arXiv subjects

Norbert Lütkenhaus

Publications and source records attributed to Norbert Lütkenhaus.

At least 55 records · Page 3Linked to original sources

arXiv2018

Simple security analysis of phase-matching measurement-device-independent quantum key distribution

Variations of phase-matching measurement-device-independent quantum key distribution (PM-MDI QKD) protocols have been investigated before, but it was recently discovered that this type of protocol (under the name of twin-field QKD) can beat the linear scaling of the repeaterless bound on secret key rate capacity. We propose a variation of PM-MDI QKD protocol, which reduces the sifting cost and uses non-phase-randomized coherent states as test states. We provide a security proof in the infinite key limit. Our proof is conceptually simple and gives tight key rates. We obtain an analytical key rate formula for the loss-only scenario, confirming the square root scaling and also showing the loss limit. We simulate the key rate for realistic imperfections and show that PM-MDI QKD can overcome the repeaterless bound with currently available technology.

quant-ph↗

arXiv2018

Security-proof framework for two-way Gaussian quantum-key-distribution protocols

Two-way Gaussian protocols have the potential to increase quantum key distribution (QKD) protocols' secret-key rates by orders of magnitudes~[Phys.~Rev.~A {\bf 94}, 012322 (2016)]. Security proofs for two-way protocols, however, are underdeveloped at present. In this paper, we establish a security proof framework for the general coherent attack on two-way Gaussian protocols in the asymptotic regime. We first prove that coherent-attack security can be reduced to collective-attack security for all two-way QKD protocols. Next, we identify two different constraints that each provide intrusion parameters which bound an eavesdropper's coherent-attack information gain for any two-way Gaussian QKD protocol. Finally, we apply our results to two such protocols.

quant-ph↗

arXiv2018

Eavesdropping and countermeasures for backflash side channel in quantum cryptography

Quantum key distribution (QKD) promises information theoretic secure key as long as the device performs as assumed in the theoretical model. One of the assumptions is an absence of information leakage about individual photon detection outcomes of the receiver unit. Here we investigate the information leakage from a QKD receiver due to photon emission caused by detection events in single-photon detectors (backflash). We test commercial silicon avalanche photodiodes and a photomultiplier tube, and find that the former emit backflashes. We study the spectral, timing and polarization characteristics of these backflash photons. We experimentally demonstrate on a free-space QKD receiver that an eavesdropper can distinguish which detector has clicked inside it, and thus acquire secret information. A set of countermeasures both in theory and on the physical devices are discussed.

quant-ph↗

arXiv2018

Reliable numerical key rates for quantum key distribution

In this work, we present a reliable, efficient, and tight numerical method for calculating key rates for finite-dimensional quantum key distribution (QKD) protocols. We illustrate our approach by finding higher key rates than those previously reported in the literature for several interesting scenarios (e.g., the Trojan-horse attack and the phase-coherent BB84 protocol). Our method will ultimately improve our ability to automate key rate calculations and, hence, to develop a user-friendly software package that could be used widely by QKD researchers.

quant-ph↗

arXiv2018

Practical Quantum Appointment Scheduling

We propose a protocol based on coherent states and linear optics operations for solving the appointment-scheduling problem. Our main protocol leaks strictly less information about each party's input than the optimal classical protocol, even when considering experimental errors. Along with the ability to generate constant-amplitude coherent states over two modes, this protocol requires the ability to transfer these modes back-and-forth between the two parties multiple times with low coupling loss. The implementation requirements are thus still challenging. Along the way, we develop new tools to study quantum information cost of interactive protocols in the finite regime.

