Efficient Hidden-Variable Simulation of Measurements in Quantum Experiments

We prove that the results of a finite set of general quantum measurements on an arbitrary dimensional quantum system can be simulated using a polynomial (in measurements) number of hidden-variable states. In the limit of infinitely many measurements, our method gives models with the minimal number of hidden-variable states, which scales linearly with the number of measurements. These results can find applications in foundations of quantum theory, complexity studies, and classical simulations of quantum systems.

Figure 1

Preparation-universal HV models and dual polytopes. (a) The vertices of the octahedron inside the Bloch sphere define the three complementary qubit measurements. A preparation-universal HV model for these measurements requires eight HV states, which are written near their representative vertices of the cube containing the sphere. It generalizes the Spekkens model [5], which is not universal and utilizes only four out of eight states (see main text). Their corresponding vertices span a tetrahedron inside the cube, which does not contain the whole Bloch sphere. (b) Here, the measurement directions form a cube inside the sphere. Although more measurements are to be simulated, the universal HV model requires only six HV states, which are written near their representative vertices of the octahedron containing the sphere.