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

On the performance of two protocols: SARG04 and BB84

We compare the performance of BB84 and SARG04, the later of which was proposed by V. Scarani et al., in Phys. Rev. Lett. 92, 057901 (2004). Specifically, in this paper, we investigate SARG04 with two-way classical communications and SARG04 with decoy states. In the first part of the paper, we show that SARG04 with two-way communications can tolerate a higher bit error rate (19.4% for a one-photon source and 6.56% for a two-photon source) than SARG04 with one-way communications (10.95% for a one-photon source and 2.71% for a two-photon source). Also, the upper bounds on the bit error rate for SARG04 with two-way communications are computed in a closed form by considering an individual attack based on a general measurement. In the second part of the paper, we propose employing the idea of decoy states in SARG04 to obtain unconditional security even when realistic devices are used. We compare the performance of SARG04 with decoy states and BB84 with decoy states. We find that the optimal mean-photon number for SARG04 is higher than that of BB84 when the bit error rate is small. Also, we observe that SARG04 does not achieve a longer secure distance and a higher key generation rate than BB84, assuming a typical experimental parameter set.Comment: 48 pages, 10 figures, 1 column, changed Figs. 7 and

Unconditionally Secure Key Distribution Based on Two Nonorthogonal States

We prove the unconditional security of the Bennett 1992 protocol, by using a reduction to an entanglement distillation protocol initiated by a local filtering process. The bit errors and the phase errors are correlated after the filtering, and we can bound the amount of phase errors from the observed bit errors by an estimation method involving nonorthogonal measurements. The angle between the two states shows a trade-off between accuracy of the estimation and robustness to noises.Comment: 5 pages, 1 figur

Simulation Subsumption or Déjà vu on the Web

Simulation unification is a special kind of unification adapted to retrieving semi-structured data on the Web. This article introduces simulation subsumption, or containment, that is, query subsumption under simulation unification. Simulation subsumption is crucial in general for query optimization, in particular for optimizing pattern-based search engines, and for the termination of recursive rule-based web languages such as the XML and RDF query language Xcerpt. This paper first motivates and formalizes simulation subsumption. Then, it establishes decidability of simulation subsumption for advanced query patterns featuring descendant constructs, regular expressions, negative subterms (or subterm exclusions), and multiple variable occurrences. Finally, we show that subsumption between two query terms can be decided in O(n!n) where n is the sum of the sizes of both query terms

Unconditional Security of Single-Photon Differential Phase Shift Quantum Key Distribution

In this Letter, we prove the unconditional security of single-photon differential phase shift quantum key distribution (DPS-QKD) protocol, based on the conversion to an equivalent entanglement-based protocol. We estimate the upper bound of the phase error rate from the bit error rate, and show that DPS-QKD can generate unconditionally secure key when the bit error rate is not greater than 4.12%. This proof is the first step to the unconditional security proof of coherent state DPS-QKD.Comment: 5 pages, 2 figures; shorten the length, improve clarity, and correct typos; accepted for publication in Physical Review Letter

Unconditional security of the Bennett 1992 quantum key-distribution scheme with strong reference pulse

We prove the unconditional security of the original Bennett 1992 protocol with strong reference pulse. We show that we may place a projection onto suitably defined qubit spaces before the receiver, which makes the analysis as simple as qubit-based protocols. Unlike the single-photon-based qubits, the qubits identified in this scheme are almost surely detected by the receiver even after a lossy channel. This leads to the key generation rate that is proportional to the channel transmission rate for proper choices of experimental parameters.Comment: More detailed presentation and a bit modified security proo

Generic features of Einstein-Aether black holes

We reconsider spherically symmetric black hole solutions in Einstein-Aether theory with the condition that this theory has identical PPN parameters as those for general relativity, which is the main difference from the previous research. In contrast with previous study, we allow superluminal propagation of a spin-0 Aether-gravity wave mode. As a result, we obtain black holes having a spin-0 "horizon" inside an event horizon. We allow a singularity at a spin-0 "horizon" since it is concealed by the event horizon. If we allow such a configuration, the kinetic term of the Aether field can be large enough for black holes to be significantly different from Schwarzschild black holes with respect to ADM mass, innermost stable circular orbit, Hawking temperature, and so on. We also discuss whether or not the above features can be seen in more generic vector-tensor theories.Comment: 9 pages, 9 figures, basic equations and their analytic arguments are adde

Some Cohomotopy Groups of Suspended Projective Planes

In this paper we compute some cohomotopy groups of the suspended complex and quaternionic projective plane by use of the exact sequence associated with the canonical cofiber sequence and a formula about a multiple of the identity class of the suspended projective plane.</p

Continuous area spectrum in regular black hole

We investigate highly damped quasinormal modes of regular black hole coupled to nonlinear electrodynamics. Using the WKB approximation combined with complex-integration technique, we show that the real part of the frequency disappears in the highly damped limit. If we use the Bohr's correspondence principle, the area spectrum of this black hole is continuous. We discuss its implication in the loop quantum gravity.Comment: 5 pages, 1 figure

Properties of global monopoles with an event horizon

We investigate the properties of global monopoles with an event horizon. We find that there is an unstable circular orbit even if a particle does not have an angular momentum when the core mass is negative. We also obtain the asymptotic form of solutions when the event horizon is much larger than the core radius of the monopole, and discuss if they could be a model of galactic halos.Comment: 5 pages, 7 figure