Some Remarks on Non-Separability

Oliver Rudolph

Paolo Faglia

Using a 'reformulation of Bell's theorem', Waegell and McQueen, (2020) argue that any local theory which does not involve retro-causation or fine-tuning must be a many-worlds theory. Moreover they argue that non-separable many-worlds theories whose ontology is given by the wavefunction involve superluminal causation, as opposed to separable many-worlds theories (e.g. Waegell, 2021; Deutsch and Hayden 2000). I put forward three claims. (A) I challenge their argument for relying on a non-trivial, unquestioned assumption about elements of reality which allows Healey's approach (Healey, 2017b) to evade their claim. In an attempt to respond to (A), Waegell and McQueen may restrict their claim to theories which satisfy such an assumption, however, I also argue that (B) their argument fails to prove even the so weakened claim, as exemplified by theories that are both non-separable and local. Finally, (C) by arguing for the locality of the decoherence-based Everettian approach (Wallace, 2012) I refute Waegell and McQueen's claim that wavefunction-based ontologies, and more generally non-separable ontologies, involve superluminal causation. I close with some doubtful remarks about separable Everettian interpretations as compared to non-separable ones.

D. L. Cox, Andrei E. Ruckenstein

We present an analytical solution of a SU(N)\ifmmode\times\else\texttimes\fi{}SU(M) generalization of the multichannel single-impurity Kondo model in the limit N\ensuremath{\rightarrow}\ensuremath{\infty}, M\ensuremath{\rightarrow}\ensuremath{\infty}, with \ensuremath{\gamma}=M/N fixed. Non-Fermi-liquid behavior of the single electron Green function and of the local spin and flavor susceptibilities occurs in both regimes, N\ensuremath{\le}M and N>M, with leading critical exponents identical to those found in the conformal field theory solution for all N and M (with M\ensuremath{\ge}2). We explain this remarkable agreement and connect it to ``spin-flavor separation,'' the essential feature of the non-Fermi-liquid, fixed point.

Shengjun Wu, J. Anandan

Zeqian Chen

A family of Bell-type inequalities is present, which are constructed directly from the "standard" Bell inequalities involving two dichotomic observables per site. It is shown that the inequalities are violated by all the generalized Greenberger-Horne-Zeilinger states of multiqubits. Remarkably, our new inequalities can provide stronger non-locality tests in a sense that the local reality inequalities are exponentially stronger than the corresponding multipartite separability inequalities. This reveals that the exponential violation of local realism by separable states is an interesting consequence of quantum fluctuation of multipartite systems.

Claudio Calosi