arXiv subjects

Norbert Lütkenhaus

Publications and source records attributed to Norbert Lütkenhaus.

At least 37 records · Page 2Linked to original sources

arXiv2024

Security of quantum key distribution with imperfect phase randomisation

The performance of quantum key distribution (QKD) is severely limited by multiphoton emissions, due to the photon-number-splitting attack. The most efficient solution, the decoy-state method, requires that the phases of all transmitted pulses are independent and uniformly random. In practice, however, these phases are often correlated, especially in high-speed systems, which opens a security loophole. Here, we address this pressing problem by providing a security proof for decoy-state QKD with correlated phases that offers key rates close to the ideal scenario. Our work paves the way towards high-performance secure QKD with practical laser sources, and may have applications beyond QKD.

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arXiv2023

Using Cascade in Quantum Key Distribution

We point out a critical flaw in the analysis of Quantum Key Distribution (QKD) protocols that employ the two-way error correction protocol Cascade. Specifically, this flaw stems from an incom-plete consideration of all two-way communication that occurs during the Cascade protocol. We present a straightforward and elegant alternative approach that addresses this flaw and produces valid key rates. We exemplify our new approach by comparing its key rates with those generated using older, incorrect approaches, for Qubit BB84 and Decoy-State BB84 protocols. We show that in many practically relevant situations, our rectified approach produces the same key rate as older, incorrect approaches. However, in other scenarios, our approach produces valid key rates that are lower, highlighting the importance of properly accounting for all two-way communication during Cascade.

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arXiv2023

Finite-Size Security for Discrete-Modulated Continuous-Variable Quantum Key Distribution Protocols

Discrete-Modulated (DM) Continuous-Variable Quantum Key Distribution (CV-QKD) protocols are promising candidates for commercial implementations of quantum communication networks due to their experimental simplicity. While tight security analyses in the asymptotic limit exist, proofs in the finite-size regime are still subject to active research. We present a composable finite-size security proof against independently and identically distributed collective attacks for a general DM CV-QKD protocol. We introduce a new energy testing theorem to bound the effective dimension of Bob's system and rigorously prove security within Renner's epsilon-security framework and address the issue of acceptance sets in protocols and their security proof. We want to highlight, that our method also allows for nonunique acceptance statistics, which is necessary in practise. Finally, we extend and apply a numerical security proof technique to calculate tight lower bounds on the secure key rate. To demonstrate our method, we apply it to a quadrature phase-shift keying protocol, both for untrusted, ideal and trusted nonideal detectors. The results show that our security proof method yields secure finite-size key rates under experimentally viable conditions up to at least 72km transmission distance.

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arXiv2023

Imperfect Phase-Randomisation and Generalised Decoy-State Quantum Key Distribution

Decoy-state methods [1-3] are essential to perform quantum key distribution (QKD) at large distances in the absence of single photon sources. However, the standard techniques apply only if laser pulses are used that are independent and identically distributed (iid). Moreover, they require that the laser pulses are fully phase-randomised. However, realistic high-speed QKD setups do not meet these stringent requirements [4]. In this work, we generalise decoy-state analysis to accommodate laser sources that emit imperfectly phase-randomised states. We also develop theoretical tools to prove the security of protocols with lasers that emit pulses that are independent, but not identically distributed. These tools can be used with recent work [5] to prove the security of laser sources with correlated phase distributions as well. We quantitatively demonstrate the effect of imperfect phase-randomisation on key rates by computing the key rates for a simple implementation of the three-state protocol.

