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

Multicritical Behaviours in One-Dimensional Traffic Flow

The effect of the on-ramp and off-ramp positions i1 and i2 , respectively, on the one dimensional-cellular automaton traffic flow behaviour, is investigated numerically. The on-ramp and off-ramp rates at  i1 and i2 are α0 and β0 , respectively. However, in the open boundary conditions, with injecting and extracting rates α and β and using parallel dynamics, several phases occur, depending on the position of i1 by respect to i2. Namely, low density phase (LDP), intermediate density phase (IDP), plateau current phase (PCP) and high density phase (HDP). Furthermore, critical, tricritical and multicritical behaviours take place in the ( i1 , α0 ) phase diagrams.The effect of the on-ramp and off-ramp positions i1 and i2 , respectively, on the one dimensional-cellular automaton traffic flow behaviour, is investigated numerically. The on-ramp and off-ramp rates at  i1 and i2 are α0 and β0 , respectively. However, in the open boundary conditions, with injecting and extracting rates α and β and using parallel dynamics, several phases occur, depending on the position of i1 by respect to i2. Namely, low density phase (LDP), intermediate density phase (IDP), plateau current phase (PCP) and high density phase (HDP). Furthermore, critical, tricritical and multicritical behaviours take place in the ( i1 , α0 ) phase diagrams

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