Unbounded sequence of observers exhibiting Einstein-Podolsky-Rosen steering

TL;DR

This paper demonstrates that an unbounded number of observers can sequentially demonstrate Einstein-Podolsky-Rosen steering using the same entangled state, with the number scaling as the local dimension divided by its logarithm.

Contribution

It introduces a method for multiple observers to sequentially demonstrate EPR steering on the same entangled state, expanding the understanding of quantum steering's robustness.

Findings

Number of Bobs able to steer scales as d / log d

Successive steering is possible with unbiased inputs

Results hold for both orthonormal bases and mutually unbiased bases

Abstract

A sequential steering scenario is investigated, where multiple Bobs aim at demonstrating steering using successively the same half of an entangled quantum state. With isotropic entangled states of local dimension $d$, the number of Bobs that can steer Alice is found to be $N_\mathrm{Bob}\sim d/\log{d}$, thus leading to an arbitrary large number of successive instances of steering with independently chosen and unbiased inputs. This scaling is achieved when considering a general class of measurements along orthonormal bases, as well as complete sets of mutually unbiased bases. Finally, we show that similar results can be obtained in an anonymous sequential scenario, where none of the Bobs know their position in the sequence.