Upper bounds for the secure key rate of decoy state quantum key distribution

The use of decoy states in quantum key distribution (QKD) has provided a method for substantially increasing the secret key rate and distance that can be covered by QKD protocols with practical signals. The security analysis of these schemes, however, leaves open the possibility that the development of better proof techniques, or better classical post-processing methods, might further improve their performance in realistic scenarios. In this paper, we derive upper bounds on the secure key rate for decoy state QKD. These bounds are based basically only on the classical correlations established by the legitimate users during the quantum communication phase of the protocol. The only assumption about the possible post-processing methods is that double click events are randomly assigned to single click events. Further we consider only secure key rates based on the uncalibrated device scenario which assigns imperfections such as detection inefficiency to the eavesdropper. Our analysis relies on two preconditions for secure two-way and one-way QKD: The legitimate users need to prove that there exists no separable state (in the case of two-way QKD), or that there exists no quantum state having a symmetric extension (one-way QKD), that is compatible with the available measurements results. Both criteria have been previously applied to evaluate single-photon implementations of QKD. Here we use them to investigate a realistic source of weak coherent pulses. The resulting upper bounds can be formulated as a convex optimization problem known as a semidefinite program which can be efficiently solved. For the standard four-state QKD protocol, they are quite close to known lower bounds, thus showing that there are clear limits to the further improvement of classical post-processing techniques in decoy state QKD.Comment: 10 pages, 3 figure

Upper bound on the secret key rate distillable from effective quantum correlations with imperfect detectors

We provide a simple method to obtain an upper bound on the secret key rate that is particularly suited to analyze practical realizations of quantum key distribution protocols with imperfect devices. We consider the so-called trusted device scenario where Eve cannot modify the actual detection devices employed by Alice and Bob. The upper bound obtained is based on the available measurements results, but it includes the effect of the noise and losses present in the detectors of the legitimate users.Comment: 9 pages, 1 figure; suppress sifting effect in the figure, final versio

Passive decoy state quantum key distribution with practical light sources

Decoy states have been proven to be a very useful method for significantly enhancing the performance of quantum key distribution systems with practical light sources. While active modulation of the intensity of the laser pulses is an effective way of preparing decoy states in principle, in practice passive preparation might be desirable in some scenarios. Typical passive schemes involve parametric down-conversion. More recently, it has been shown that phase randomized weak coherent pulses (WCP) can also be used for the same purpose [M. Curty {\it et al.}, Opt. Lett. {\bf 34}, 3238 (2009).] This proposal requires only linear optics together with a simple threshold photon detector, which shows the practical feasibility of the method. Most importantly, the resulting secret key rate is comparable to the one delivered by an active decoy state setup with an infinite number of decoy settings. In this paper we extend these results, now showing specifically the analysis for other practical scenarios with different light sources and photo-detectors. In particular, we consider sources emitting thermal states, phase randomized WCP, and strong coherent light in combination with several types of photo-detectors, like, for instance, threshold photon detectors, photon number resolving detectors, and classical photo-detectors. Our analysis includes as well the effect that detection inefficiencies and noise in the form of dark counts shown by current threshold detectors might have on the final secret ket rate. Moreover, we provide estimations on the effects that statistical fluctuations due to a finite data size can have in practical implementations.Comment: 17 pages, 14 figure

One-way quantum key distribution: Simple upper bound on the secret key rate

We present a simple method to obtain an upper bound on the achievable secret key rate in quantum key distribution (QKD) protocols that use only unidirectional classical communication during the public-discussion phase. This method is based on a necessary precondition for one-way secret key distillation; the legitimate users need to prove that there exists no quantum state having a symmetric extension that is compatible with the available measurements results. The main advantage of the obtained upper bound is that it can be formulated as a semidefinite program, which can be efficiently solved. We illustrate our results by analysing two well-known qubit-based QKD protocols: the four-state protocol and the six-state protocol. Recent results by Renner et al., Phys. Rev. A 72, 012332 (2005), also show that the given precondition is only necessary but not sufficient for unidirectional secret key distillation.Comment: 11 pages, 1 figur

Analysing multiparticle quantum states

The analysis of multiparticle quantum states is a central problem in quantum information processing. This task poses several challenges for experimenters and theoreticians. We give an overview over current problems and possible solutions concerning systematic errors of quantum devices, the reconstruction of quantum states, and the analysis of correlations and complexity in multiparticle density matrices.Comment: 20 pages, 4 figures, prepared for proceedings of the "Quantum [Un]speakables II" conference (Vienna, 2014

