Greenberger-Horne-Zeilinger Paradox and Quantum Entanglement Swapping in One-Dimensional Lipkin-Meshkov-Glick Model

Based on the ground states of the one-dimensional Lipkin-Meshkov-Glick model (LMGM), we show an all-versus-nothing proof of violation of local realism in this model. Moreover, the quantum entanglement swapping is also investigated in terms of the braiding transformations.     

There and back again: Two views on the protein folding puzzle

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10–11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: “U-to-N” and “N-to-U”. In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the “N-to-U” transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical “detailed balance” principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the “N-to-U” transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the “U-to-N” transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the “foldable” protein domains.     

Unthermal Charged Massive Hawking Radiation from a Reissner-Nordström Black Hole

Using Damour-Ruffini’s method, the massive charged particles’ Hawking radiation from a Reissner-Nordström black hole is investigated. When the back-reaction of particles’ energy and charge to spacetime is considered, we get the unthermal spectrum. It is possible that the information will get out from the black hole with the corrected spectrum. It can be used to explain the information loss paradox, and the underlying unitary theory will be satisfied. The same conclusion as the works finished before can be drawn. However, our work is different from them, and the method is more simple and explicit.     

Bounds on bipartitely shared entanglement reduced from superposed tripartite quantum states

For a tripartite pure state superposed by two individual states, the bipartitely shared entanglement can always be achieved by local measurements of the third party. Consider the different aims of the third party, i.e. maximizing or minimizing the bipartitely shared entanglement, we find bounds on both the possible bipartitely shared entanglement of the superposition state in terms of the corresponding entanglement of the two states being superposed. In particular, by choosing the concurrence as bipartite entanglement measure, we obtain calculable bounds for tripartite (2 ⊗ 2 ⊗ n)-dimensional cases.     

Propositions in Prepositional Logic Provable Only by Indirect Proofs

In this paper it is shown that addition of certain reductions to the standard cut removing reductions of deductions in prepositional logic makes prepositional logic non-normalizable. From this follows that some provable propositions in prepositional logic has no direct proof.     

Equity,efficiency and rights in social choice

The impossibility of a Paretian liberal presented by Sen shows the incompatibility of the Pareto principle with a mild claim of libertarian rights when they are required of the collective choice rule with unrestricted domain. In view of the profound implications of this paradox, it is no wonder that there are many serious attempts in the literature to seek for a general resolution thereof. In this paper, we try to explore an avenue which has been left relatively less cultivated in the attempts to try to find a way out of this paradox, the essential idea thereof being to restrict the ‘legitimate’ exercise of the liberatarian rights by the claims of justice or equity. It will be shown that the gist of the successful resolution of the Pareto libertarian paradox along this line lies in the impartiality of the principle of justice held by the individuals and the prevalence of the sympathetic acceptance of each other's subjective preferences.     

On a reconsideration of classical nucleation theory

A correct account of the collective motion of a cluster does not require the Lothe-Pound correction; furthermore, this correction is shown to contradict the laws of thermodynamics.     

Renewal-theoretic considerations in evaluation of forecast monitoring schemes

To evaluate the performance of a scheme for monitoring forecasts that are generated by exponential smoothing, forecasters have traditionally used a simulation-based estimator of some characteristic of the associated run-length distribution. The most frequently cited performance measures are the average run length and the probability that the run length does not exceed a user-specified cut-off point. However, there is disagreement about the definition of run length that is appropriate in the context of forecasting. In this paper we use fundamental results from renewal theory to establish the precise relationships between conflicting formulations both of the average run length and of the probability density function for the run length. More generally we derive the asymptotic mean and the asymptotic distribution function of the forward recurrence time for both ordinary and delayed renewal processes whose interoccurrence distributions are arithmetic with a given span. We discuss the practical significance of these results in the context of forecasting. Our findings bear directly on the way in which simulation experiments should be designed and executed to compare alternative forecast monitoring schemes.     

Two-qutrit entanglement witnesses and Gell-Mann matrices

The Gell-Mann λ matrices for Lie algebra su(3) are the natural basis for the Hilbert space of Hermitian operators acting on the states of a three-level system(qutrit). So the construction of EWs for two-qutrit states by using these matrices may be an interesting problem. In this paper, several two-qutrit EWs are constructed based on the Gell-Mann matrices by using the linear programming (LP) method exactly or approximately. The decomposability and non-decomposability of constructed EWs are also discussed and it is shown that the λ-diagonal EWs presented in this paper are all decomposable but by adding λ-non-diagonal terms, one can obtain various non-decomposable EWs.     

Quantum state sharing of an arbitrary multiqubit state using nonmaximally entangled GHZ states

We explicitly present a scheme for quantum state sharing of an arbitrary multiqubit state using nonmaximally entangled GHZ states as the quantum channel and generalized Bell states as the measurement basis. The scheme succeeds only probabilistically with its total success probability depending on the degree of entanglement matching between the quantum channel and the generalized Bell states. Security of the scheme is guaranteed by the fact that attacks of an outside eavesdropper or/and an inside dishonest party will inevitably introduce detectable errors.