Probing hierarchy of temporal correlation requires either generalised measurement or nonunitary evolution

TL;DR

This paper explores how different measurement and evolution methods affect the ability to detect quantum temporal correlations, revealing that generalized measurements or noisy evolution can distinguish between two approaches.

Contribution

It demonstrates that the equivalence of temporal steering and Leggett-Garg inequality violations breaks down when using generalized measurements or nonunitary evolution.

Findings

Under unitary evolution and projective measurements, temporal steering and Leggett-Garg inequality are equivalent.

Generalized measurements or noisy evolution reveal differences between the two temporal correlation probes.

The study provides examples illustrating the conditions under which the two approaches diverge.

Abstract

Temporal steering and violation of the Leggett-Garg inequality are two different ways of probing the violation of macro-realistic assumptions in quantum mechanics. It is shown here that under unitary evolution and projective measurements the two types of temporal correlations lead to similar results. However, their inequivalence may be exhibited if either one of them is relaxed, i.e., by employing either generalized measurements, or noisy evolution, as we show here using relevant examples.