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arXiv2023

Oscillating photonic Bell state from a semiconductor quantum dot for quantum key distribution

An on-demand source of bright entangled photon pairs is desirable for quantum key distribution (QKD) and quantum repeaters. The leading candidate to generate entangled photon pairs is based on spontaneous parametric down-conversion (SPDC) in a non-linear crystal. However, there exists a fundamental trade-off between entanglement fidelity and efficiency in SPDC sources due to multiphoton emission at high brightness, which limits the pair extraction efficiency to 0.1% when operating at near-unity fidelity. Quantum dots in photonic nanostructures can in principle overcome this trade-off; however, the quantum dots that have achieved entanglement fidelities on par with SPDC sources (99%) have poor pair extraction efficiencies of 0.01%. Here, we demonstrate a 65-fold increase in the pair extraction efficiency compared to quantum dots with equivalent peak fidelity from an InAsP quantum dot in a photonic nanowire waveguide. We measure a raw peak concurrence and fidelity of 95.3% $\pm$ 0.5% and 97.5% $\pm$ 0.8%, respectively. Finally, we show that an oscillating two-photon Bell state generated by a semiconductor quantum dot can be utilized to establish a secure key for QKD, alleviating the need to remove the quantum dot energy splitting of the intermediate exciton states in the biexciton-exciton cascade.

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arXiv2022

An Improved Correction Term for Dimension Reduction in Quantum Key Distribution

The dimension reduction method enables security proofs of quantum key distribution (QKD) protocols that are originally formulated in infinite dimensions via reduction to a tractable finite-dimensional optimization. The reduction of dimensions is associated with a correction term in the secret key rate calculation. The previously derived correction term is loose when the protocol measurements are nearly block-diagonal with respect to the projection onto the reduced finite-dimensional subspace. Here, we provide a tighter correction term. It interpolates between the two extreme cases where all measurement operators are block-diagonal, and where at least one has maximally large off-diagonal blocks. This new correction term can reduce the computational overhead of applying the dimension reduction method by reducing the required dimension of the chosen subspace.

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arXiv2022

Robust Interior Point Method for Quantum Key Distribution Rate Computation

Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the methods are limited by computational resources and the efficiency and accuracy of the underlying algorithms for convex optimization. We derive a stable reformulation of the convex nonlinear semidefinite programming, SDP, model for the key rate calculation problems. We use this to develop an efficient, accurate algorithm. The stable reformulation is based on novel forms of facial reduction, FR, for both the linear constraints and nonlinear quantum relative entropy objective function. This allows for a Gauss-Newton type interior-point approach that avoids the need for perturbations to obtain strict feasibility, a technique currently used in the literature. The result is high accuracy solutions with theoretically proven lower bounds for the original QKD from the FR stable reformulation. This provides novel contributions for FR for general SDP. We report on empirical results that dramatically improve on speed and accuracy, as well as solving previously intractable problems.

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arXiv2021

Numerical Security Proof for Decoy-State BB84 and Measurement-Device-Independent QKD Resistant against Large Basis Misalignment

In this work, we incorporate decoy-state analysis into a well-established numerical framework for key rate calculation, and apply the numerical framework to decoy-state BB84 and measurement-device-independent (MDI) QKD protocols as examples. Additionally, we combine with these decoy-state protocols what is called "fine-grained statistics", which is a variation of existing QKD protocols that makes use of originally discarded data to get a better key rate. We show that such variations can grant protocols resilience against any unknown and slowly changing rotation along one axis, similar to reference-frame-independent QKD, but without the need for encoding physically in an additional rotation-invariant basis. Such an analysis can easily be applied to existing systems, or even data already recorded in previous experiments, to gain significantly higher key rate when considerable misalignment is present, extending the maximum distance for BB84 and MDI-QKD and reducing the need for manual alignment in an experiment.

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arXiv2021

Dimension Reduction in Quantum Key Distribution for Continuous- and Discrete-Variable Protocols

We develop a method to connect the infinite-dimensional description of optical continuous-variable quantum key distribution (QKD) protocols to a finite-dimensional formulation. The secure key rates of the optical QKD protocols can then be evaluated using recently-developed reliable numerical methods for key rate calculations. We apply this method to obtain asymptotic key rates for discrete-modulated continuous-variable QKD protocols, which are of practical significance due to their experimental simplicity and potential for large-scale deployment in quantum-secured networks. Importantly, our security proof does not require the photon-number cutoff assumption relied upon in previous works. We also demonstrate that our method can provide practical advantages over the flag-state squasher when applied to discrete-variable protocols.

