We show that a von Neumann measurement on a part of a composite quantum system unavoidably creates distillable entanglement between the measurement apparatus and the system if the state has nonzero quantum discord. The minimal distillable entanglement is equal to the one-way information deficit. The quantum discord is shown to be equal to the minimal partial distillable entanglement that is the part of entanglement which is lost, when we ignore the subsystem which is not measured. We then show that any entanglement measure corresponds to some measure of quantum correlations. This powerful correspondence also yields necessary properties for quantum correlations. We generalize the results to multipartite measurements on a part of the system and on the total system.

We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channels this is indeed the case: The amount of quantum correlations can only decrease under the action of unital channels. However, nonunital channels (e.g., such as dissipation) can create quantum correlations for some initially classical states. Furthermore, for higher-dimensional systems even unital channels may increase the amount of quantum correlations. Thus, counterintuitively, local decoherence can generate quantum correlations.

-The effect of turbulence on entanglementbased free-space quantum key distribution with photonic orbital angular momentum Sandeep K Goyal, Alpha Hamadou Ibrahim, Filippus S Roux et al. - Recent citationsSemi-device-independent multiparty quantum key distribution in the asymptotic limit Yonggi Jo and Wonmin Son AbstractThe laws of quantum mechanics allow for the distribution of a secret random key between two parties.Here we analyse the security of a protocol for establishing a common secret key between N parties (i.e. a conference key), using resource states with genuine N-partite entanglement. We compare this protocol to conference key distribution via bipartite entanglement, regarding the required resources, achievable secret key rates and threshold qubit error rates. Furthermore we discuss quantum networks with bottlenecks for which our multipartite entanglement-based protocol can benefit from network coding, while the bipartite protocol cannot. It is shown how this advantage leads to a higher secret key rate.In the quantum world, randomness and security are built-in properties [1][2][3]: two parties may establish a random secret key by exploiting the no-cloning theorem [4], as in the BB84 protocol [5], or by using the monogamy of entanglement [6], as in the Ekert protocol [7]. Several variations of these seminal protocols have been suggested [8][9][10][11][12], and their security has been analysed in detail [13][14][15][16][17][18][19].In the advent of quantum technologies, much effort is devoted to building quantum networks [20][21][22][23][24][25] and creating global quantum states across them [26,27]. Thus, the generalisation of quantum key distribution (QKD) to multipartite scenarios is topical. In order to establish a common secret key (the conference key) for N parties, one can follow mainly two different paths: building up the multipartite key from bipartite QKD links (2QKD) [28], see figure 1(a), or exploiting correlations of genuinely multipartite entangled states (NQKD) [29][30][31][32], see figure 1(b).In this article we devise a protocol based on the Greenberger-Horne-Zeilinger (GHZ) state and three measurement settings per party. While, for reasons discussed below, previous work also uses the GHZ state, the measurements differ. We provide an information theoretic security analysis of our NQKD protocol, by generalising methods developed for 2QKD in [16,33], and perform an analytical calculation of secret key rates. To the best of our knowledge this is the first explicit key rate calculation for multipartite QKD. This enables us to quantitatively compare the two approaches; we find that NQKD may outperform 2QKD, for example in networks with bottlenecks.The article is structured as follows. In the section 1 we introduce the NQKD protocol and its prepare-andmeasure variant, perform a detailed security analysis and the secret key rate calculation. In section 2 we define the 2QKD protocol, summarise the steps of the NQKD protocol in an implementation and calculate the secret key rate for the example...

Establishing quantum entanglement between two distant parties is an essential step of many protocols in quantum information processing [1, 2]. One possibility for providing long-distance entanglement is to create an entangled composite state within a lab and then physically send one subsystem to a distant lab. However, is this the "cheapest" way? Here, we investigate the minimal "cost" that is necessary for establishing a certain amount of entanglement between two distant parties. We prove that this cost is intrinsically quantum, and is specified by quantum correlations. Our results provide an optimal protocol for entanglement distribution and show that quantum correlations are the essential resource for this task.Imagine that one wants to send a letter in the oldfashioned way. The postage cost that the sender has to invest depends on the amount of the transmitted substance, quantified by the weight of the letter. If the receiver had already provided some pre-paid envelope, the sender may have to add an appropriate stamp if he/she wants to send a heavier letter. Naturally, the allowed weight of the letter is smaller or equal to a limit which is linked to the total postage. Now, imagine that a sender wants to send quantum entanglement to a receiver. How does the cost that the sender has to invest depend on the amount of entanglement sent, quantified by some entanglement measure? Is this cost reduced when sender and receiver already shared some pre-established entanglement? And what is the nature of this cost -can one pay in classical quantities, or does one have to invest a quantum cost?One might be tempted to consider these questions and their answers as obvious matters. However, quantum mechanics has often surprised us with puzzling features: Counterintuitively, as shown in [3], separable states (i.e. states without entanglement) can be used to distribute entanglement. What is then the resource that makes this process possible and enables entanglement distribution without actually sending an entangled state?In order to address this question in a well-defined and quantitative way we will consider the following setting, see Fig. 1: the sender is called Alice (A), and the distant receiver Bob (B). Each of them has a quantum particle in his/her possession. In addition, they have a third quantum particle or ancilla (C) available, which is at the beginning located in Alice's lab, and then sent (via a noiseless quantum channel) to Bob's lab. This is a general model for any interaction: One can consider the particle C as the intermediate particle that realises the global interaction between A and B. A similar scenario was also considered in a different context in [4,5]. Initially, the total joint quantum state may or may not carry entanglement. In the following we will be only interested in bipartite entanglement, i.e. two out of the three particles A, B and C are grouped together. We quantify the initial entanglement between AC and B as E AC|B , and the final entanglement, after sending C to Bob, as E A|BC . As a quan...

The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.

An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement is established. We present a new expression for the geometric measure of entanglement in terms of the maximal fidelity with a separable state. A direct application of this result provides a closed expression for the Bures measure of entanglement of two qubits. We also prove that the number of elements in an optimal decomposition w.r.t. the geometric measure of entanglement is bounded from above by the Caratheodory bound, and we find necessary conditions for the structure of an optimal decomposition.

Quantum coherence is a fundamental feature of quantum mechanics and an underlying requirement for most quantum information tasks. In the resource theory of coherence, incoherent states are diagonal with respect to a fixed orthonormal basis, i.e., they can be seen as arising from a von Neumann measurement. Here, we introduce and study a generalization to a resource theory of coherence defined with respect to the most general quantum measurement, i.e., to an arbitrary positive-operator-valued measure (POVM). We establish POVMbased coherence measures and POVM-incoherent operations which coincide for the case of von Neumann measurements with their counterparts in standard coherence theory. We provide a semidefinite program that allows to characterize interconversion properties of resource states, and exemplify our framework by means of the qubit trine POVM, for which we also show analytical results. arXiv:1812.00018v1 [quant-ph] 30 Nov 2018

We generalize measurement-device-independent quantum key distribution [ H.-K. Lo, M. Curty, and B. Qi, Phys. Rev. Lett. 108, 130503 (2012) ] to the scenario where the Bell-state measurement station contains also heralded quantum memories. We find analytical formulas, in terms of device imperfections, for all quantities entering in the secret key rates, i.e., the quantum bit error rate and the repeater rate. We assume either single-photon sources or weak coherent pulse sources plus decoy states. We show that it is possible to significantly outperform the original proposal, even in presence of decoherence of the quantum memory. Our protocol may represent the first natural step for implementing a two-segment quantum repeater.