The Depth and Breadth of John Bell's Physics

John Bell's investigations in foundations of quantum mechanics, particle physics, and quantum field theory are recalled.Comment: 46 pages, 1 figure, LaTeX; editorial corrections; email correspondence to R. Jackiw <[email protected]

Nonlocality with less Complementarity

In quantum mechanics, nonlocality (a violation of a Bell inequality) is intimately linked to complementarity, by which we mean that consistently assigning values to different observables at the same time is not possible. Nonlocality can only occur when some of the relevant observables do not commute, and this noncommutativity makes the observables complementary. Beyond quantum mechanics, the concept of complementarity can be formalized in several distinct ways. Here we describe some of these possible formalizations and ask how they relate to nonlocality. We partially answer this question by describing two toy theories which display nonlocality and obey the no-signaling principle, although each of them does not display a certain kind of complementarity. The first toy theory has the property that it maximally violates the CHSH inequality, although the corresponding local observables are pairwise jointly measurable. The second toy theory also maximally violates the CHSH inequality, although its state space is classical and all measurements are mutually nondisturbing: if a measurement sequence contains some measurement twice with any number of other measurements in between, then these two measurements give the same outcome with certainty.Comment: 6 pages, published versio

Determination of hidden variable models reproducing the spin-singlet

The experimental violation of Bell inequality establishes necessary but not sufficient conditions that any theory must obey. Namely, a theory compatible with the experimental observations can satisfy at most two of the three hypotheses at the basis of Bell's theorem: free will, no-signaling, and outcome-Independence. Quantum mechanics satisfies the first two hypotheses but not the latter. Experiments not only violate Bell inequality, but show an excellent agreement with quantum mechanics. This fact restricts further the class of admissible theories. In this work, the author determines the form of the hidden-variable models that reproduce the quantum mechanical predictions for a spin singlet while satisfying both the hypotheses of free will and no-signaling. Two classes of hidden-variable models are given as an example, and a general recipe to build infinitely many possible models is provided.Comment: Slightly revised version, 7 pages, no figures, to appear in PRA. Final version, removed extra references no longer cite

Pre- and post-selected ensembles and time-symmetry in quantum mechanics

An expression is proposed for the quantum mechanical state of a pre- and post-selected ensemble, which is an ensemble determined by the final as well as the initial state of the quantum systems involved. It is shown that the probabilities calculated from the proposed state agree with previous expressions, for cases where they both apply. The same probabilities are found when they are calculated in the forward- or reverse-time directions. This work was prompted by several problems raised by Shimony recently in relation to the state, and time symmetry, of pre- and post-selected ensembles.Comment: RevTex4, 17 pages, no fig

Bounds on the multipartite entanglement of superpositions

We derive the lower and upper bounds on the entanglement of a given multipartite superposition state in terms of the entanglement of the states being superposed. The first entanglement measure we use is the geometric measure, and the second is the q-squashed entanglement. These bounds allow us to estimate the amount of the multipartite entanglement of superpositions. We also show that two states of high fidelity to one another do not necessarily have nearly the same q-squashed entanglement.Comment: 4 pages, 2 figure. few typos correcte

Conditions for compatibility of quantum state assignments

Suppose N parties describe the state of a quantum system by N possibly different density operators. These N state assignments represent the beliefs of the parties about the system. We examine conditions for determining whether the N state assignments are compatible. We distinguish two kinds of procedures for assessing compatibility, the first based on the compatibility of the prior beliefs on which the N state assignments are based and the second based on the compatibility of predictive measurement probabilities they define. The first procedure leads to a compatibility criterion proposed by Brun, Finkelstein, and Mermin [BFM, Phys. Rev. A 65, 032315 (2002)]. The second procedure leads to a hierarchy of measurement-based compatibility criteria which is fundamentally different from the corresponding classical situation. Quantum mechanically none of the measurement-based compatibility criteria is equivalent to the BFM criterion.Comment: REVTEX 4, 19 pages, 1 postscript figur

Pretreatment cognitive and neural differences between sapropterin dihydrochloride responders and non-responders with phenylketonuria

Sapropterin dihydrochloride (BH4) reduces phenylalanine (Phe) levels and improves white matter integrity in a subset of individuals with phenylketonuria (PKU) known as “responders.” Although prior research has identified biochemical and genotypic differences between BH4 responders and non-responders, cognitive and neural differences remain largely unexplored. To this end, we compared intelligence and white matter integrity prior to treatment with BH4 in 13 subsequent BH4 responders with PKU, 16 subsequent BH4 non-responders with PKU, and 12 healthy controls. Results indicated poorer intelligence and white matter integrity in non-responders compared to responders prior to treatment. In addition, poorer white matter integrity was associated with greater variability in Phe across the lifetime in non-responders but not in responders. These results underscore the importance of considering PKU as a multi-faceted, multi-dimensional disorder and point to the need for additional research to delineate characteristics that predict response to treatment with BH4

Bell inequalities for random fields

The assumptions required for the derivation of Bell inequalities are not usually satisfied for random fields in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical two point particle models. Classical random field models that explicitly include the effects of quantum fluctuations on measurement are possible for experiments that violate Bell inequalities.Comment: 18 pages; 1 figure; v4: Essentially the published version; extensive improvements. v3: Better description of the relationship between classical random fields and quantum fields; better description of random field models. More extensive references. v2: Abstract and introduction clarifie

Comment on "Consistency, amplitudes, and probabilities in quantum theory"

In a recent article [Phys. Rev. A 57, 1572 (1998)] Caticha has concluded that ``nonlinear variants of quantum mechanics are inconsistent.'' In this note we identify what it is that nonlinear quantum theories have been shown to be inconsistent with.Comment: LaTeX, 5 pages, no figure