800011 (2018) [2] A. Denys et al., Quantum 5, 540 (2021) [3] F. Roumestan et al., arXiv:2207.11702 (2022) [4] Y. Pan et al., Optics Letters 47, 3307-3310 (2022) [5] F. Kanitschar et al., arXiv:2301.08686v1 (2023) [6] V. Usenko et al., New J. Phys. 14, 093048 (2012) [7] B. Heim et al., New J. Phys. 16, 113018 (2014)

Advances in the security analysis of continuous-variable quantum key distribution (CVQKD) protocols with true discrete modulation aim to unlock the same performance as that obtained from `traditional' protocols based on Gaussian modulation. We report a CVQKD experiment using 4 states that utilizes a composable security proof to generate a secret key fraction of $5.6 \times 10^{-3}$ bits/symbol over 10 km channel, while providing security against collective attacks.