Structure of temporal correlations of a qubit

TL;DR

This paper characterizes the structure of temporal quantum correlations in a single qubit, identifies limitations based on system dimension, and proposes a temporal inequality for dimension testing with potential NV center implementation.

Contribution

It introduces a comprehensive characterization of temporal correlations and derives a dimension test inequality for qubits.

Findings

Not all general correlations are realizable with a qubit

A specific temporal inequality acts as a dimension witness

Potential implementation with nitrogen-vacancy centers in diamond

Abstract

In quantum mechanics, spatial correlations arising from measurements at separated particles are well studied. This is not the case, however, for the temporal correlations arising from a single quantum system subjected to a sequence of generalized measurements. We first characterize the polytope of temporal quantum correlations coming from the most general measurements. We then show that if the dimension of the quantum system is bounded, only a subset of the most general correlations can be realized and identify the correlations in the simplest scenario that can not be reached by two-dimensional systems. This leads to a temporal inequality for a dimension test, and we discuss a possible implementation using nitrogen-vacancy centers in diamond.