Compressing the hidden variable space of a qubit

In previously exhibited hidden variable models of quantum state preparation and measurement, the number of continuous hidden variables describing the actual state of a single realization is never smaller than the quantum state manifold dimension. We introduce a simple model for a qubit whose hidden variable space is one-dimensional, i.e., smaller than the two-dimensional Bloch sphere. The hidden variable probability distributions associated with the quantum states satisfy reasonable criteria of regularity. Possible generalizations of this shrinking to a N-dimensional Hilbert space are discussed.Comment: References updated and added some more discussions of result

Correlation functions for a Bose-Einstein condensate in the Bogoliubov approximation

In this article we introduce a differential equation for the first order correlation function $G^{(1)}$ of a Bose-Einstein condensate at T=0. The Bogoliubov approximation is used. Our approach points out directly the dependence on the physical parameters. Furthermore it suggests a numerical method to calculate $G^{(1)}$ without solving an eigenvector problem. The $G^{(1)}$ equation is generalized to the case of non zero temperature.Comment: 9 pages, ps format. This article was published in EPJD vol. 14(1) (2001), pp.105-11

Lower bounds on the communication complexity of two-party (quantum) processes

The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the minimum of a convex functional over a space of suitable probability distributions. It is now proved that this optimization problem is the dual of a geometric programming maximization problem, which displays some appealing properties. First, the number of variables grows linearly with the input size. Second, the objective function is linear in the input parameters and the variables. Finally, the constraints do not depend on the input parameters. These properties imply that, once a feasible point is found, the computation of a lower bound on the communication cost in any two-party process is linearly complex. The studied scenario goes beyond quantum processes and includes the communication complexity scenario introduced by Yao. We illustrate the method by analytically deriving some non-trivial lower bounds. Finally, we conjecture the lower bound $n 2^n$ for a noiseless quantum channel with capacity $n$ qubits. This bound can have an interesting consequence in the context of the recent quantum-foundational debate on the reality of the quantum state.Comment: Conference version. A more extensive version with more details will be available soo