Experimental Tests of Classical and Quantum Dimensions

There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

Abstract

We report on an experimental test of classical and quantum dimension. We have used a dimension witness which can distinguish between quantum and classical systems of dimension 2,3 and 4 and performed the experiment for all five cases. The witness we have chosen is a base of semi-device independent cryptographic and randomness expansion protocols. Therefore, the part of the experiment, in which qubits were used, is a realization of these protocols. In our work we also present an analytic method for finding the maximal quantum value of the witness along with corresponding measurements and preparations. This method is quite general and can be applied to any linear dimension witness.

Related collections

Most cited references 3

Record: found
Abstract: found
Article: found

Is Open Access

Device-independent tests of classical and quantum dimensions

Antonio Acin, Rodrigo Gallego, Christopher Hadley … (2010)

We address the problem of testing the dimensionality of classical and quantum systems in a `black-box' scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension necessary to reproduce given measurement data. Furthermore, we generalise the concept of quantum dimension witnesses to arbitrary quantum systems, allowing one to place a lower bound on the Hilbert space dimension necessary to reproduce certain data. Illustrating these ideas, we provide simple examples of classical and quantum dimension witnesses.

0 comments Cited 32 times – based on 0 reviews

Preprint

     Review now

Bookmark

Record: found
Abstract: found
Article: found

Is Open Access

A lower bound on the dimension of a quantum system given measured data

Andrew C. Doherty, Matthias Christandl, Stephanie Wehner (2008)

We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given enough time, the probability of a given outcome a: p(a|M,rho). How large does the Hilbert space of the quantum system have to be in order to allow us to find density matrices and measurement operators that will reproduce the given probability distribution? In this note, we prove a simple lower bound for the dimension of the Hilbert space. The main insight is to relate this problem to the construction of quantum random access codes, for which interesting bounds on Hilbert space dimension already exist. We discuss several applications of our result to hidden variable, or ontological models, to Bell inequalities and to properties of the smooth min-entropy.