Network Synthesis of Linear Dynamical Quantum Stochastic Systems

The purpose of this paper is to develop a synthesis theory for linear dynamical quantum stochastic systems that are encountered in linear quantum optics and in phenomenological models of linear quantum circuits. In particular, such a theory will enable the systematic realization of coherent/fully quantum linear stochastic controllers for quantum control, amongst other potential applications. We show how general linear dynamical quantum stochastic systems can be constructed by assembling an appropriate interconnection of one degree of freedom open quantum harmonic oscillators and, in the quantum optics setting, discuss how such a network of oscillators can be approximately synthesized or implemented in a systematic way from some linear and non-linear quantum optical elements. An example is also provided to illustrate the theory.Comment: Revised and corrected version, published in SIAM Journal on Control and Optimization, 200

Extremal Quantum Correlations and Cryptographic Security

We investigate a fundamental property of device independent security in quantum cryptography by characterizing probability distributions which are necessarily independent of the measurement results of any eavesdropper. We show that probability distributions that are secure in this sense are exactly the extremal quantum probability distributions. This allows us to give a characterization of security in algebraic terms. We apply the method to common examples for two-party as well as multi-party setups and present a scheme for verifying security of probability distributions with two parties, two measurement settings, and two outcomes.Comment: 7 pages, 2 figures, revised version, accepted for publication in Phys. Rev. Let

Partial mixing and the formation of 13C pockets in AGB stars: effects on the s-process elements

The production of the elements heavier than iron via slow neutron captures (the s process) is a main feature of the contribution of asymptotic giant branch (AGB) stars of low mass (< 5 Msun) to the chemistry of the cosmos. However, our understanding of the main neutron source, the 13C(alpha,n)16O reaction, is still incomplete. It is commonly assumed that in AGB stars mixing beyond convective borders drives the formation of 13C pockets. However, there is no agreement on the nature of such mixing and free parameters are present. By means of a parametric model we investigate the impact of different mixing functions on the final s-process abundances in low-mass AGB models. Typically, changing the shape of the mixing function or the mass extent of the region affected by the mixing produce the same results. Variations in the relative abundance distribution of the three s-process peaks (Sr, Ba, and Pb) are generally within +/-0.2 dex, similar to the observational error bars. We conclude that other stellar uncertainties - the effect of rotation and of overshoot into the C-O core - play a more important role than the details of the mixing function. The exception is at low metallicity, where the Pb abundance is significantly affected. In relation to the composition observed in stardust SiC grains from AGB stars, the models are relatively close to the data only when assuming the most extreme variation in the mixing profile.Comment: 17 pages, 8 figures, 6 tables, accepted for publications on Monthly Notices of the Royal Astronomical Societ

Entanglement of indistinguishable particles in condensed matter physics

The concept of entanglement in systems where the particles are indistinguishable has been the subject of much recent interest and controversy. In this paper we study the notion of entanglement of particles introduced by Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] in several specific physical systems, including some that occur in condensed matter physics. The entanglement of particles is relevant when the identical particles are itinerant and so not distinguished by their position as in spin models. We show that entanglement of particles can behave differently to other approaches that have been used previously, such as entanglement of modes (occupation-number entanglement) and the entanglement in the two-spin reduced density matrix. We argue that the entanglement of particles is what could actually be measured in most experimental scenarios and thus its physical significance is clear. This suggests entanglement of particles may be useful in connecting theoretical and experimental studies of entanglement in condensed matter systems.Comment: 13 pages, 6 figures, comments welcome, published version (minor changes, added references

Mechanical squeezing via parametric amplification and weak measurement

Nonlinear forces allow motion of a mechanical oscillator to be squeezed below the zero-point motion. Of existing methods, mechanical parametric amplification is relatively accessible, but previously thought to be limited to 3 dB of squeezing in the steady state. We consider the effect of applying continuous weak measurement and feedback to this system. If the parametric drive is optimally detuned from resonance, correlations between the quadratures of motion allow unlimited steady-state squeezing. Compared to backaction evasion, we demonstrate that the measurement strength, temperature and efficiency requirements for quantum squeezing are significantly relaxed