A Note on Pseudo-Hermitian Systems with Point Interactions and Quantum Separability

We study the quantum entanglement and separability of Hermitian and pseudo-Hermitian systems of identical bosonic or fermionic particles with point interactions. The separability conditions are investigated in detail.Comment: 6 page

Bell's inequalities for states with positive partial transpose

We study violations of n particle Bell inequalities (as developed by Mermin and Klyshko) under the assumption that suitable partial transposes of the density operator are positive. If all transposes with respect to a partition of the system into p subsystems are positive, the best upper bound on the violation is 2^((n-p)/2). In particular, if the partial transposes with respect to all subsystems are positive, the inequalities are satisfied. This is supporting evidence for a recent conjecture by Peres that positivity of partial transposes could be equivalent to existence of local classical models.Comment: 4 pages, REVTe

Sum Rules of Neutrino Masses and CP Violation in the Four-Neutrino Mixing Scheme

We show that the commutator of lepton mass matrices is invariant under terrestial matter effects in the four-neutrino mixing scheme. A set of model-independent sum rules for neutrino masses, which may be generalized to hold for an arbitrary number of neutrino families, are for the first time uncovered. Useful sum rules for the rephasing-invariant measures of leptonic CP violation have also been found. Finally we present a generic formula of T-violating asymmetries and expect it to be applicable to the future long-baseline neutrino oscillation experiments.Comment: RevTex 8 pages. 3 references added. Phys. Rev. D (in printing

Quantum Cryptography Using Single Particle Entanglement

A quantum cryptography scheme based on entanglement between a single particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single particle states. Existence of an eavesdropper can be detected by using a variant of Bell's inequality.Comment: 4 pages, 3figures, revte

Single-particle nonlocality and entanglement with the vacuum

We propose a single-particle experiment that is equivalent to the conventional two-particle experiment used to demonstrate a violation of Bell's inequalities. Hence, we argue that quantum mechanical nonlocality can be demonstrated by single-particle states. The validity of such a claim has been discussed in the literature, but without reaching a clear consensus. We show that the disagreement can be traced to what part of the total state of the experiment one assigns to the (macroscopic) measurement apparatus. However, with a conventional and legitimate interpretation of the measurement process one is led to the conclusion that even a single particle can show nonlocal properties.Comment: 6 pages, 5 figure

Characterizing the entanglement of bipartite quantum systems

We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.Comment: 5 pages, 2 figures. Revised versio

Supernova Neutrinos and the LSND Evidence for Neutrino Oscillations

The observation of the $\bar{\nu}_e$ energy spectrum from a supernova burst can provide constraints on neutrino oscillations. We derive formulas for adiabatic oscillations of supernova antineutrinos for a variety of 3- and 4-neutrino mixing schemes and mass hierarchies which are consistent with the LSND evidence for $\bar{\nu}_{\mu}\to \bar{\nu}_e$ oscillations. Finally, we explore the constraints on these models and LSND given by the supernova SN1987A $\bar{\nu}_e$'s observed by the Kamiokande-2 and IMB-3 detectors.Comment: 8 pages, 3 figures. Changes with respect to original version: appendix added; minor changes in text, figures, reference

Finding optimal strategies for minimum-error quantum-state discrimination

We propose a numerical algorithm for finding optimal measurements for quantum-state discrimination. The theory of the semidefinite programming provides a simple check of the optimality of the numerically obtained results.Comment: 4 pages, 2 figure

Separability and entanglement in 2x3xN composite quantum systems

The separability and entanglement of quantum mixed states in \Cb^2 \otimes \Cb^3 \otimes \Cb^N composite quantum systems are investigated. It is shown that all quantum states $\rho$ with positive partial transposes and rank $r(\rho)\leq N$ are separable.Comment: Latex, 15 page