Iterations of nonlinear entanglement witnesses

We describe a generic way to improve a given linear entanglement witness by a quadratic, nonlinear term. This method can be iterated, leading to a whole sequence of nonlinear witnesses, which become stronger in each step of the iteration. We show how to optimize this iteration with respect to a given state, and prove that in the limit of the iteration the nonlinear witness detects all states that can be detected by the positive map corresponding to the original linear witness.Comment: 11 pages, 5 figure

Class I major histocompatibility complexes loaded by a periodate trigger

Class I major histocompatibility complexes (MHCs) present peptide ligands on the cell surface for recognition by appropriate cytotoxic T cells. The unstable nature of unliganded MHC necessitates the production of recombinant class I complexes through in vitro refolding reactions in the presence of an added excess of peptides. This strategy is not amenable to high-throughput production of vast collections of class I complexes. To address this issue, we recently designed photocaged MHC ligands that can be cleaved by a UV light trigger in the MHC bound state under conditions that do not affect the integrity of the MHC structure. The results obtained with photocaged MHC ligands demonstrate that conditional MHC ligands can form a generally applicable concept for the creation of defined peptide−MHCs. However, the use of UV exposure to mediate ligand exchange is unsuited for a number of applications, due to the lack of UV penetration through cell culture systems and due to the transfer of heat upon UV irradiation, which can induce evaporation. To overcome these limitations, here, we provide proof-of-concept for the generation of defined peptide−MHCs by chemical trigger-induced ligand exchange. The crystal structure of the MHC with the novel chemosensitive ligand showcases that the ligand occupies the expected binding site, in a conformation where the hydroxyl groups should be reactive to periodate. We proceed to validate this technology by producing peptide−MHCs that can be used for T cell detection. The methodology that we describe here should allow loading of MHCs with defined peptides in cell culture devices, thereby permitting antigen-specific T cell expansion and purification for cell therapy. In addition, this technology will be useful to develop miniaturized assay systems for performing high-throughput screens for natural and unnatural MHC ligands

Rank-based model selection for multiple ions quantum tomography

The statistical analysis of measurement data has become a key component of many quantum engineering experiments. As standard full state tomography becomes unfeasible for large dimensional quantum systems, one needs to exploit prior information and the "sparsity" properties of the experimental state in order to reduce the dimensionality of the estimation problem. In this paper we propose model selection as a general principle for finding the simplest, or most parsimonious explanation of the data, by fitting different models and choosing the estimator with the best trade-off between likelihood fit and model complexity. We apply two well established model selection methods -- the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) -- to models consising of states of fixed rank and datasets such as are currently produced in multiple ions experiments. We test the performance of AIC and BIC on randomly chosen low rank states of 4 ions, and study the dependence of the selected rank with the number of measurement repetitions for one ion states. We then apply the methods to real data from a 4 ions experiment aimed at creating a Smolin state of rank 4. The two methods indicate that the optimal model for describing the data lies between ranks 6 and 9, and the Pearson $\chi^{2}$ test is applied to validate this conclusion. Additionally we find that the mean square error of the maximum likelihood estimator for pure states is close to that of the optimal over all possible measurements.Comment: 24 pages, 6 figures, 3 table

Delphi survey on conventional conservative treatment of functional posterior shoulder instability

Background: Posterior shoulder instability is caused by structural or functional defects. While the former are mostly treated surgically, physiotherapy is considered the treatment of choice in functional shoulder instability. However, it often has limited success unless very specific and intensive training programs are applied by trained experts. Currently, there is no consensus on the treatment of functional posterior shoulder instability. Objective: To improve treatment of this pathology, a standardized treatment recommendation is required to serve as a guideline for physiotherapy. The aim of this study was to establish expert consensus for treatment recommendations for functional posterior shoulder instability. Design: The Delphi survey technique was employed. Methods: A standardized training program for treatment of functional posterior shoulder instability was developed by a local expert committee. Two rounds of an online Delphi survey were then conducted. The panel of the Delphi survey comprised nine leading scientific experts in the field of functional shoulder instability who treat patients with shoulder-related problems conservatively and operatively. Results: The response rate was 100% and there were no dropouts. The final program consists of three groups of exercises with increasing difficulty. The exercises are mostly easy to perform and focus on the scapula-retracting muscles and the muscles responsible for external rotation of the shoulder. The treatment program should be executed under the supervision of a therapist at the beginning and later may be performed by the patients themselves. Conclusion: Consensus on a new exercise guideline dedicated to the treatment of functional posterior shoulder instability was achieved. This guideline should not only help to treat this challenging pathology but also provide a starting point for further scientific research and ongoing improvement