Bounding sets of sequential quantum correlations and device-independent randomness certification

TL;DR

This paper extends the NPA hierarchy to sequential quantum measurements on entangled states, enabling better bounds on quantum correlations and device-independent randomness certification.

Contribution

It introduces a generalized NPA hierarchy for sequential measurements, facilitating improved bounds and randomness certification in quantum information tasks.

Findings

Robust certification of over 2.3 bits of local randomness from a two-qubit state.

Tight upper bounds established for sequential Bell test tasks.

The hierarchy converges with resource requirements similar to the original NPA.

Abstract

An important problem in quantum information theory is that of bounding sets of correlations that arise from making local measurements on entangled states of arbitrary dimension. Currently, the best-known method to tackle this problem is the NPA hierarchy; an infinite sequence of semidefinite programs that provides increasingly tighter outer approximations to the desired set of correlations. In this work we consider a more general scenario in which one performs sequences of local measurements on an entangled state of arbitrary dimension. We show that a simple adaptation of the original NPA hierarchy provides an analogous hierarchy for this scenario, with comparable resource requirements and convergence properties. We then use the method to tackle some problems in device-independent quantum information. First, we show how one can robustly certify over 2.3 bits of device-independent local randomness from a two-quibt state using a sequence of measurements, going beyond the theoretical maximum of two bits that can be achieved with non-sequential measurements. Finally, we show tight upper bounds to two previously defined tasks in sequential Bell test scenarios.