A Classical Formulation of Quantum Theory?

We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start with is epistemically restricted, in the spirit of a model introduced by Spekkens. We obtain quantum theory only by combining a collection of restricted classical pictures. Our main challenge in this paper is to find a simple way of characterizing the allowed sets of classical pictures. We present one promising approach to this problem and show how it works out for the case of a single qubit.     

Superfluid Avalanches in Nuclepore: Constrained versus Free-Boundary Experiments and Simulations

Superfluid 4He exhibits hysteretic behavior in the percolated nanoporous material Nuclepore during the filling and draining of pores due to capillary condensation, and one observes avalanches during the pore draining. We observe that the size and frequency of the avalanches depend upon whether the fluid flow off the substrate during draining is impeded or unimpeded. We simulate the draining of superfluid 4He from Nuclepore with and without a perturbation of the pore menisci and find results similar to the results seen in the experiments in the presence or the absence of flow inhibition.     

Random quantum states

This paper examines the statistical properties of random quantum states, for four different kinds of random state:(1) a pure state chosen at random with respect to the uniform measure on the unit sphere in a finite-dimensional Hilbert space;(2) a random pure state in a real space;(3) a pure state chosen at random except that a certain expectation value is fixed;(4) a random mixed state with fixed eigenvalues. For the first two of these, we give examples of simple states of a model system, the kicked top, which have the statistical properties of random states. Interestingly, examples of both kinds of randomness can be found in the same system. In studying the last two kinds of random state, we obtain new results concerning the application of information theory to quantum systems.     

Bogoliubov transformation for a spatially varying gap

It is shown that a general Bogoliubov transformation can be used as an alternative to Gorkov's equations in studying the properties of superfluid ³He with a position-dependent gap matrix. Expressions are derived for the current density and the gradient free energy which are exact to first and second order, respectively, in the spatial inhomogeneity.     

Quantum mechanics without probability amplitudes

First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are represented not by state vectors or density matrices but by probability tables, which contain only the probabilities of the outcomes of certain special measurements. The rule for computing transition probabilities, normally given by the squared modulus of the inner product of two state vectors, is re-expressed in terms of probability tables. The new version of the rule is surprisingly simple, especially when one considers that the notion of complex phases, so crucial in the evaluation of inner products, is entirely absent from the representation of states used here.     

Configuration spaces of convex and embedded polygons in the plane

This paper concerns the topology of configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that, modulo translations and rotations, each component of the space of convex configurations is homeomorphic to a closed Euclidean ball and each component of the space of embedded configurations is homeomorphic to a Euclidean space. This represents an elaboration on the topological information that follows from the convexification theorem of Connelly, Demaine, and Rote.     

Entanglement Sharing in Real-Vector-Space Quantum Theory

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.