Popper's Experiment and Superluminal Communication

We comment on Tabesh Qureshi, "Understanding Popper's Experiment," AJP 73, 541 (June 2005), in particular on the implications of its section IV. We show, in the situation envisaged by Popper, that analysis solely with conventional non-relativistic quantum mechanics suffices to exclude the possibility of superluminal communication.Comment: Submitted to American Journal of Physic

Lower Bound on Entanglement of Formation for the Qubit-Qudit System

Wootters [PRL 80, 2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed form expression for the EOF of an arbitrary mixed state in any system more complicated than two qubits. This paper, via a relatively straightforward generalization of Wootters' original derivation, obtains a closed form lower bound on the EOF of an arbitary mixed state of a system composed of a qubit and a qudit (a d-level quantum system, with d greater than or equal to 3). The derivation of the lower bound is detailed for a system composed of a qubit and a qutrit (d = 3); the generalization to d greater than 3 then follows readily.Comment: 14 pages, 0 Figures, 0 Table

Controls on Scientific Information Exportst

This article analyzes recent attempts by the United States government to restrict the release of scientific and technical information in particular research conducted under the auspices of universities- to foreign nationals. Until quite recently, the government\u27s virtually exclusive instrument for restricting transfers of information was classification. On grounds of national security, certain information was classified as secret, to be revealed only to a comparatively small group of people, those with clearance and a need to know

Identities related to variational principles

The existence of a well-known identity associated with variational principles for any scattering parameter Q, and often serving as the starting point for the development of a variational bound on Q, strongly suggests that it might be useful to construct identities associated with variational principles for quantities other than scattering parameters. An identity associated with the variational principle for the determination of inner products of the linear form g†φ a generalization of the aforementioned identity, is presented. Here, g is a known function, and φ is an unknown function satisfying Mφ = ω and specified boundary conditions, where M is a known linear operator and ω is a known function. The generalized identity is obtained from a variational principle for g†φ, this variational principle being itself a generalization of the usual Kohn variational principle for scattering amplitudes and phase shifts. An identity associated with a variational principle for the quadratic form φ†Wφ, with φ as above and W a known linear operator, is also obtained. Finally, we obtain an identity for φ(∞), where φ is defined as the solution of a nonlinear differential equation. The generalized identity related to g†φ is verified for a simple exactly solvable problem

Useful extremum principle for the variational calculation of matrix elements

Variational principles for the estimation of the matrix element Wnn(φn, Wφn) for an arbitrary operator W are of great interest. The variational estimates are constructed from a trial wave function φn t, an approximation to the nth normalized bound-state eigenfunction φn, and of a trial auxiliary function Lt, an approximation to L which satisfies (H-En)L=(Wn n-W)φnq(φn). Variational-principle applications have been limited by the difficulty of obtaining a reasonable Lt, among other things, one demands that Lt approach L as φn t approaches φn. The equation (H-En t)Lt=q(φn t), where En t=(φn t,Hφn t), is known not to provide such an Lt. A practical procedure for handling complicated systems given a reasonably accurate Rayleigh-Ritz trial function φn t is called for. This paper provides such a procedure using techniques developed in the establishment of variational bounds on scattering lengths. Given H and φn t, we define Lt by A Lt=q(φn t), where A differs from H-En in that the influence of states 1 through n has effectively been subtracted out ; the operator A is non-negative. A functional M(Lt t) is constructed which is an extremum for Lt t=Lt. Variational parameters contained in Lt t can be determined by extremizing M(Lt t), thereby providing an approximation to Lt. The method is analogous to the determination of parameters in φn t by the minimization of (φn t,Hφn t)(φn t,φn t). The method is immediately applicable to the variational determination of off-diagonal matrix elements Wn m and of diagonal matrix elements of normal and of modified Green\u27s functions. © 1974 The American Physical Society