A very brief introduction to quantum computing and quantum information theory for mathematicians

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs of most statements can be found in standard references

Unconditional security at a low cost

By simulating four quantum key distribution (QKD) experiments and analyzing one decoy-state QKD experiment, we compare two data post-processing schemes based on security against individual attack by L\"{u}tkenhaus, and unconditional security analysis by Gottesman-Lo-L\"{u}tkenhaus-Preskill. Our results show that these two schemes yield close performances. Since the Holy Grail of QKD is its unconditional security, we conclude that one is better off considering unconditional security, rather than restricting to individual attacks.Comment: Accepted by International Conference on Quantum Foundation and Technology: Frontier and Future 2006 (ICQFT'06

QKD in Standard Optical Telecommunications Networks

To perform Quantum Key Distribution, the mastering of the extremely weak signals carried by the quantum channel is required. Transporting these signals without disturbance is customarily done by isolating the quantum channel from any noise sources using a dedicated physical channel. However, to really profit from this technology, a full integration with conventional network technologies would be highly desirable. Trying to use single photon signals with others that carry an average power many orders of magnitude bigger while sharing as much infrastructure with a conventional network as possible brings obvious problems. The purpose of the present paper is to report our efforts in researching the limits of the integration of QKD in modern optical networks scenarios. We have built a full metropolitan area network testbed comprising a backbone and an access network. The emphasis is put in using as much as possible the same industrial grade technology that is actually used in already installed networks, in order to understand the throughput, limits and cost of deploying QKD in a real network

Allowable Low-Energy E_6 Subgroups from Leptogenesis

There are only two viable low-energy $E_6$ subgroups: $SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_N$ or $SU(3)_C \times SU(2)_L \times SU(2)'_R \times U(1)_{Y_L + Y'_R}$, which would not erase any preexisting lepton asymmetry of the Universe that may have been created by the decay of heavy singlet (right-handed) neutrinos or any other mechanism. They are also the two most favored $E_6$ subgroups from a recent analysis of present neutral-current data. We study details of the leptogenesis, as well as some salient experimental signatures of the two models.Comment: 12 page

Heavy Triplet Leptons and New Gauge Boson

A heavy triplet of leptons $(\Sigma^+, \Sigma^0, \Sigma^-)_R$ per family is proposed as the possible anchor of a small seesaw neutrino mass. A new U(1) gauge symmetry is then also possible, and the associated gauge boson $X$ may be discovered at or below the TeV scale. We discuss the phenomenology of this proposal, with and without possible constraints from the NuTeV and atomic parity violation experiments, which appear to show small discrepancies from the predictions of the standard model.Comment: 20 pages including 4 figure

Postponement of dark-count effects in practical quantum key-distribution by two-way post-processing

The influence of imperfections on achievable secret-key generation rates of quantum key distribution protocols is investigated. As examples of relevant imperfections, we consider tagging of Alice's qubits and dark counts at Bob's detectors, while we focus on a powerful eavesdropping strategy which takes full advantage of tagged signals. It is demonstrated that error correction and privacy amplification based on a combination of a two-way classical communication protocol and asymmetric Calderbank-Shor-Steane codes may significantly postpone the disastrous influence of dark counts. As a result, the distances are increased considerably over which a secret key can be distributed in optical fibres reliably. Results are presented for the four-state, the six-state, and the decoy-state protocols.Comment: Fully revised version (12 pages and 8 figures). Improved figures and discussion added. To appear in Eur. Phys. J.

Recombination Induced Softening and Reheating of the Cosmic Plasma

The atomic recombination process leads to a softening of the matter equation of state as reflected by a reduced generalized adiabatic index, with accompanying heat release. We study the effects of this recombination softening and reheating of the cosmic plasma on the ionization history, visibility function, Cold Dark Matter (CDM) transfer function, and the Cosmic Microwave Background (CMB) spectra. The resulting modifications of the CMB spectrm is 1/10 of WMAP's current error and is comparable to PLANCK's error. Therefore, this effect should be considered when data with higher accuracy are analysed.Comment: 11 pages, 6 figures, Accepted for publication in Monthly Notices of the Royal Astronomical Society; as advised by referee, omit high-baryon mode

Alternative schemes for measurement-device-independent quantum key distribution

Practical schemes for measurement-device-independent quantum key distribution using phase and path or time encoding are presented. In addition to immunity to existing loopholes in detection systems, our setup employs simple encoding and decoding modules without relying on polarization maintenance or optical switches. Moreover, by employing a modified sifting technique to handle the dead-time limitations in single-photon detectors, our scheme can be run with only two single-photon detectors. With a phase-postselection technique, a decoy-state variant of our scheme is also proposed, whose key generation rate scales linearly with the channel transmittance.Comment: 30 pages, 5 figure

Bounds of concurrence and their relation with fidelity and frontier states

The bounds of concurrence in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98 (2007) 140505] and [C. Zhang \textit{et. al.}, Phys. Rev. A 78 (2008) 042308] are proved by using two properties of the fidelity. In two-qubit systems, for a given value of concurrence, the states achieving the maximal upper bound, the minimal lower bound or the maximal difference upper-lower bound are determined analytically