Collective attacks and unconditional security in continuous variable quantum key distribution

We present here an information theoretic study of Gaussian collective attacks on the continuous variable key distribution protocols based on Gaussian modulation of coherent states. These attacks, overlooked in previous security studies, give a finite advantage to the eavesdropper in the experimentally relevant lossy channel, but are not powerful enough to reduce the range of the reverse reconciliation protocols. Secret key rates are given for the ideal case where Bob performs optimal collective measurements, as well as for the realistic cases where he performs homodyne or heterodyne measurements. We also apply the generic security proof of Christiandl et. al. [quant-ph/0402131] to obtain unconditionally secure rates for these protocols.Comment: Minor orthographic and grammatical correction

Internal Realism and the Reality of God

How do religions refer to reality in their language and symbols, and which reality do they envisage and encounter? on the basis of some examples of an understanding of religion without reference to reality, I first answer the question of what ”realism’ is. realism has been an opposite concept to nominalism, idealism, empiricism and antirealism. The paper concentrates especially on the most recent formation of realism in opposition to antirealism. In a second section the consequences for philosophy of religion and theology are considered. How the reality, as it is considered in philosophy of religion and in theology, has to be characterised, if and how this reality is relevant for human beings, and what its relation is to everything else, can only be answered and clarified in a presentation in a language that is specific for this reality, the reality of God

Optimality of Gaussian Attacks in Continuous Variable Quantum Cryptography

We analyze the asymptotic security of the family of Gaussian modulated Quantum Key Distribution protocols for Continuous Variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.Comment: See also R. Garcia-Patron and N. Cerf, quant-ph/060803

An integrality theorem of Grosshans over arbitrary base ring

We revisit a theorem of Grosshans and show that it holds over arbitrary commutative base ring $k$. One considers a split reductive group scheme $G$ acting on a $k$-algebra $A$ and leaving invariant a subalgebra $R$. If $R^U=A^U$ then the conclusion is that $A$ is integral over $R$.Comment: 5 pages; final versio

Unidimensional continuous-variable quantum key distribution

We propose the continuous-variable quantum key distribution protocol based on the Gaussian modulation of a single quadrature of the coherent states of light, which is aimed to provide simplified implementation compared to the symmetrically modulated Gaussian coherent-state protocols. The protocol waives the necessity in phase quadrature modulation and the corresponding channel transmittance estimation. The security of the protocol against collective attacks in a generally phase-sensitive Gaussian channels is analyzed and is shown achievable upon certain conditions. Robustness of the protocol to channel imperfections is compared to that of the symmetrical coherent-state protocol. The simplified unidimensional protocol is shown possible at a reasonable quantitative cost in terms of key rate and of tolerable channel excess noise.Comment: 7 pages, 5 figures, close to the published versio