No Arabic abstract
Secure quantum conferencing refers to a protocol where a number of trusted users generate exactly the same secret key to confidentially broadcast private messages. By a modification of the techniques first introduced in [Pirandola, arXiv:1601.00966], we derive a single-letter upper bound for the maximal rates of secure conferencing in a quantum network with arbitrary topology, where the users are allowed to perform the most powerful local operations assisted by two-way classical communications, and the quantum systems are routed according to the most efficient multipath flooding strategies. More precisely, our analysis allows us to bound the ultimate rates that are achievable by single-message multiple-multicast protocols, where N senders distribute N independent secret keys, and each key is to be shared with an ensemble of M receivers.
Last years, bounds on the maximal quantum violation of general Bell inequalities were intensively discussed in the literature via different mathematical tools. In the present paper, we analyze quantum violation of general Bell inequalities via the LqHV (local quasi hidden variable) modelling framework, correctly reproducing the probabilistic description of every quantum correlation scenario. The LqHV mathematical framework allows us to derive for all d and N a new upper bound (2d-1)^{N-1} on the maximal violation by an N-qudit state of all general Bell inequalities, also, new upper bounds on the maximal violation by an N-qudit state of general Bell inequalities for S settings per site. These new upper bounds essentially improve all the known precise upper bounds on quantum violation of general multipartite Bell inequalities. For some S, d and N, the new upper bounds are attainable.
For the optimal success probability under minimum-error discrimination between $rgeq2$ arbitrary quantum states prepared with any a priori probabilities, we find new general analytical lower and upper bounds and specify the relations between these new general bounds and the general bounds known in the literature. We also present the example where the new general analytical bounds, lower and upper, on the optimal success probability are tighter than most of the general analytical bounds known in the literature. The new upper bound on the optimal success probability explicitly generalizes to $r>2$ the form of the Helstrom bound. For $r=2$, each of our new bounds, lower and upper, reduces to the Helstrom bound.
A family of rigorous upper bounds on the growth rate of local gyrokinetic instabilities in magnetized plasmas is derived from the evolution equation for the Helmholtz free energy. These bounds hold for both electrostatic and electromagnetic instabilities, regardless of the number of particle species, their collision frequency, and the geometry of the magnetic field. A large number of results that have earlier been derived in special cases and observed in numerical simulations are thus brought into a unifying framework. These bounds apply not only to linear instabilities but also imply an upper limit to the nonlinear growth of the free energy.
The property of superadditivity of the quantum relative entropy states that, in a bipartite system $mathcal{H}_{AB}=mathcal{H}_A otimes mathcal{H}_B$, for every density operator $rho_{AB}$ one has $ D( rho_{AB} || sigma_A otimes sigma_B ) ge D( rho_A || sigma_A ) +D( rho_B || sigma_B) $. In this work, we provide an extension of this inequality for arbitrary density operators $ sigma_{AB} $. More specifically, we prove that $ alpha (sigma_{AB})cdot D({rho_{AB}}||{sigma_{AB}}) ge D({rho_A}||{sigma_A})+D({rho_B}||{sigma_B})$ holds for all bipartite states $rho_{AB}$ and $sigma_{AB}$, where $alpha(sigma_{AB})= 1+2 || sigma_A^{-1/2} otimes sigma_B^{-1/2} , sigma_{AB} , sigma_A^{-1/2} otimes sigma_B^{-1/2} - mathbb{1}_{AB} ||_infty$.
We consider the evolution of an arbitrary quantum dynamical semigroup of a finite-dimensional quantum system under frequent kicks, where each kick is a generic quantum operation. We develop a generalization of the Baker-Campbell-Hausdorff formula allowing to reformulate such pulsed dynamics as a continuous one. This reveals an adiabatic evolution. We obtain a general type of quantum Zeno dynamics, which unifies all known manifestations in the literature as well as describing new types.