Unified picture of Q-balls and boson stars via catastrophe theory

We make an analysis of Q-balls and boson stars using catastrophe theory, as an extension of the previous work on Q-balls in flat spacetime. We adopt the potential $V_3(\phi)={m^2\over2}\phi^2-\mu\phi^3+\lambda\phi^4$ for Q-balls and that with $\mu =0$ for boson stars. For solutions with $|g^{rr}-1|\sim 1$ at its peak, stability of Q-balls has been lost regardless of the potential parameters. As a result, phase relations, such as a Q-ball charge versus a total Hamiltonian energy, approach those of boson stars, which tell us an unified picture of Q-balls and boson stars.Comment: 10 pages, 13 figure

On hit-and-miss hyperspace topologies

summary:The Vietoris topology and Fell topologies on the closed subsets of a Hausdorff uniform space are prototypes for hit-and-miss hyperspace topologies, having as a subbase all closed sets that hit a variable open set, plus all closed sets that miss (= fail to intersect) a variable closed set belonging to a prescribed family $\Delta$ of closed sets. In the case of the Fell topology, where $\Delta$ consists of the compact sets, a closed set $A$ misses a member $B$ of $\Delta$ if and only if $A$ is far from $B$ in a uniform sense. With the Fell topology as a point of departure, one can consider proximal hit-and-miss hyperspace topologies, where ``miss'' is replaced by ``far from'' in the above formulation. Interest in these objects has been driven by their applicability to convex analysis, where the Mosco topology, the slice topology, and the linear topology have received close scrutiny in recent years. In this article we look closely at the relationship between hit-and-miss and proximal hit-and-miss topologies determined by a class $\Delta$. In the setting of metric spaces, necessary and sufficient conditions on $\Delta$ are given for one to contain the other. Particular attention is given to these topologies when $\Delta$ consists of the family of closed balls in a metric space, and their interplay with the Wijsman topology is considered in some detail

Unconditional Security of Three State Quantum Key Distribution Protocols

Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the BB84 and B92 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has only been shown for the trivial intercept/resend eavesdropping strategy. In this paper, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss on how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.Comment: 4 pages, published versio

Unconditionally secure key distillation from multi-photons

In this paper, we prove that the unconditionally secure key can be surprisingly extracted from {\it multi}-photon emission part in the photon polarization-based QKD. One example is shown by explicitly proving that one can indeed generate an unconditionally secure key from Alice's two-photon emission part in ``Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulses implementations'' proposed by V. Scarani {\it et al.,} in Phys. Rev. Lett. {\bf 92}, 057901 (2004), which is called SARG04. This protocol uses the same four states as in BB84 and differs only in the classical post-processing protocol. It is, thus, interesting to see how the classical post-processing of quantum key distribution might qualitatively change its security. We also show that one can generate an unconditionally secure key from the single to the four-photon part in a generalized SARG04 that uses six states. Finally, we also compare the bit error rate threshold of these protocols with the one in BB84 and the original six-state protocol assuming a depolarizing channel.Comment: The title has changed again. We considerably improved our presentation, and furthermore we proposed & analyzed a security of a modified SARG04 protocol, which uses six state