Correlation functions, Bell's inequalities and the fundamental conservation laws

I derive the correlation function for a general theory of two-valued spin variables that satisfy the fundamental conservation law of angular momentum. The unique theory-independent correlation function is identical to the quantum mechanical correlation function. I prove that any theory of correlations of such discrete variables satisfying the fundamental conservation law of angular momentum violates the Bell's inequalities. Taken together with the Bell's theorem, this result has far reaching implications. No theory satisfying Einstein locality, reality in the EPR-Bell sense, and the validity of the conservation law can be constructed. Therefore, all local hidden variable theories are incompatible with fundamental symmetries and conservation laws. Bell's inequalities can be obeyed only by violating a conservation law. The implications for experiments on Bell's inequalities are obvious. The result provides new insight regarding entanglement, and its measures.Comment: LaTeX, 12pt, 11 pages, 2 figure

Maximal violation of Bell inequality for any given two-qubit pure state

In the case of bipartite two qubits systems, we derive the analytical expression of bound of Bell operator for any given pure state. Our result not only manifest some properties of Bell inequality, for example which may be violated by any pure entangled state and only be maximally violated for a maximally entangled state, but also give the explicit values of maximal violation for any pure state. Finally we point out that for two qubits systems there is no mixed state which can produce maximal violation of Bell inequality.Comment: 3 pages, 1 figure

On separability of quantum states and the violation of Bell-type inequalities

In contrast to the wide-spread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where a separable quantum state does not satisfy the original Bell inequality although the latter inequality, in its perfect correlation form, is valid for all joint classical measurements. In a very general setting, we discuss inequalities for joint experiments upon a bipartite quantum system in a separable state. We derive quantum analogues of the original Bell inequality and specify the conditions sufficient for a separable state to satisfy the original Bell inequality. We introduce the extended CHSH inequality and prove that, for any separable quantum state, this inequality holds for a variety of linear combinations.Comment: 13 pages, extended versio

Creation and localization of entanglement in a simple configuration of coupled harmonic oscillators

We investigate a simple arrangement of coupled harmonic oscillators which brings out some interesting effects concerning creation of entanglement. It is well known that if each member in a linear chain of coupled harmonic oscillators is prepared in a ``classical state'', such as a pure coherent state or a mixed thermal state, no entanglement is created in the rotating wave approximation. On the other hand, if one of the oscillators is prepared in a nonclassical state (pure squeezed state, for instance), entanglement may be created between members of the chain. In the setup considered here, we found that a great family of nonclassical (squeezed) states can localize entanglement in such a way that distant oscillators never become entangled. We present a detailed study of this particular localization phenomenon. Our results may find application in future solid state implementations of quantum computers, and we suggest an electromechanical system consisting of an array of coupled micromechanical oscillators as a possible implementation.Comment: 7 pages, 8 figures, minor typos fixe

Two destructive effects of decoherence on Bell inequality violation

We consider a system of two spin-1/2 particles, initially in an entangled Bell state. If one of the particles is interacting with an environment (e.g. a collection of N independent spins), the two-particle system undergoes decoherence. Using a simple model of decoherence, we show that this process has two consequences. First, the maximal amount by which the CHSH inequality is violated decays to zero. Second, the set of directions of measurement for which the inequality is violated is reduced in the course of decoherence. The volume of that set is bounded above by C|r|^2, where r is the decoherence factor. We obtain similar results for the case when each of the two particles is in interaction with a separate environment.Comment: v2: added results for decoherence due to interactions of both particles + minor changes; v3: minor change

ASRM case insulation design and development

This paper describes the achievements made on the Advanced Solid Rocket Motor (ASRM) case insulation design and development program. The ASRM case insulation system described herein protects the metal case and joints from direct radiation and hot gas impingement. Critical failure of solid rocket systems is often traceable to failure of the insulation design. The wide ranging accomplishments included the development of a nonasbestos insulation material for ASRM that replaced the existing Redesigned Solid Rocket Motor (RSRM) asbestos-filled nitrile butadiene rubber (NBR) along with a performance gain of 300 pounds, and improved reliability of all the insulation joint designs, i.e., segmented case joint, case-to-nozzle and case-to-igniter joint. The insulation process development program included the internal stripwinding process. This process advancement allowed Aerojet to match to exceed the capability of other propulsion companies

Amplitude control of quantum interference

Usually, the oscillations of interference effects are controlled by relative phases. We show that varying the amplitudes of quantum waves, for instance by changing the reflectivity of beam splitters, can also lead to quantum oscillations and even to Bell violations of local realism. We first study theoretically a generalization of the Hong-Ou-Mandel experiment to arbitrary source numbers and beam splitter transmittivity. We then consider a Bell type experiment with two independent sources, and find strong violations of local realism for arbitrarily large source number $N$; for small $N$, one operator measures essentially the relative phase of the sources and the other their intensities. Since, experimentally, one can measure the parity of the number of atoms in an optical lattice more easily than the number itself, we assume that the detectors measure parity.Comment: 4 pages; 4 figure

The stellar populations of spiral galaxies

We have used a large sample of low-inclination spiral galaxies with radially-resolved optical and near-infrared photometry to investigate trends in star formation history with radius as a function of galaxy structural parameters. A maximum likelihood method was used to match all the available photometry of our sample to the colours predicted by stellar population synthesis models. The use of simplistic star formation histories, uncertainties in the stellar population models and regarding the importance of dust all compromise the absolute ages and metallicities derived in this work, however our conclusions are robust in a relative sense. We find that most spiral galaxies have stellar population gradients, in the sense that their inner regions are older and more metal rich than their outer regions. Our main conclusion is that the surface density of a galaxy drives its star formation history, perhaps through a local density dependence in the star formation law. The mass of a galaxy is a less important parameter; the age of a galaxy is relatively unaffected by its mass, however the metallicity of galaxies depends on both surface density and mass. This suggests that galaxy mass-dependent feedback is an important process in the chemical evolution of galaxies. In addition, there is significant cosmic scatter suggesting that mass and density may not be the only parameters affecting the star formation history of a galaxy.Comment: 25 pages; 17 figures; re-submitted to MNRAS after replying to referee's repor

The New South Wales iVote System: Security Failures and Verification Flaws in a Live Online Election

In the world's largest-ever deployment of online voting, the iVote Internet voting system was trusted for the return of 280,000 ballots in the 2015 state election in New South Wales, Australia. During the election, we performed an independent security analysis of parts of the live iVote system and uncovered severe vulnerabilities that could be leveraged to manipulate votes, violate ballot privacy, and subvert the verification mechanism. These vulnerabilities do not seem to have been detected by the election authorities before we disclosed them, despite a pre-election security review and despite the system having run in a live state election for five days. One vulnerability, the result of including analytics software from an insecure external server, exposed some votes to complete compromise of privacy and integrity. At least one parliamentary seat was decided by a margin much smaller than the number of votes taken while the system was vulnerable. We also found protocol flaws, including vote verification that was itself susceptible to manipulation. This incident underscores the difficulty of conducting secure elections online and carries lessons for voters, election officials, and the e-voting research community