Undetectable Werner states using linear Bell inequalities

Bell inequality serves as an important method to detect quantum entanglement, a problem which is generally known to be NP-hard. Our goal in this work is to detect Werner states using linear Bell inequality. Surprisingly, we show that Werner states of almost all generalized multipartite Greenberger-Horne-Zeilinger (GHZ) states cannot be detected by homogeneous linear Bell inequalities with dichotomic inputs and outputs of each local observer. The main idea is to estimate the largest violations of Werner states in the case of general linear Bell inequalities. The presented method is then applied to Werner states of all pure states to show a similar undetectable result. Moreover, we provide an accessible method to determine undetectable Werner states for general linear Bell inequality including sub-correlations. The numeric algorithm shows that there are nonzero measures of Werner states with small number of particles that cannot be detected by general linear Bell inequalities.Comment: 23 page

Computationally Efficient Nonlinear Bell Inequalities for General Quantum Networks

The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The main problem is that no computationally efficient method is available for constructing useful Bell inequalities for general quantum networks. In this work, we show a significant improvement by presenting new, explicit Bell-type inequalities for general networks including cyclic networks. These nonlinear inequalities are related to the matching problem of an equivalent unweighted bipartite graph that allows constructing a polynomial-time algorithm. For the quantum resources consisting of bipartite entangled pure states and generalized Greenberger-Horne-Zeilinger (GHZ) states, we prove the generic non-multilocality of quantum networks with multiple independent observers using new Bell inequalities. The violations are maximal with respect to the presented Tsirelson's bound for Einstein-Podolsky-Rosen (EPR) states and GHZ states. Moreover, these violations hold for Werner states or some general noisy states. Our results suggest that the presented Bell inequalities can be used to characterize experimental quantum networks.Comment: 34 pages, 7 figures (Almost version of publication

A new kind of solutions of the Einstein's field equations with non-vanishing cosmological constant

In this paper we construct a new kind of solutions of the Einstein's field equations with non-vanishing cosmological constant, which possess some interesting physical properties. The singularities of this kind of solutions are investigated. According to the general form of this kind of solutions, we give some examples.Comment: 9 page

Delivery-Secrecy Tradeoff for Cache-Enabled Stochastic Networks: Content Placement Optimization

Wireless caching has been widely recognized as a promising technique for efficient content delivery. In this paper, by taking different file secrecy levels into consideration, physical-layer security oriented content placement is optimized in a stochastic cache-enabled cellular network. We propose an analytical framework to investigate the nontrivial file delivery-secrecy tradeoff. Specifically, we first derive the closed-form expressions for the file hit and secrecy probabilities. The global optimal probabilistic content placement policy is then analytically derived in terms of hit probability maximization under file secrecy constraints. Numerical results are demonstrated to verify our analytical findings and show that the targeted file secrecy levels are crucial in balancing the file delivery-secrecy tradeoff.Comment: 5 pages, 4 figures, accepted to be published in IEEE Transactions on Vehicular Technolog

Secure and Energy-Efficient Transmissions in Cache-Enabled Heterogeneous Cellular Networks: Performance Analysis and Optimization

This paper studies physical-layer security for a cache-enabled heterogeneous cellular network comprised of a macro base station and multiple small base stations (SBSs). We investigate a joint design on caching placement and file delivery for realizing secure and energy-efficient transmissions against randomly distributed eavesdroppers. We propose a novel hybrid "most popular content" and "largest content diversity" caching placement policy to distribute files of different popularities. Depending on the availability and placement of the requested file, we employ three cooperative transmission schemes, namely, distributed beamforming, frequency-domain orthogonal transmission, and best SBS relaying, respectively. We derive analytical expressions for the connection outage probability and secrecy outage probability for each transmission scheme. Afterwards, we design the optimal transmission rates and caching allocation successively to achieve a maximal overall secrecy throughput and secrecy energy efficiency, respectively. Numerical results verify the theoretical analyses and demonstrate the superiority of the proposed hybrid caching policy.Comment: 13 pages in double-column, 9 figures, accepted for publication on IEEE Transactions on Communication

The twist-3 distribution amplitudes in the B→πB\to\pi transition form factor

We derive an expression for the $B\to\pi$ transition form factor only depending the twist-3 distribution amplitudes by choosing an adequate chiral current correlator in the light-cone QCD sum rules. Our result show that the contribution from the twist-3 distribution amplitudes to the $f_{B\pi}^+(q^2)$ give a constraint on the twist-3 light-cone distribution amplitude.Comment: 6 pages, 1 figur

Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals

Cooper instability associated with superconductivity in the two-dimensional semi-Dirac semimetals is attentively studied in the presence of attractive Cooper-pairing interaction, which is the projection of an attractive fermion-fermion interaction. Performing the standard renormalization group analysis shows that the Cooper theorem is violated at zero chemical potential but instead Cooper instability can be generated only if the absolute strength of fermion-fermion coupling exceeds certain critical value and transfer momentum is restricted to a confined region, which is determined by the initial conditions. Rather, the Cooper theorem would be instantly restored once a finite chemical potential is introduced and thus a chemical potential-tuned phase transition is expected. Additionally, we briefly examine the effects of impurity scatterings on the Cooper instability at zero chemical potential, which in principle are harmful to Cooper instability although they can enhance the density of states of systems. Furthermore, the influence of competition between a finite chemical potential and impurities upon the Cooper instability is also simply investigated. These results are expected to provide instructive clues for exploring unconventional superconductors in the kinds of semimetals.Comment: 18 pages; 14 figure

Analytic calculation of Energy-Energy Correlation in e+e−e^+ e^- annihilation at NLO

We present the first fully analytic calculation of the Quantum Chromodynamics (QCD) event shape observable Energy-Energy Correlation in electron-positron annihilation at Next-To-Leading Order (NLO). This result sheds light on the analytic structure of the event shape observables beyond Leading Order (LO) and serves as a motivation to employ our methods in the investigation of other event shape observables that so far have not been calculated analytically.Comment: 10 pages, 1 figure. Contribution to the proceedings of Loops and Legs 2018, C18-04-29.

The Energy-Energy Correlation at Next-to-Leading Order in QCD, Analytically

The energy-energy correlation (EEC) between two detectors in $e^+e^-$ annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of EEC in the collinear and back-to-back regions through to next-to-leading power, information which should aid resummation in these regions.Comment: 6 pages, 1 figure, plus 6 pages and 4 figures; v2: uploaded the ancillary file EEC_NLO_supplemental.

Distribution of quantum Fisher information in asymmetric cloning machines

An unknown quantum state cannot be copied on demand and broadcast freely due to the famous no-cloning theorem. Approximate cloning schemes have been proposed to achieve the optimal cloning characterized by the maximal fidelity between the original and its copies. Here, from the perspective of quantum Fisher information (QFI), we investigate the distribution of QFI in asymmetric cloning machines which produce two nonidentical copies. As one might expect, improving the QFI of one copy results in decreasing the QFI of the other copy, roughly the same as that of fidelity. It is perhaps also unsurprising that asymmetric phase-covariant cloning machine outperforms universal cloning machine in distributing QFI since a priori information of the input state has been utilized. However, interesting results appear when we compare the distributabilities of fidelity (which quantifies the full information of quantum states), and QFI (which only captures the information of relevant parameters) in asymmetric cloning machines. In contrast to the results of fidelity, where the distributability of symmetric cloning is always optimal for any d-dimensional cloning, we find that asymmetric cloning performs always better than symmetric cloning on the distribution of QFI for $d\leq18$, but this conclusion becomes invalid when $d>18$.Comment: 9 pages, 5 figures. Comments are welcom