A particle-wave steering mechanism

L. M. Arévalo Aguilar

In 1927, at the Solvay conference, Einstein posed a thought experiment with the primary intention of showing the incompleteness of quantum mechanics; to prove it, he employed the instantaneous nonlocal effects caused by the collapse of the wavefunction of a single particle-the spooky action at a distance-, when a measurement is done. This historical event preceded the well-know Einstein-Podolsk-Rosen criticism over the incompleteness of quantum mechanics. Here, by using the Stern-Gerlach experiment, we demonstrate how the instantaneous nonlocal feature of the collapse of the wavefunction together with the single-particle entanglement can be used to produce the nonlocal effect of steering, i.e. the single-particle steering. In the steering process Bob gets a quantum state depending on which observable Alice decides to measure. To accomplish this, we fully exploit the spreading (over large distances) of the entangled wavefunction of the single-particle. In particular, we demonstrate that the nonlocality of the single-particle entangled state allows the particle to "know" about the kind of detector Alice is using to steer Bob's state. Therefore, notwithstanding strong counterarguments, we prove that the single-particle entanglement gives rise to truly nonlocal effects at two faraway places. This opens the possibility of using the single-particle entanglement for implementing truly nonlocal task.

Paul Peter Urone, Roger A. Hinrichs

H. Chau Nguyen, Huy-Viet Nguyen, Otfried Gühne

Correlations between distant particles are central to many puzzles and paradoxes of quantum mechanics and, at the same time, underpin various applications such as quantum cryptography and metrology. Originally in 1935, Einstein, Podolsky, and Rosen (EPR) used these correlations to argue against the completeness of quantum mechanics. To formalize their argument, Schrödinger subsequently introduced the notion of quantum steering. Still, the question of which quantum states can be used for EPR steering and which cannot remained open. Here we show that quantum steering can be viewed as an inclusion problem in convex geometry. For the case of two spin-1/2 particles, this approach completely characterizes the set of states leading to EPR steering. In addition, we discuss the generalization to higher-dimensional systems as well as generalized measurements. Our results find applications in various protocols in quantum information processing, and moreover they are linked to quantum mechanical phenomena such as uncertainty relations and the question of which observables in quantum mechanics are jointly measurable.

David O Hayward

Erika Andersson, Stig Stenholm

This paper discusses the time-dependent quantum description of logical operations based on channelled atomic particles. We envisage particle traps in the form of grooves which steer atoms or ions, make them switch potential channels or interact with each other. Thus the presence of a particle can act as a control bit steering a target particle from one course into another. This phenomenon may be used to effect conditional logic operations. We discuss the quantum dynamics of the system using a simple analytic model whose proposed behaviour is verified by wave packet calculation.

Hans Luth