Unambiguous state discrimination in quantum cryptography with weak coherent states

The use of linearly independent signal states in realistic implementations of quantum key distribution (QKD) enables an eavesdropper to perform unambiguous state discrimination. We explore quantitatively the limits for secure QKD imposed by this fact taking into account that the receiver can monitor to some extend the photon number statistics of the signals even with todays standard detection schemes. We compare our attack to the beamsplitting attack and show that security against beamsplitting attack does not necessarily imply security against the attack considered here.Comment: 10 pages, 6 figures, updated version with added discussion of beamsplitting attac

Security of quantum cryptography using balanced homodyne detection

In this paper we investigate the security of a quantum cryptographic scheme which utilizes balanced homodyne detection and weak coherent pulse (WCP). The performance of the system is mainly characterized by the intensity of the WCP and postselected threshold. Two of the simplest intercept/resend eavesdropping attacks are analyzed. The secure key gain for a given loss is also discussed in terms of the pulse intensity and threshold.Comment: RevTeX4, 8pages, 7 figure

Coherent pulse implementations of quantum cryptography protocols resistant to photon number splitting attacks

A new class of quantum cryptography (QC) protocols that are robust against the most general photon number splitting attacks in a weak coherent pulse implementation has been recently proposed. In this article we give a quite exhaustive analysis of several eavesdropping attacks on these schemes. The eavesdropper (Eve) is supposed to have unlimited technological power while the honest parties (Alice and Bob) use present day technology, in particular an attenuated laser as an approximation of a single-photon source. They exploit the nonorthogonality of quantum states for decreasing the information accessible to Eve in the multi-photon pulses accidentally produced by the imperfect source. An implementation of some of these protocols using present day technology allow for a secure key distribution up to distances of $\sim$ 150 km. We also show that strong-pulse implementations, where a strong pulse is included as a reference, allow for key distribution robust against photon number splitting attacks.Comment: 16 pages, 11 figure

Unambiguous State Discrimination of Coherent States with Linear Optics: Application to Quantum Cryptography

We discuss several methods for unambiguous state discrimination of N symmetric coherent states using linear optics and photodetectors. One type of measurements is shown to be optimal in the limit of small photon numbers for any N. For the special case of N=4 this measurement can be fruitfully used by the receiving end (Bob) in an implementation of the BB84 quantum key distribution protocol using faint laser pulses. In particular, if Bob detects only a single photon the procedure is equivalent to the standard measurement that he would have to perform in a single-photon implementation of BB84, if he detects two photons Bob will unambiguously know the bit sent to him in 50% of the cases without having to exchange basis information, and if three photons are detected, Bob will know unambiguously which quantum state was sent.Comment: 5 RevTeX pages, 2 eps figure

miRNAs are essential for survival and differentiation of newborn neurons but not for expansion of neural progenitors during early neurogenesis in the mouse embryonic neocortex

Neurogenesis during the development of the mammalian cerebral cortex involves a switch of neural stem and progenitor cells from proliferation to differentiation. To explore the possible role of microRNAs (miRNAs) in this process, we conditionally ablated Dicer in the developing mouse neocortex using Emx1-Cre, which is specifically expressed in the dorsal telencephalon as early as embryonic day (E) 9.5. Dicer ablation in neuroepithelial cells, which are the primary neural stem and progenitor cells, and in the neurons derived from them, was evident from E10.5 onwards, as ascertained by the depletion of the normally abundant miRNAs miR-9 and miR-124. Dicer ablation resulted in massive hypotrophy of the postnatal cortex and death of the mice shortly after weaning. Analysis of the cytoarchitecture of the Dicer-ablated cortex revealed a marked reduction in radial thickness starting at E13.5, and defective cortical layering postnatally. Whereas the former was due to neuronal apoptosis starting at E12.5, which was the earliest detectable phenotype, the latter reflected dramatic impairment of neuronal differentiation. Remarkably, the primary target cells of Dicer ablation, the neuroepithelial cells, and the neurogenic progenitors derived from them, were unaffected by miRNA depletion with regard to cell cycle progression, cell division, differentiation and viability during the early stage of neurogenesis, and only underwent apoptosis starting at E14.5. Our results support the emerging concept that progenitors are less dependent on miRNAs than their differentiated progeny, and raise interesting perspectives as to the expansion of somatic stem cells

Security against individual attacks for realistic quantum key distribution

I prove the security of quantum key distribution against individual attacks for realistic signals sources, including weak coherent pulses and downconversion sources. The proof applies to the BB84 protocol with the standard detection scheme (no strong reference pulse). I obtain a formula for the secure bit rate per time slot of an experimental setup which can be used to optimize the performance of existing schemes for the considered scenario.Comment: 10 pages, 4 figure

Interference in dielectrics and pseudo-measurements

Inserting a lossy dielectric into one arm of an interference experiment acts in many ways like a measurement. If two entangled photons are passed through the interferometer, a certain amount of information is gained about which path they took, and the interference pattern in a coincidence count measurement is suppressed. However, by inserting a second dielectric into the other arm of the interferometer, one can restore the interference pattern. Two of these pseudo-measurements can thus cancel each other out. This is somewhat analogous to the proposed quantum eraser experiments.Comment: 7 pages RevTeX 3.0 + 2 figures (postscript). Submitted to Phys. Rev.

Conditional beam splitting attack on quantum key distribution

We present a novel attack on quantum key distribution based on the idea of adaptive absorption [calsam01]. The conditional beam splitting attack is shown to be much more efficient than the conventional beam spitting attack, achieving a performance similar to the, powerful but currently unfeasible, photon number splitting attack. The implementation of the conditional beam splitting attack, based solely on linear optical elements, is well within reach of current technology.Comment: Submitted to Phys. Rev.

Singularities of nn-fold integrals of the Ising class and the theory of elliptic curves

We introduce some multiple integrals that are expected to have the same singularities as the singularities of the $n$-particle contributions $\chi^{(n)}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for $n=1, 2, 3, 4$ and only modulo some primes for $n=5$ and $6$, thus providing a large set of (possible) new singularities of the $\chi^{(n)}$. We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to $n= 6$) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a {\em finite number of one dimensional integrals}. Among the singularities found, we underline the fact that the quadratic polynomial condition $1+3 w +4 w^2 = 0$, that occurs in the linear differential equation of $\chi^{(3)}$, actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves.Comment: 39 pages, 7 figure