Multi-time quantum correlations with no spatial analog

Martin Ringbauer,Andrew G White,Fabio Costa,Michael E Goggin,Alessandro Fedrizzi

doi:10.1038/s41534-018-0086-y

Abstract

Multipartite quantum correlations are a powerful resource that underpins applications from quantum metrology to quantum computing. While most research has focused on spatial correlations, it is now becoming clear that a sequence of measurements on a single quantum system at different points in time reveals a similarly rich, yet fundamentally different structure of multipartite temporal correlations. Here we experimentally observe genuine multi-time correlations in a sequence of three generalized measurements on a single photon. These correlations, manifest by a simultaneous violation of all pairwise Bell inequalities, cannot be reproduced by any spatial quantum state of equal dimension. Our work lays the foundation for the exploration of temporal correlations arising in quantum networks for quantum information applications.

Highlights

First studied in the context of macroscopic realism,[1] temporal quantum correlations have become of increasing interest for fundamental questions,[2] and quantum information applications.[3,4,5,6] Beyond the simplest scenarios, the equivalence between spatial and temporal correlations breaks down, revealing a rich structure of correlations in either domain
Where AxBy = a;b abPða; bjx; yÞ denotes the joint expectation value for Alice’s and Bob’s measurements for settings x and y and outcomes a and b, respectively. This inequality can be derived from the assumptions of realism, free choice, and no fine-tuning, which implies that if there is no observable signaling between two variables, there should be no hidden signaling in the underlying reality
Correlations obtained from entangled quantum states, can violate the CHSH inequality, indicating that they cannot be reproduced by any classical model without resorting to additional causal influences which are carefully hidden from the observable statistics

Summary

Introduction

First studied in the context of macroscopic realism,[1] temporal quantum correlations have become of increasing interest for fundamental questions,[2] and quantum information applications.[3,4,5,6] Beyond the simplest scenarios, the equivalence between spatial and temporal correlations breaks down, revealing a rich structure of correlations in either domain. We study multi-time correlations between three parties and observe a form of temporal correlations that cannot be reproduced by any multipartite quantum state of equal dimension These correlations, which are revealed by temporal measurements that have no spatial analog, manifest in the simultaneous violation of pairwise Bell inequalities between all pairs of parties. This is in stark contrast to one of the fundamental features of spatial correlations—monogamy of entanglement.[8,9] The fact that in the spatial scenario, Alice can either violate a Bell inequality with Bob, or with Charlie, but not both at the same time, is the basis for the security of entanglement-based quantum key distribution. Despite being polygamous in this sense, we show that multi-time correlations are still bound by a new polygamy relation that we derive

Methods

Results

Conclusion