Spatial Incompatibility Witnesses for Quantum Temporal Correlations

TL;DR

This paper presents a novel witness-based method using the pseudo-density matrix formalism to certify quantum temporal correlations, highlighting the role of measurement disturbance and coherence in detecting such correlations.

Contribution

It introduces spatial incompatibility as a new measure for quantum temporal correlations and develops experimentally accessible witnesses based on negativity.

Findings

SI can be quantified via negativity of the PDM.

Channels satisfying LG inequality can still show SI.

Measurement disturbance enhances temporal correlation certification.

Abstract

We introduce a witness-based framework for certifying quantum temporal correlations via the pseudo-density matrix (PDM) formalism, which is a spatiotemporal generalization of the density matrix. We define spatial incompatibility (SI) as the minimum distance between a PDM and valid density matrices. For trace-norm distance, we show that this reduces to the PDM's negativity, enabling the construction of experimentally accessible SI witnesses. We derive a tight bound on SI for quantum channels and analyze the respective roles of state and channel coherence in witnessing SI. Our approach, unlike the LG framework, exploits measurements that generate coherence through state disturbance. We further show that channels satisfying the LG inequality for incoherent states can still exhibit detectable SI, demonstrating that measurement disturbance enhances the certification of temporal correlations.