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arXiv2021

Numerical Calculations of Finite Key Rate for General Quantum Key Distribution Protocols

Finite key analysis of quantum key distribution (QKD) is an important tool for any QKD implementation. While much work has been done on the framework of finite key analysis, the application to individual protocols often relies on the the specific protocol being simple or highly symmetric as well as represented in small finite-dimensional Hilbert spaces. In this work, we extend our pre-existing reliable, efficient, tight, and generic numerical method for calculating the asymptotic key rate of device-dependent QKD protocols in finite-dimensional Hilbert spaces to the finite key regime using the security analysis framework of Renner. We explain how this extension preserves the reliability, efficiency, and tightness of the asymptotic method. We then explore examples which illustrate both the generality of our method as well as the importance of parameter estimation and data processing within the framework.

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arXiv2020

Trusted detector noise analysis for discrete modulation schemes of continuous-variable quantum key distribution

Discrete-modulated continuous-variable quantum key distribution protocols are promising candidates for large-scale deployment due to the large technological overlap with deployed modern optical communication devices. The security of discrete modulation schemes has previously analyzed in the ideal detector scenario in the asymptotic limit. In this work, we calculate asymptotic key rates against collective attacks in the trusted detector noise scenario. Our results show that we can thus cut out most of the effect of detector noise and obtain asymptotic key rates similar to those had we access to ideal detectors.

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arXiv2020

Erasable Bit Commitment from Temporary Quantum Trust

We introduce a new setting for two-party cryptography with temporarily trusted third parties. In addition to Alice and Bob in this setting, there are additional third parties, which Alice and Bob both trust to be honest during the protocol. However, once the protocol concludes, there is no guarantee over the behaviour of these third parties. It is possible that they collaborate and act adversarially. Our goal is to use these third parties to facilitate protocols which are impossible in two-party cryptography. We implement a variant of bit commitment in this setting, which we call erasable bit commitment. In this primitive, Alice has the choice of either opening or erasing her commitment after the commit phase. The ability to ask for an erasure allows Alice to ask the trusted parties to erase her commitment in case the trust period is about to expire. This erasure prevents a future coalition of the third parties and Bob from extracting any information about the commitment. However, this ability also makes erasable bit commitment weaker than the standard version of bit commitment. In addition to satisfying the security requirements of bit commitment, our protocol also does not reveal any information about the commitment to the third parties. Lastly, our protocol for this primitive requires a constant number of trusted third parties and can tolerate a small number of corrupt trusted parties as well as implementation errors.

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arXiv2020

Improving key rates of the unbalanced phase-encoded BB84 protocol using the flag-state squashing model

All phase-encoded BB84 implementations have signal states with unbalanced amplitudes in practice. Thus, the original security analyses a priori do not apply to them. Previous security proofs use signal tagging of multi-photon pulses to recover the behaviour of regular BB84. This is overly conservative, as for unbalanced signals, the photon-number splitting attack does not leak full information to Eve. In this work, we exploit the flag-state squashing model to preserve some parts of the multi-photon generated private information in our analysis. Using a numerical proof technique, we obtain significantly higher key rates compared with previously published results in the low-loss regime. It turns out that the usual scenario of untrusted dark counts runs into conceptual difficulties in some parameter regime. Thus, we discuss the trusted dark count scenario in this paper as well. We also report a gain in key rates when part of the total loss is known to be induced by a trusted device. We highlight that all these key rate improvements can be achieved without modification of the experimental setup.