quant-ph↗

arXiv2017

Families of Quantum Fingerprinting Protocols

We introduce several families of quantum fingerprinting protocols to evaluate the equality function on two $n$-bit strings in the simultaneous message passing model. The original quantum fingerprinting protocol uses a tensor product of a small number of $\mathcal{O}(\log n)$-qubit high dimensional signals [Buhrman et al. 2001], whereas a recently-proposed optical protocol uses a tensor product of $\mathcal{O}(n)$ single-qubit signals, while maintaining the $\mathcal{O}(\log n)$ information leakage of the original protocol [Arrazola and Lütkenhaus 2014]. We find a family of protocols which interpolate between the original and optical protocols while maintaining the $\mathcal{O}(\log n)$ information leakage, thus demonstrating a trade-off between the number of signals sent and the dimension of each signal. There has been interest in experimental realization of the recently-proposed optical protocol using coherent states [Xu et al. 2015, Guan et al. 2016], but as the required number of laser pulses grows linearly with the input size $n$, eventual challenges for the long-time stability of experimental set-ups arise. We find a coherent state protocol which reduces the number of signals by a factor $1/2$ while also reducing the information leakage. Our reduction makes use of a simple modulation scheme in optical phase space, and we find that more complex modulation schemes are not advantageous. Using a similar technique, we improve a recently-proposed coherent state protocol for evaluating the Euclidean distance between two real unit vectors [Kumar et al. 2017] by reducing the number of signals by a factor $1/2$ and also reducing the information leakage.

quant-ph↗

arXiv2017

The Engineering of a Scalable Multi-Site Communications System Utilizing Quantum Key Distribution (QKD)

Quantum Key Distribution (QKD) is a means of generating keys between a pair of computing hosts that is theoretically secure against cryptanalysis, even by a quantum computer. Although there is much active research into improving the QKD technology itself, there is still significant work to be done to apply engineering methodology and determine how it can be practically built to scale within an enterprise IT environment. Significant challenges exist in building a practical key management service for use in a metropolitan network. QKD is generally a point-to-point technique only and is subject to steep performance constraints. The integration of QKD into enterprise-level computing has been researched, to enable quantum-safe communication. A novel method for constructing a key management service is presented that allows arbitrary computing hosts on one site to establish multiple secure communication sessions with the hosts of another site. A key exchange protocol is proposed where symmetric private keys are granted to hosts while satisfying the scalability needs of an enterprise population of users. The key management service operates within a layered architectural style that is able to interoperate with various underlying QKD implementations. Variable levels of security for the host population are enforced through a policy engine. A network layer provides key generation across a network of nodes connected by quantum links. Scheduling and routing functionality allows quantum key material to be relayed across trusted nodes. Optimizations are performed to match the real-time host demand for key material with the capacity afforded by the infrastructure. The result is a flexible and scalable architecture that is suitable for enterprise use and independent of any specific QKD technology.

cs.CR↗

arXiv2017

Numerical evidence for bound secrecy from two-way post-processing in quantum key distribution

Bound secret information is classical information that contains secrecy but from which secrecy cannot be extracted. The existence of bound secrecy has been conjectured but is currently unproven, and in this work we provide analytical and numerical evidence for its existence. Specifically, we consider two-way post-processing protocols in prepare-and-measure quantum key distribution based on the well-known six-state signal states. In terms of the quantum bit-error rate $Q$ of the classical data, such protocols currently exist for $Q<\frac{5-\sqrt{5}}{10}\approx 27.6\%$. On the other hand, for $Q\geq\frac{1}{3}$ no such protocol can exist as the observed data is compatible with an intercept-resend attack. This leaves the interesting question of whether successful protocols exist in the interval $\frac{5-\sqrt{5}}{10}\leq Q<\frac{1}{3}$. Previous work has shown that a necessary condition for the existence of two-way post-processing protocols for distilling secret key is breaking the symmetric extendability of the underlying quantum state shared by Alice and Bob. Using this result, it has been proven that symmetric extendability can be broken up to the $27.6\%$ lower bound using the advantage distillation protocol. In this work, we first show that to break symmetric extendability it is sufficient to consider a generalized form of advantage distillation consisting of one round of post-selection by Bob on a block of his data. We then provide evidence that such generalized protocols cannot break symmetric extendability beyond $27.6\%$. We thus have evidence to believe that $27.6\%$ is an upper bound on two-way post-processing and that the interval $\frac{5-\sqrt{5}}{10}\leq Q<\frac{1}{3}$ is a domain of bound secrecy.

quant-ph↗

arXiv2016

Role of syndrome information on a one-way quantum repeater using teleportation-based error correction

We investigate a quantum repeater scheme for quantum key distribution based on the work by Muralidharan et al., Phys. Rev. Lett. 112, 250501 (2014). Our scheme extends that work by making use of error syndrome measurement outcomes available at the repeater stations. We show how to calculate the secret key rates for the case of optimizing the syndrome information, while the known key rate is based on a scenario of coarse-graining the syndrome information. We show that these key rates can surpass the Pirandola-Laurenza-Ottaviani-Banchi bound on secret key rates of direct transmission over lossy bosonic channels.

