Entanglement Sharing in Real-Vector-Space Quantum TheoryWootters, William
doi: 10.1007/s10701-010-9488-1pmid: N/A
The limitation on the sharing of entanglement is a basic feature of quantum theory. For example, if two qubits are completely entangled with each other, neither of them can be at all entangled with any other object. In this paper we show, at least for a certain standard definition of entanglement, that this feature is lost when one replaces the usual complex vector space of quantum states with a real vector space. Moreover, the difference between the two theories is extreme: in the real-vector-space theory, there exist states of arbitrarily many binary objects, “rebits,” in which every rebit in the system is maximally entangled with each of the other rebits.
Entanglement Between Degrees of Freedom inaSingle-Particle System Revealed in Neutron InterferometryHasegawa, Yuji
doi: 10.1007/s10701-010-9499-ypmid: N/A
Initially Einstein, Podolsky, and Rosen (EPR) and later Bell shed light on the non-local properties exhibited by subsystems in quantum mechanics. Separately, Kochen and Specker analyzed sets of measurements of compatible observables and found that a consistent coexistence of these results is impossible, i.e., quantum indefiniteness of measurement results. As a consequence, quantum contextuality, a more general concept compared to non-locality, leads to striking phenomena predicted by quantum theory. Here, we report neutron interferometric experiments which investigate entangled states in a single-particle system: entanglement is, in this case, achieved not between particles, but between degrees of freedom i.e., between spin, path, and energy degrees of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter in the interferometer allow an experimental verification of the violation of a Bell-like inequality. In addition, state tomography, tomographic analysis of the density matrix of a quantum system, and Kochen-Specker-like phenomena are presented to characterize neutrons’ entangled states and their peculiarity. Furthermore, a coherent energy manipulation scheme is accomplished with a radio-frequency (RF) spin-flipper. This scheme allows the (total) energy degree of freedom to be entangled: the remarkable behavior of a triply entangled GHZ-like state is demonstrated.
The Tic-Tac-Toe Theory of GravityGreenberger, Daniel
doi: 10.1007/s10701-010-9500-9pmid: N/A
The Tic-Tac-Toe theory is a qualitative, phenomenological theory that automatically explains many of the features of the universe that we see, such as dark matter and dark energy. In that sense it is a Copernican theory that gives an alternate approach, which immediately and intuitively explains phenomena,independently of any detailed dynamics, for which the explanations in accepted standard theories are usually somewhat ad-hoc.
The Role of Bounded Memory in the Foundations ofQuantum MechanicsCabello, Adán
doi: 10.1007/s10701-010-9507-2pmid: N/A
If quantum mechanics is correct and there is a finite upper bound for the speed of causal influences (e.g., the speed of light), then quantum mechanics is complete (i.e., it does not admit a more detailed description in terms of hidden variables). Here I show that the conclusion holds if we replace the assumption of bounded velocity by the assumption that there is a finite upper bound to the memory a finite physical system can store (e.g., the Holevo bound). On the way to this conclusion I first show that, although the quantum violation of an inequality valid for any non-contextual model can be explained with a classical contextual model, the inequality can be promoted to a Bell inequality in which, if the model is contextual, then it must be also non-local. This suggests that there is something non-classical in any contextual explanation of the individual systems, and leads us to the question of which are the minimum resources (and specifically memory) any contextual explanation should consume.
The Construction of Quantum RealityStenholm, Stig
doi: 10.1007/s10701-010-9519-ypmid: N/A
This paper recognizes that quantum theory is not satisfactorily formulated; in spite of its empirical success, we may wish to consider the possibility to find more intuitively acceptable foundations. It is emphasized that the difference between classical physics and quantum theory lies in the fact that the latter depends in an essential way on classical descriptions of the observations from preparation to recording. In addition, only statistical predictions are possible. We discuss the case of entangled quantum systems. Performing an experiment on one subsystem, we move a realized prediction to be a precondition for subsequent observations. The quantum features presented do not fit into a unified interpretation, they are found to be incompletely defined but pragmatically applied. No uniquely well defined interpretation is adequate for all cases.
New Prospects for de Broglie InterferometryJuffmann, Thomas; Nimmrichter, Stefan; Arndt, Markus; Gleiter, Herbert; Hornberger, Klaus
doi: 10.1007/s10701-010-9520-5pmid: N/A
We consider various effects that are encountered in matter wave interference experiments with massive nanoparticles. The text-book example of far-field interference at a grating is compared with diffraction into the dark field behind an opaque aperture, commonly designated as Poisson’s spot or the spot of Arago. Our estimates indicate that both phenomena may still be observed in a mass range exceeding present-day experiments by at least two orders of magnitude. They both require, however, the development of sufficiently cold, intense and coherent cluster beams. While the observation of Poisson’s spot offers the advantage of non-dispersiveness and a simple distinction between classical and quantum fringes in the absence of particle wall interactions, van der Waals forces may severely limit the distinguishability between genuine quantum wave diffraction and classically explicable spots already for moderately polarizable objects and diffraction elements as thin as 100 nm.
Prime Number Decomposition, the Hyperbolic Function and Multi-Path Michelson InterferometersTamma, V.; Alley, C.; Schleich, W.; Shih, Y.
doi: 10.1007/s10701-010-9522-3pmid: N/A
The phase φ of any wave is determined by the ratio x/λ consisting of the distance x propagated by the wave and its wavelength λ. Hence, the dependence of φ on λ constitutes an analogue system for the mathematical operation of division, that is to obtain the hyperbolic function f(ξ)≡1/ξ. We take advantage of this observation to decompose integers into primes and implement this approach towards factorization of numbers in a multi-path Michelson interferometer. This work is part of a larger program geared towards unraveling the connections between quantum mechanics and number theory. We briefly summarize this aspect.
Observation of Berry’s Geometric Phase by Neutron InterferometryWerner, Sam
doi: 10.1007/s10701-010-9526-zpmid: N/A
On the 25th anniversary of Berry’s historic papers on the geometric phase, I discuss here our neutron interferometry experiment in which this phase is clearly separated from the dynamical phase. The connection of this experiment to the observation of the sign reversal of the wave function of a fermion during a 2π precession in a magnetic field by three groups independently in 1975 is discussed.