Cloning and Cryptography with Quantum Continuous Variables

The cloning of quantum variables with continuous spectra is investigated. We define a Gaussian 1-to-2 cloning machine, which copies equally well two conjugate variables such as position and momentum or the two quadrature components of a light mode. The resulting cloning fidelity for coherent states, namely $F=2/3$, is shown to be optimal. An asymmetric version of this Gaussian cloner is then used to assess the security of a continuous-variable quantum key distribution scheme that allows two remote parties to share a Gaussian key. The information versus disturbance tradeoff underlying this continuous quantum cryptographic scheme is then analyzed for the optimal individual attack. Methods to convert the resulting Gaussian keys into secret key bits are also studied. The extension of the Gaussian cloner to optimal $N$-to-$M$ continuous cloners is then discussed, and it is shown how to implement these cloners for light modes, using a phase-insensitive optical amplifier and beam splitters. Finally, a phase-conjugated inputs $(N,N')$-to-$(M,M')$ continuous cloner is defined, yielding $M$ clones and $M'$ anticlones from $N$ replicas of a coherent state and $N'$ replicas of its phase-conjugate (with $M'-M=N'-N$). This novel kind of cloners is shown to outperform the standard $N$-to-$M$ cloners in some situations.Comment: 8 pages, 3 figures, submitted to the special issue of the European Physical Journal D on "Quantum interference and cryptographic keys: novel physics and advancing technologies", proceedings of the conference QUICK 2001, Corsica, April 7-13 2001. Minor correction, references adde

Sexual and marital trajectories and HIV infection among ever-married women in rural Malawi.

OBJECTIVE: To explore how sexual and marital trajectories are associated with HIV infection among ever-married women in rural Malawi. METHODS: Retrospective survey data and HIV biomarker data for 926 ever-married women interviewed in the Malawi Diffusion and Ideational Change Project were used. The associations between HIV infection and four key life course transitions considered individually (age at sexual debut, premarital sexual activity, entry into marriage and marital disruption by divorce or death) were examined. These transitions were then sequenced to construct trajectories that represent the variety of patterns in the data. The association between different trajectories and HIV prevalence was examined, controlling for potentially confounding factors such as age and region. RESULTS: Although each life course transition taken in isolation may be associated with HIV infection, their combined effect appeared to be conditional on the sequence in which they occurred. Although early sexual debut, not marrying one's first sexual partner and having a disrupted marriage each increased the likelihood of HIV infection, their risk was not additive. Women who both delayed sexual debut and did not marry their first partner are, once married, more likely to experience marital disruption and to be HIV-positive. Women who marry their first partner but who have sex at a young age, however, are also at considerable risk. CONCLUSIONS: These findings identify the potential of a life course perspective for understanding why some women become infected with HIV and others do not, as well as the differentials in HIV prevalence that originate from the sequence of sexual and marital transitions in one's life. The analysis suggests, however, the need for further data collection to permit a better examination of the mechanisms that account for variations in life course trajectories and thus in lifetime probabilities of HIV infection

Security of Quantum Key Distribution with Coherent States and Homodyne Detection

We assess the security of a quantum key distribution protocol relying on the transmission of Gaussian-modulated coherent states and homodyne detection. This protocol is shown to be equivalent to a squeezed state protocol based on a CSS code construction, and is thus provably secure against any eavesdropping strategy. We also briefly show how this protocol can be generalized in order to improve the net key rate.Comment: 7 page

Secure Coherent-state Quantum Key Distribution Protocols with Efficient Reconciliation

We study the equivalence between a realistic quantum key distribution protocol using coherent states and homodyne detection and a formal entanglement purification protocol. Maximally-entangled qubit pairs that one can extract in the formal protocol correspond to secret key bits in the realistic protocol. More specifically, we define a qubit encoding scheme that allows the formal protocol to produce more than one entangled qubit pair per coherent state, or equivalently for the realistic protocol, more than one secret key bit. The entanglement parameters are estimated using quantum tomography. We analyze the properties of the encoding scheme and investigate its application to the important case of the attenuation channel.Comment: REVTeX, 11 pages, 2 figure

Exactly Solvable Birth and Death Processes

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable `matrix' quantum mechanics, which is recently proposed by Odake and the author. The ($q$-)Askey-scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of $q^x$ ($x$ being the population) corresponding to the $q$-Racah polynomial.Comment: LaTeX, amsmath, amssymb, 24 pages, no figure