quant-ph↗

arXiv2016

Numerical approach for unstructured quantum key distribution

Quantum key distribution (QKD) allows for communication with security guaranteed by quantum theory. The main theoretical problem in QKD is to calculate the secret key rate for a given protocol. Analytical formulas are known for protocols with symmetries, since symmetry simplifies the analysis. However, experimental imperfections break symmetries, hence the effect of imperfections on key rates is difficult to estimate. Furthermore, it is an interesting question whether (intentionally) asymmetric protocols could outperform symmetric ones. Here, we develop a robust numerical approach for calculating the key rate for arbitrary discrete-variable QKD protocols. Ultimately this will allow researchers to study "unstructured" protocols, that is, those that lack symmetry. Our approach relies on transforming the key rate calculation to the dual optimization problem, which dramatically reduces the number of parameters and hence the calculation time. We illustrate our method by investigating some unstructured protocols for which the key rate was previously unknown.

quant-ph↗

arXiv2016

Sifting attacks in finite-size quantum key distribution

A central assumption in quantum key distribution (QKD) is that Eve has no knowledge about which rounds will be used for parameter estimation or key distillation. Here we show that this assumption is violated for iterative sifting, a sifting procedure that has been employed in some (but not all) of the recently suggested QKD protocols in order to increase their efficiency. We show that iterative sifting leads to two security issues: (1) some rounds are more likely to be key rounds than others, (2) the public communication of past measurement choices changes this bias round by round. We analyze these two previously unnoticed problems, present eavesdropping strategies that exploit them, and find that the two problems are independent. We discuss some sifting protocols in the literature that are immune to these problems. While some of these would be inefficient replacements for iterative sifting, we find that the sifting subroutine of an asymptotically secure protocol suggested by Lo et al (2005 J. Cryptol. 18 133-65), which we call LCA sifting, has an efficiency on par with that of iterative sifting. One of our main results is to show that LCA sifting can be adapted to achieve secure sifting in the finite-key regime. More precisely, we combine LCA sifting with a certain parameter estimation protocol, and we prove the finite-key security of this combination. Hence we propose that LCA sifting should replace iterative sifting in future QKD implementations. More generally, we present two formal criteria for a sifting protocol that guarantee its finite-key security. Our criteria may guide the design of future protocols and inspire a more rigorous QKD analysis, which has neglected sifting-related attacks so far.

quant-ph↗

arXiv2016

Practical Quantum Retrieval Games

Complex cryptographic protocols are often constructed from simpler building-blocks. In order to advance quantum cryptography, it is important to study practical building-blocks that can be used to develop new protocols. An example is quantum retrieval games (QRGs), which have broad applicability and have already been used to construct quantum money schemes. In this work, we introduce a general construction of quantum retrieval games based on the hidden matching problem and show how they can be implemented in practice using available technology. More precisely, we provide a general method to construct (1-out-of-k) QRGs, proving that their cheating probabilities decrease exponentially in $k$. In particular, we define new QRGs based on coherent states of light, which can be implemented even in the presence of experimental imperfections. Our results constitute a new tool in the arsenal of the practical quantum cryptographer.

quant-ph↗

arXiv2015

Experimental quantum key distribution with simulated ground-to-satellite photon losses and processing limitations

Quantum key distribution (QKD) has the potential to improve communications security by offering cryptographic keys whose security relies on the fundamental properties of quantum physics. The use of a trusted quantum receiver on an orbiting satellite is the most practical near-term solution to the challenge of achieving long-distance (global-scale) QKD, currently limited to a few hundred kilometers on the ground. This scenario presents unique challenges, such as high photon losses and restricted classical data transmission and processing power due to the limitations of a typical satellite platform. Here we demonstrate the feasibility of such a system by implementing a QKD protocol, with optical transmission and full post-processing, in the high-loss regime using minimized computing hardware at the receiver. Employing weak coherent pulses with decoy states, we demonstrate the production of secure key bits at up to 56.5 dB of photon loss. We further illustrate the feasibility of a satellite uplink by generating secure key while experimentally emulating the varying channel losses predicted for realistic low-Earth-orbit satellite passes at 600 km altitude. With a 76 MHz source and including finite-size analysis, we extract 3374 bits of secure key from the best pass. We also illustrate the potential benefit of combining multiple passes together: while one suboptimal "upper-quartile" pass produces no finite-sized key with our source, the combination of three such passes allows us to extract 165 bits of secure key. Alternatively, we find that by increasing the signal rate to 300 MHz it would be possible to extract 21570 bits of secure finite-sized key in just a single upper-quartile pass.

