Three dimensional quantum key distribution in the presence of several eavesdroppers

Quantum key distribution based on encoding in three dimensional systems in the presence of several eavesdroppers is proposed. This extends the BB84 protocol in the presence of many eavesdroppers where two-level quantum systems (qubits) are replaced by three-level systems (qutrits). We discuss the scenarios involving two, three and four complementary bases. We derive the explicit form of Alice and Bob mutual information and the information gained by each eavesdropper. In particular, we show that, in the presence of only one eavesdropper, the protocol involving four bases is safer than the other ones. However, for two eavesdroppers, the security is strongly dependent on the attack probabilities. The effect of a large number of eavesdroppers is also investigated

Entropy as logarithmic term of the central charge and modified Friedmann equation in AdS/CFT correspondence

This paper is about the extended thermodynamics of AdS black holes and its relation to CFT thermodynamics. The logarithmic term of the central charge is interpreted as black hole entropy. We have obtain a modified Friedmann equation from the Smarr formula. We find that the AdS radius is the critical shadow radius. We obtain the Hawking-Bekenstein formula with logarithmic corrections, which depends on the central charge. The real gas in AdS is a dual of an ideal gas in CFT. This work can be extended to the AdS-Kerr black holes.Comment: 22 pages, 4 figure

A Monte Carlo Study of the Order-Disorder Layering Transitions in the Blume-Capel Model

The order-disorder layering transitions, of the Blume-Capel model, are studied using the Monte Carlo (MC) simulations, in the presence of a variable crystal field. For a very low temperature, the results are in good agreement with the ground state study. The first order transition line, found for low temperatures, is connected to the second order transition line, seen for higher temperatures, by a tri-critical point, for each layer. The reentrant phenomena, caused by a competition of thermal fluctuations and an inductor magnetic field created by the deeper layers, is found for the first k0 layers from the surface, where k0 is exactly the number of layering transitions allowed by the ground state study. For each layer 'k', the layer magnetisations mk , the magnetic susceptibilities χm,k and the quarupolar magnetic susceptibilities χq,k are also investigated.The order-disorder layering transitions, of the Blume-Capel model, are studied using the Monte Carlo (MC) simulations, in the presence of a variable crystal field. For a very low temperature, the results are in good agreement with the ground state study. The first order transition line, found for low temperatures, is connected to the second order transition line, seen for higher temperatures, by a tri-critical point, for each layer. The reentrant phenomena, caused by a competition of thermal fluctuations and an inductor magnetic field created by the deeper layers, is found for the first k0 layers from the surface, where k0 is exactly the number of layering transitions allowed by the ground state study. For each layer 'k', the layer magnetisations mk , the magnetic susceptibilities χm,k and the quarupolar magnetic susceptibilities χq,k are also investigated

Wetting of an Ising system with perfect and corrugated surfaces in a transverse field

Using the mean field theory, a comparative study of the wetting and layering transitions of a spin-1/2 Ising model with perfect and corrugated surfaces, is established. The phase diagrams are investigated and compared in the presence of both a longitudinal and surface fields. The effect of both the temperature and the transverse field on the wetting and layering transitions are established.Using the mean field theory, a comparative study of the wetting and layering transitions of a spin-1/2 Ising model with perfect and corrugated surfaces, is established. The phase diagrams are investigated and compared in the presence of both a longitudinal and surface fields. The effect of both the temperature and the transverse field on the wetting and layering transitions are established

