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From a practical perspective it is advantageous to develop experimental methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of measurements needed to detect bound entanglement in bipartite $(dtimes d)$-dimensional states, i.e. entangled states that are positive under partial transposition. In particular, we show that a class of entanglement witnesses composed of mutually unbiased bases (MUBs) can detect bound entanglement if the number of measurements is greater than $d/2+1$. This is a substantial improvement over other detection methods, requiring significantly fewer resources than either full quantum state tomography or measuring a complete set of $d+1$ MUBs. Our approach is based on a partial characterisation of the (non-)decomposability of entanglement witnesses. We show that non-decomposability is a universal property of MUBs, which holds regardless of the choice of complementary observables, and we find that both the number of measurements and the structure of the witness play an important role in the detection of bound entanglement.
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It is widely believed that the practical success of Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) owes to the fact that CNNs and RNNs use a more compact parametric representation than their Fully-Connected Neural Network (FNN) counterparts, and consequently require fewer training examples to accurately estimate their parameters. We initiate the study of rigorously characterizing the sample-complexity of estimating CNNs and RNNs. We show that the sample-complexity to learn CNNs and RNNs scales linearly with their intrinsic dimension and this sample-complexity is much smaller than for their FNN counterparts. For both CNNs and RNNs, we also present lower bounds showing our sample complexities are tight up to logarithmic factors. Our main technical tools for deriving these results are a localized empirical process analysis and a new technical lemma characterizing the convolutional and recurrent structure. We believe that these tools may inspire further developments in understanding CNNs and RNNs.
Unequivocally, a single man in possession of a strong password is not enough to solve the issue of security. Studies indicate that passwords have been subjected to various attacks, regardless of the applied protection mechanisms due to the human factor. The keystone for the adoption of more efficient authentication methods by the different markets is the trade-off between security and usability. To bridge the gap between user-friendly interfaces and advanced security features, the Fast Identity Online (FIDO) alliance defined several authentication protocols. Although FIDOs biometric-based authentication is not a novel concept, still daunts end users and developers, which may be a contributor factor obstructing FIDOs complete dominance of the digital authentication market. This paper traces the evolution of FIDO protocols, by identifying the technical characteristics and security requirements of the FIDO protocols throughout the differe
In this article we show that, in a two-arm interferometer, pure quantum states of perfect path distinguishability (particles) are geometrically equidistant from all states with constant path distinguishability D. This property is not shared by other states, such as perfect fringe-visibility (waves) or maximally entangled quantum states (entanglon). Indeed, the Bures distance between a particle and any other state depends only the distinguishability of the latter. On the contrary, the Bures distance between a wave or an entanglon, and any other single photon state depends on other set of parameters.
We prove that the bipartite entangled state of rank three is distillable. So there is no rank three bipartite bound entangled state. By using this fact, We present some families of rank four states that are distillable. We also analyze the relation between the low rank state and the Werner state.
We derive an explicit analytic estimate for the entanglement of a large class of bipartite quantum states which extends into bound entanglement regions. This is done by using an efficiently computable concurrence lower bound, which is further employed to numerically construct a volume of $3 times 3$ bound entangled states.
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