quant-ph↗

arXiv2015

Self-referenced continuous-variable quantum key distribution protocol

We introduce a new continuous-variable quantum key distribution (CV-QKD) protocol, self-referenced CV-QKD, that eliminates the need for transmission of a high-power local oscillator between the communicating parties. In this protocol, each signal pulse is accompanied by a reference pulse (or a pair of twin reference pulses), used to align Alice's and Bob's measurement bases. The method of phase estimation and compensation based on the reference pulse measurement can be viewed as a quantum analog of intradyne detection used in classical coherent communication, which extracts the phase information from the modulated signal. We present a proof-of-principle, fiber-based experimental demonstration of the protocol and quantify the expected secret key rates by expressing them in terms of experimental parameters. Our analysis of the secret key rate fully takes into account the inherent uncertainty associated with the quantum nature of the reference pulse(s) and quantifies the limit at which the theoretical key rate approaches that of the respective conventional protocol that requires local oscillator transmission. The self-referenced protocol greatly simplifies the hardware required for CV-QKD, especially for potential integrated photonics implementations of transmitters and receivers, with minimum sacrifice of performance. As such, it provides a pathway towards scalable integrated CV-QKD transceivers, a vital step towards large-scale QKD networks.

quant-ph↗

arXiv2015

Efficient long distance quantum communication

Despite the tremendous progress of quantum cryptography, efficient quantum communication over long distances (>1000km) remains an outstanding challenge due to fiber attenuation and operation errors accumulated over the entire communication distance. Quantum repeaters, as a promising approach, can overcome both photon loss and operation errors, and hence significantly speedup the communication rate. Depending on the methods used to correct loss and operation errors, all the proposed QR schemes can be classified into three categories (generations). Here we present the first systematic comparison of three generations of quantum repeaters by evaluating the cost of both temporal and physical resources, and identify the optimized quantum repeater architecture for a given set of experimental parameters. Our work provides a roadmap for the experimental realizations of highly efficient quantum networks over transcontinental distances.

quant-ph↗

arXiv2015

Overcoming lossy channel bounds using a single quantum repeater node

We propose a scheme for performing quantum key distribution (QKD) which has the potential to beat schemes based on the direct transmission of photons between the communicating parties. In our proposal, the communicating parties exchange photons with two quantum memories placed between them. This is a very simple quantum repeater scheme and can be implemented with currently available technology. Ideally, its secret key rate scales as the square root of the transmittivity of the optical channel, which is superior to QKD schemes based on direct transmission because key rates for the latter scale at best linearly with transmittivity. Taking into account various imperfections in each component of our setup, we present parameter regimes in which our protocol outperforms protocols based on direct transmission.

quant-ph↗

arXiv2014

Could Gaussian regenerative stations act as quantum repeaters?

Higher transmission loss diminishes the performance of optical communication|be it the rate at which classical or quantum data can be sent reliably, or the secure key generation rate of quantum key distribution (QKD). Loss compounds with distance|exponentially in an optical fiber, and inverse-square with distance for a free-space channel. In order to boost classical communication rates over long distances, it is customary to introduce regenerative relays at intermediate points along the channel. It is therefore natural to speculate whether untended regenerative stations, such as phase-insensitive or phase-sensitive optical amplifiers, could serve as repeaters for long-distance QKD. The primary result of this paper rules out all bosonic Gaussian channels to be useful as QKD repeaters, which include phase-insensitive and phase-sensitive amplifiers as special cases, for any QKD protocol. We also delineate the conditions under which a Gaussian relay renders a lossy channel entanglement breaking, which in turn makes the channel useless for QKD.

quant-ph↗

arXiv2014

The Security of Quantum Key Distribution using a Simplified Trusted Relay

We propose a QKD protocol for trusted node relays. Our protocol shifts the communication and computational weight of classical post-processing to the end users by reassigning the roles of error correction and privacy amplification, while leaving the exchange of quantum signals untouched. We perform a security analysis for this protocol based on the BB84 protocol on the level of infinite key formulas, taking into account weak coherent implementations involving decoy analysis.

quant-ph↗