The Optimal Velocity Traffic Flow Models With Open Boundary

The effects of the open boundaries on the dynamical behavior of the optimal velocity traffic flow models with a delay time τ allowing the car to reach its optimal velocity is studied using numerical simulations. The particles could enter the chain with a given injecting rate probability α, and could leave the system with a given extracting rate probability β. In the absence of the variation of the delay time ∆τ, it is found that the transition from unstable to metastable and from metastable to stable state occur under the effect of the probabilities rates α and β. However, for a fixed value of α, there exist a critical value of the extraction rate βc1 above which the wave density disappears and the metastable state appears and a critical value βc2 above which the metastable state disappears while the stable state appears. βc1 and βc2 depend on the values of α and the variation of the delay time ∆τ. Indeed βc1 and βc2 increase when increasing α and/or decreasing ∆τ. The flow of vehicles is calculated as a function of α, β and ∆τ for a fixed value of τ. Phase diagrams in the (α,β) plane exhibits four different phases namely, unstable, metastable, stable. The transition line between stable phase and the unstable one is curved and it is of first order type. While the transition between stable (unstable) phase and the metastable phase are of second order type. The region of the metastable phase shrinks with increasing the variation of the delay time ∆τ and disappears completely above a critical value ∆τc .The effects of the open boundaries on the dynamical behavior of the optimal velocity traffic flow models with a delay time τ allowing the car to reach its optimal velocity is studied using numerical simulations. The particles could enter the chain with a given injecting rate probability α, and could leave the system with a given extracting rate probability β. In the absence of the variation of the delay time ∆τ, it is found that the transition from unstable to metastable and from metastable to stable state occur under the effect of the probabilities rates α and β. However, for a fixed value of α, there exist a critical value of the extraction rate βc1 above which the wave density disappears and the metastable state appears and a critical value βc2 above which the metastable state disappears while the stable state appears. βc1 and βc2 depend on the values of α and the variation of the delay time ∆τ. Indeed βc1 and βc2 increase when increasing α and/or decreasing ∆τ. The flow of vehicles is calculated as a function of α, β and ∆τ for a fixed value of τ. Phase diagrams in the (α,β) plane exhibits four different phases namely, unstable, metastable, stable. The transition line between stable phase and the unstable one is curved and it is of first order type. While the transition between stable (unstable) phase and the metastable phase are of second order type. The region of the metastable phase shrinks with increasing the variation of the delay time ∆τ and disappears completely above a critical value ∆τc

The effect of mixture lenghts of vehicles on the traffic flow behavior in one- dimensional cellular automaton

The effect of mixture lengths of vehicles on the asymmetric exclusion model is studied using numerical simulations for both open and periodic boundaries in parallel dynamics. The vehicles are filed from their length, the small cars Type 1 occupy one cell whereas the big ones Type 2 takes two. In the case of open boundaries two varieties of models are presented. The former model corresponds to a chain with two entries where densities are calculated as a function of the injecting rates α1 and α2 of vehicles type 1 and type 2 respectively, and the phase diagram (α1 , α2 ) is presented for a fixed value of the extracting rate β. In this case the first order transition from low to high density phases occurs at α1 +α2 =β and disappears for α2 >β. The latter model correspond to a chain with one entry, where α is the injecting rate of vehicles independently of their nature. Type1 and type2 are injected with α1 and α2 respectively, where α2 =nα, n is the concentration of type2 and α2 ≤α1 ≤α. Densities are calculated as a function of the injecting rates α, and the phase diagrams (α,β) are established for different values of n. In this case the gap which is a characteristic of the first order transition vanishes with increasing α for n ≠ 0.However, the first order transition between high and low densities exhibit an end point above which the global density undergoes a continuous passage. The end point coordinate depends strongly on the value of n. In the periodic boundaries case, the presence of vehicles type2 in the chain leads to a modification in the fundamental phase diagram (current, density). Indeed, the maximal current value decreases with increasing the concentration of vehicles type 2, and occurs at higher values of the global density in contrast with what was found by Schadschneider et al. [20].The effect of mixture lengths of vehicles on the asymmetric exclusion model is studied using numerical simulations for both open and periodic boundaries in parallel dynamics. The vehicles are filed from their length, the small cars Type 1 occupy one cell whereas the big ones Type 2 takes two. In the case of open boundaries two varieties of models are presented. The former model corresponds to a chain with two entries where densities are calculated as a function of the injecting rates α1 and α2 of vehicles type 1 and type 2 respectively, and the phase diagram (α1 , α2 ) is presented for a fixed value of the extracting rate β. In this case the first order transition from low to high density phases occurs at α1 +α2 =β and disappears for α2 >β. The latter model correspond to a chain with one entry, where α is the injecting rate of vehicles independently of their nature. Type1 and type2 are injected with α1 and α2 respectively, where α2 =nα, n is the concentration of type2 and α2 ≤α1 ≤α. Densities are calculated as a function of the injecting rates α, and the phase diagrams (α,β) are established for different values of n. In this case the gap which is a characteristic of the first order transition vanishes with increasing α for n ≠ 0.However, the first order transition between high and low densities exhibit an end point above which the global density undergoes a continuous passage. The end point coordinate depends strongly on the value of n. In the periodic boundaries case, the presence of vehicles type2 in the chain leads to a modification in the fundamental phase diagram (current, density). Indeed, the maximal current value decreases with increasing the concentration of vehicles type 2, and occurs at higher values of the global density in contrast with what was found by Schadschneider et al. [20]