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arXiv2019

Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution

Continuous-variable quantum key distribution (CV QKD) protocols with discrete modulation are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks, but their security analysis is less advanced than that of Gaussian modulation schemes. In this work, we apply a numerical method to analyze the security of discrete-modulation protocols against collective attacks in the asymptotic limit, paving the way for a full security proof with finite-size effects. While our method is general for discrete-modulation schemes, we focus on two variants of the CV QKD protocol with quaternary modulation. Interestingly, thanks to the tightness of our proof method, we show that this protocol is capable of achieving much higher key rates over significantly longer distances with experimentally feasible parameters compared with previous security proofs of binary and ternary modulation schemes and also yielding key rates comparable to Gaussian modulation schemes. Furthermore, as our security analysis method is versatile, it allows us to evaluate variations of the discrete-modulated protocols, including direct and reverse reconciliation, and postselection strategies. In particular, we demonstrate that postselection of data in combination with reverse reconciliation can improve the key rates.

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arXiv2019

Demonstration of a 6 State-4 State Reference Frame Independent channel for Quantum Key Distribution

We study a novel protocol for reference frame independent (RFI) quantum key distribution (QKD) using six states for Alice and four states for Bob, while previous RFI protocols require a six state analyzer for Bob. Our protocol can generate a secure key for any possible phase of the entangled state, provided the variation is small compared to the measurement rate, shown by our numerical key rate analysis. We perform a proof-of-principle experiment using polarization entangled photon pairs. In the presence of a varying rotational phase, we obtain a consistently low error rate of less than $4\%$ indicating the feasibility of this protocol for QKD. Our protocol is hence beneficial but not limited to applications in satellite or mobile free-space QKD, where a communication node must limit resources and restrict the number of measured states to four instead of six.

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arXiv2019

Beating direct transmission bounds for quantum key distribution with a multiple quantum memory station

Overcoming repeaterless bounds for the secret key rate capacity of quantum key distribution protocols is still a challenge with current technology. D. Luong et al. [Applied Physics B 122, 96 (2016)] proposed a protocol to beat a repeaterless bound using one pair of quantum memories. However, the required experimental parameters for the memories are quite demanding. We extend the protocol with multiple pairs of memories, operated in a parallel manner to relax these conditions. We quantify the amount of relaxation in terms of the most crucial memory parameters, given the number of applied memory pairs. In the case of high-loss channels we found that adding only a few pair of memories can make the crossover possible.

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arXiv2019

Eavesdropper's ability to attack a free-space quantum-key-distribution receiver in atmospheric turbulence

The ability of an eavesdropper (Eve) to perform an intercept-resend attack on a free-space quantum key distribution (QKD) receiver by precisely controlling the incidence angle of an attack laser has been previously demonstrated. However, such an attack could be ineffective in the presence of atmospheric turbulence due to beam wander and spatial mode aberrations induced by the air's varying index of refraction. We experimentally investigate the impact turbulence has on Eve's attack on a free-space polarization-encoding QKD receiver by emulating atmospheric turbulence with a spatial light modulator. Our results identify how well Eve would need to compensate for turbulence to perform a successful attack by either reducing her distance to the receiver, or using beam wavefront correction via adaptive optics. Furthermore, we use an entanglement-breaking scheme to find a theoretical limit on the turbulence strength that hinders Eve's attack.

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arXiv2019

Characterization of Gram matrices of multimode coherent states

Quantum communication protocols are typically formulated in terms of abstract qudit states and operations, leaving the question of an experimental realization open. Direct translation of these protocols, say into single photons with some d-dimensional degree of freedom, are typically challenging to realize. Multi-mode coherent states, on the other hand, can be easily generated experimentally. Reformulation of protocols in terms of these states has been a successful strategy for implementation of quantum protocols. Quantum key distribution and the quantum fingerprinting protocol have both followed this route. In this paper, we characterize the Gram matrices of multi-mode coherent states in an attempt to understand the class of communication protocols, which can be implemented using these states. As a side product, we are able to use this characterization to show that the Hadamard exponential of a Euclidean distance matrix is positive semidefinite. We also derive the closure of the Gram matrices, which can be implemented in this way, so that we also characterize those matrices, which can be approximated arbitrarily well using multi-mode coherent states. Using this we show that Gram matrices of mutually unbiased bases cannot be approximated arbitrarily well using multi-mode coherent states.

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