arXiv subjects
Publications and source records attributed to Rob Clifton.
We investigate a new class of entangled states, which we call 'hyperentangled',that have EPR correlations identical to those in the vacuum state of a relativistic quantum field. We show that whenever hyperentangled states exist in any quantum theory, they are dense in its state space. We also give prescriptions for constructing hyperentangled states that involve an arbitrarily large collection of systems.
John Bell once argued that one ought to select, out of the 'observables' of quantum theory, some subset of 'beables' that can be consistently ascribed determinate values. Moreover, this subset should be selected so as to guarantee (among other things) that we can dispense with the orthodox interpretation's loose talk about 'measurement values': "...the probability of a beable being a particular value would be calculated just as was formerly calculated the probability of observing that value". Working in the framework of C*-algebras (in particular, Segal algebras), I propose an algebraic characterization of those subsets of bounded observables of a quantum system that can have beable status with respect to any (fixed) state of the system. It turns out that observables with beable status in a state need not all commute (a possibility Bell himself does not consider), but they must at least form a certain kind of 'quasicommutative' subalgebra determined by the state. A virtue of the analysis is that it applies to beables with continuous spectra, usually neglected in discussions of the no-hidden-variables theorems. In the (very) special case where the algebra of observables for a system is representable on a finite-dimensional Hilbert space, I give a complete characterization of the maximal beable subalgebras determined by any state of the system; the infinite-dimensional case remains open. These results are discussed in relation to previous results of a similar nature, to 'no-collapse' interpretations of quantum mechanics, and to algebraic relativistic quantum field theory.